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WO1992004701A1 - Systeme de construction d'images visuelles - Google Patents

Systeme de construction d'images visuelles Download PDF

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Publication number
WO1992004701A1
WO1992004701A1 PCT/US1991/006618 US9106618W WO9204701A1 WO 1992004701 A1 WO1992004701 A1 WO 1992004701A1 US 9106618 W US9106618 W US 9106618W WO 9204701 A1 WO9204701 A1 WO 9204701A1
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WO
WIPO (PCT)
Prior art keywords
pixel
pixels
picture element
edges
color
Prior art date
Application number
PCT/US1991/006618
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English (en)
Inventor
Uri Geva
Original Assignee
Uri Geva
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
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Publication of WO1992004701A1 publication Critical patent/WO1992004701A1/fr

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Classifications

    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B29/00—Maps; Plans; Charts; Diagrams, e.g. route diagram
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B44—DECORATIVE ARTS
    • B44C—PRODUCING DECORATIVE EFFECTS; MOSAICS; TARSIA WORK; PAPERHANGING
    • B44C1/00—Processes, not specifically provided for elsewhere, for producing decorative surface effects
    • B44C1/28—Uniting ornamental elements on a support, e.g. mosaics
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B11/00—Teaching hand-writing, shorthand, drawing, or painting
    • G09B11/10—Teaching painting

Definitions

  • the present invention relates to a new form of art and craft based on a self-supporting system of picture elements having different coloring schemes.
  • Imaging Any method, system or technique of creating visual images such as painting, drawing, quilting, printing, mosaic, paint-by-the-numbers, computer graphics, sculpting, photography, cutting and pasting. Note that solving a jig-saw puzzle, the user merely reassembles a pre-existing image which has originally been produced by some imaging; no creation is taking place. Thus, solving a jig-saw puzzle is not imaging.
  • mosaic is a form of digital imaging.
  • stained glass may also be considered digital imaging.
  • Picture Element or Pixel - The smallest image detail that an imaging is capable of producing, may be defined as a picture element of that particular imaging.
  • a picture element alone contains no information which may be uniquely linked to the image to which it belongs.
  • each pixel of an imaging system is unique only within the system itself and it is generic to all of the images that can be produced by that system.
  • the picture element is the most primitive building block, the atom, of the visual imaging system.
  • Friction Fit A property that facilitates assembly. Tight manufacturing tolerances of the dimensions of the pieces to be assembled provide tight fitting joints, i.e., provides the necessary friction to hold them together. Interlocl ⁇ ng or coupling. A method that facilitates the formation of stable joints between individual elements for the purpose of assembling and constructing objects. In an interlocking joint that is stable in only one dimension, the two elements can be easily pulled apart, but none can be moved along the edge which it shares with the other. Together with friction, the one- dimensional interlocking joint makes nails useful.
  • a two-dimensionally stable interlocking joint is formed by a peninsula on a male edge of one component that is inserted into a bay in a female edge of the other component such that forces, acting on the joint within the plane that is common to both elements, will not separate them.
  • the force(s) must act in the third dimension that is perpendicular to the plane of the joint. If the two flat elements form a three-dimensional joint, that is the two components do not share the same plane, then an angular force must act on one of the elements (i.e., one element has to be rotated) around its axis that lies in its own plane and intersects the plane of the other element.
  • dovetail joints are used to join flooring panels and two perpendicular surfaces such as in furniture.
  • Cementing Any method that facilitates joining individual elements for the purpose of assembly and construction of an object by increasing the friction coefficient between the joining elements as high as possible.
  • imaging construction systems which utilize the bonding properties of their imaging materials or of additional materials, specifically used for this reason, to adhere the image to a surface and/or to other elements of the image.
  • mosaic cementing bonds the pieces both to the surface and to each other.
  • stained glass the pieces are bonded to each other.
  • cementing is a layer of material that has been permanently applied to the tiles.
  • static electricity is used to adhere high-static vinyl pieces to each other and to the carrying surface.
  • Color A general term for any color or color gradation (see below) including black, white, silver, gold, skin tone, etc.
  • a color combination may be composed of various gradations of a single color, such as in a gray scale, or of several colors, such as in a rainbow. It may be created in discrete steps as in a gray scale, or in continuous gradation as in a rainbow.
  • Opaque Any surface which is not transparent. This includes light reflecting as well as light emitting surfaces.
  • a color-gradation scale may have discrete incremental steps or a single continuous change in its range. Whether it is digital or analog, the scale may be between two values of a single color or it may be between the values of two or more colors (e.g., in this sense a rainbow is a linear spectral scale and the CIE Standard Chromaticity Diagram is a two-dimensional spectral scale.) In the first case we shall say that it is a monochromatic color-gradation scale and in the second case it is a spectral color-gradation scale. In any case, a single gradation, that is, a single hue, shade or tone of a color, is any discernible step or segment within its range.
  • Pattern A generic term for any repetitive or non- repetitive arrangement of geometric elements (dots, lines, dashes, squiggles, etc.) in any color, color gradation or color combination.
  • Color Contour The imaginary line that is formed where two colors or two patterns butt. Under certain conditions, such as where the distinct colors of two adjacent areas blend together, there is no well defined color contour.
  • Solution Let a subject be mapped into a visual image. If a lay viewer can visually recognize the correspondence between the original subject and the image that is the result of the mapping, then this mapping is a correct solution. Solution is used (for lack of a better term) to describe situations in which several images of the same model, all closely resembling the original and yet each is slightly different from all the others, having its own perceptual quality, may be produced. In this sort of a case, multiple correct solutions exist. Clearly this is universally true for every image producing system. However, if certain restrictions are placed on the imaging system, this may no longer be true.
  • the fundamental principle of all visual-image production methods is the arrangement of some light transmitting or light reflecting elements, in consideration of the complex human vision system and psychology of perception, such that the desired visual image will be perceived.
  • These elements may transmit the light directly, being its source, as the light bulbs of a scoreboard or the fluorescent dots of a television screen.
  • the light may be transmitted through these elements as is the case of stained-glass images or the light may be reflected off of these elements as is the case of most visual-image production techniques like drawing, painting, sculpting, etching, curving, writing, printing, mosaic, photography and quilting.
  • Each perceived color or shape is affected by the other colors and shapes that are in view.
  • every visual-image producing technique must satisfy two necessary conditions.
  • Most visual-image production methods including painting, mosaic, drawing, printing, photography, tiling, video, curving, etching, laserium, quilting and others, utilize a medium onto which the image is applied for decorative and/or utilitarian purposes.
  • the medium is a surface as the drafting paper, the tiled wall, the mosaic floor, the television screen, the etched glass, the projection screen or the quilted blanket.
  • the most common and popular methods cover the surface with the image and in most cases, the image is supported by its medium by cementing.
  • Other methods embed the image in the surface, superficially alter the surface or project the image onto the surface.
  • Very few imaging methods utilize a medium which is three dimensional. In air writing, which is produced by aircraft smoke, for example, the atmosphere is the canvas, so to speak.
  • a few visual image production systems require no preexisting medium. These techniques manipulate raw materials to produce the image and construct its support simultaneously. Such systems including sculpting, stained glass and glass blowing. Another system involves constructing shapes with "LEGO".
  • the “LEGO” employs a unique joint to achieve stable and solid construction.
  • the “LEGO” elementary construction unit is a three-dimensional block and the joint utilizes the principle of nailing.
  • the "LEGO” pieces are fastened to each other as the prongs of one piece are friction fit into the other. In the direction of the insertion, stability of the joint is achieved by the friction fit. Stability in the plane that is perpendicular to this direction is achieved by the presence of the prong or prongs of one piece in the cavity or cavities of the other.
  • Rotational stability i.e., preventing rotation
  • the "LEGO" pieces have a single male surface and a single female surface and the two are opposite each other.
  • This arrangement provides for only one- axis joints, commonly it is the Z or the vertical axis.
  • Structural strength in the X and Y axes is achieved by staggering the vertical joints.
  • One of the properties of every visual image production method is its resolution. Resolution may be defined as the limit beyond which the imaging technique is incapable of producing fine details.
  • the resolution of painting is a function of such variables as the size of the brush, the number and thickness of its hair, the shape of its tip, the size of the color pigments, the size of the canvas fiber and the painter's skill.
  • a viewer's capability to discern fine details is a function of several variables, including the viewer's distance from the observed image, the relative stability of the image with respect to the viewer, and the image illumination conditions.
  • the perceived resolution of a low resolution image may be equal to that of an image with higher resolution. For example, from the proper distance, curves and colors appear continuous on a television screen. Using low resolution may also have a desired visual effect beyond the viewer's capability to discern fine details.
  • the impressionists like Van Gogh and Cezanne applied paint to their canvas in loose and coarse strokes, they dabbed, splattered dots and avoided minutely precise painting techniques.
  • a visual image production technique may be defined as a picture element, or pixel, of that particular method.
  • a picture element alone contains no information which may be uniquely linked to the image to which it belongs.
  • each picture element of a visual-imaging system is unique only within the system itself and it is generic to all of the images that can be produced by the system.
  • picture elements There are different types of application of picture elements.
  • the most primitive picture element is the kind of which all properties, including its dimensions, that is, its size and shape, its color and its spatial positioning scheme, are all fixed and unchangeable.
  • An image is formed by either placing such a picture element or not.
  • the combination of the presence and absence of picture elements produces an approximation of the desired details, such as curves and colors.
  • This technique is common in such popular applications as newsprint, silk screening, computer applications like dot-matrix printers and scoreboards.
  • the image area can be divided into a grid of some sort and the picture elements are positioned in it so that they cover the image without overlapping and with minimal gaps.
  • Such a system contains a finite number of different picture elements, differing in the size of grid-cell area that each one covers.
  • the arrangement of these picture elements and the combination of the covered area and its background produces feature details and color gradations.
  • the technique of producing images by using alphanumeric characters and U.S. Patent Nos. 3,987,558 and 4,398,890 belong to this category.
  • Some techniques provide infinitely many different picture elements. Such are mosaic and Cezanne's painting.
  • some systems utilize picture elements which themselves are conglomerations of more primitive picture elements.
  • computer graphics may make use of the alphanumeric characters to form images, utilizing the complete shape and density of the characters; at the same time each character is composed (on a video screen or by a dot-matrix printer) of an array of dots.
  • Such a computer graphic system does not attempt to use the individual dots to achieve a finer degree of resolution.
  • Some systems utilize three-dimensional picture elements to produce two dimensional images. Among these are mosaic, tiling, and the techniques based on U.S. Patent Nos. 3,987,558 and 4,398,890.
  • Other systems utilize three-dimensional picture elements to produce three-dimensional structures. The most common of these are the use of bricks to construct buildings and structures and the "LEGO" construction toys; the bricks and the "LEGO” pieces are their respective picture elements.
  • the process of visual perception is very complex. Developing the present invention took into consideration the recent scientific discoveries and the current descriptions of the visual perception and, in particular, that of color and form.
  • the brain processes the color and the form elements of the perceived separately; the results are integrated, affecting one another in the totality of the wholly perceived image. For example, using paint-by-the-numbers it is not necessary to perfectly color to the border lines; the viewer's brain will form the image by adjusting miscoloring to the perceived form.
  • the bottom line is that using picture elements to approximate an image, one can cause a viewer to actually perceive the image (which the creator used as a model.)
  • the same model may inspire multiple images, created from picture elements, all correct solutions yet perceptually different from one another. Images, illusionary at times, can be recognized when only a few scant details are presented.
  • Another method achieves a similar result by using very fine pixels only wherever the ordinary, more coarse pixels cause curves to appear discontinuous, having a "staircase" visual effect.
  • picture elements There are important mathematical aspects to picture elements that deserve consideration. Of utmost value are the geometric properties of the picture elements, among which are symmetry and asymmetry, tessellation and lattice.
  • a one-to-one mapping PQ --> Pi from all the points in a plane (or in a space) to all the points in the same plane is called transformation.
  • a reflection is an isometry in which all the invariant points coincide with the line of reflection, or the mirror.
  • a set of transformation is said to form a group if it contains the inverse of each and the product of every two.
  • a figure is said to be symmetrical if there exists an isometry which maps every point PQ on the figure to point P j on the same figure.
  • the four fundamental symmetry operations are reflection, rotation, translation and glide reflection.
  • Glide reflection is the product of reflection in a line and translation along the same line. There are seventeen symmetry groups.
  • Tessellation is the property of any arrangement of two- dimensional regions (e.g., polygons, any area bounded by a simple closed curve) fitting together without leaving gaps or without overlapping so as to cover the whole plane.
  • the basic tessellating polygons are the triangle, the quadrangle and the hexagon. Every triangle and every quadrangle, including scalene (all sides are of unique lengths) are tessellating.
  • the circle, the equilateral pentagon and the equilateral octagon are not tessellating shapes.
  • a figure has bilateral symmetry if and only if there exists at least one line that bisects the figure such that for every point in one section of the figure there exists one and only one corresponding point on the other section of the figure, and the following holds true: (a) Any line between any pair of such points is perpendicular to the bisecting line, (b) The distances of the two points of any such a pair from the bisecting line are equal.
  • This symmetry is often referred to as symmetry by reflection or mirror symmetry and the bisecting line is its line of reflection.
  • a figure has rotational symmetry if and only if there exists at least one point around which the figure can be rotated by an angle alpha, such that alpha is greater than 0 degrees smaller than 360 degrees and the figure in its new orientation can be precisely superpositioned over itself in its original orientation. Such a point is called axis of rotation.
  • a figure that has no rotational symmetry is called rotational asymmetric.
  • Symmetries preserve one another. For example, if a picture element is both mirror and rotational symmetric then its mirror image is also rotationally symmetric around the same axis of rotation and to the same degree of rotation and vice versa. Similarly, if a picture element is mirror symmetric and rotationally asymmetric then its mirror image also has no rotational symmetry.
  • the tessellating quality of a picture element is unchanged by any of the symmetric operations.
  • any picture element that can be derived from the original one by an isometry is also tessellating. Such is the case with mirror and rotational images whether they are symmetric or not.
  • the imaginary well-defined line that is formed where a color butts against the colors that surround it is the color contour of this color.
  • a color contour may be incomplete if the color which it surrounds butts against the edge of the picture.
  • Color contours have an important role in the way images are perceived. For instance, careful arrangement of color contours may create the illusionary presence of image features that are not really present.
  • Some image producing systems readily facilitate color contours. Among these are paint-by-the- numbers, stained glass and mosaic. With other methods it is easier to blend adjacent colors than to keep them distinct from each other.
  • the present invention provides a class of devices called picture elements, or pixels, to be used in their plurality for the production of two- and three dimensional visual images for decorative and utilitarian applications.
  • the unique feature of this invention is the fact that it is a complete imaging system. That is, the pixels, substantially flat physical objects, facilitate the simultaneous construction of the support structure of the image while creating the work of art. No additional tools or materials are necessary.
  • the invention also provides methods for producing visual images and structures in two and three dimensions from these picture elements.
  • a fundamental principle of the present invention is the introduction of a variations on tessellating shapes according to a specific set of objectives.
  • Some pixel designs provide for all the primary objectives of the invention, that is, self-support, completeness, reversibility, dual imaging, flexibility in color contouring and two- and three-dimensional imaging.
  • Other pixel design provide for some combination of said objectives.
  • the invention exploits tessellation by making use of its principles but not adhering to them. In particular, there is no restriction against gaps between picture elements.
  • An objective of this invention is to provide a picture element that alone, in its plurality, or a small finite set of picture elements in their plurality, facilitate for both the production of at least one image and simultaneously the construction of a stable support structure for said image, comprised of at least one, substantially flat medium.
  • the pixels are said to be self supporting.
  • the support structure of the invention is an integral part of the visual medium.
  • Other imaging systems such as stained glass and sculpting are similar in this manner. For example, while tiling covers an existing surface, the imaging system of the invention creates a new independently stable structure with at least two surfaces of which at least one displays an image.
  • Self support and structural stability free this imaging construction system from all of the common physical constraints that other imaging systems have to contend with.
  • Self support is the result of the application of a combination of interlocking and friction fit. Interlocking prevents any pair of picture elements from being disjointed by any linear or angular forces which may act on them in their plane or planes.
  • every picture element of this imaging construction system has to have at least one male edge or at least one female edge or at least one edge that has both a male element and a female element.
  • a male edge is composed of the normalized edge of the body of the picture element from which a protrusion extends outwardly. This protrusion is named peninsula.
  • the female edge is composed of the normalized edge of the body of the picture element from which an intrusion extends inwardly. Said intrusion corresponds in all of its dimensions to the said protrusion. Said intrusion is named bay.
  • the peninsula and the bay are complimentary to each other.
  • a non-gender edge includes at least one peninsula and at least one bay. Since the peninsula is composed of the material of the pixel and the bay is composed of the absence thereof, each is the inverse shape of the other. For all practical purposes the dimensions and the shapes of the bay and the peninsula are identical; some manufacturing technologies (e.g., due cutting) provide that, any time a peninsula is produced, a corresponding bay is also produced, and vice versa.
  • the coupling scheme of a pixel or of a set of pixels is defined as the species of said pixel or set of pixels. If two pixels have different interlocking schemes, that is, any variation in shape or dimensions which prevents stable coupling between said pixels, then said pixels belong to different species. On the other hand, if two picture elements of different shapes (e.g., a square and a triangle) can be interlocked since they have a matching male and female edge, then these pixels are of the same species.
  • a stable two-dimensional (planar) coupling joint can exist if the interlocking scheme is of either the bottleneck type (Figure 12a-i), the gooseneck type ( Figure 13a-e S-shape type ( Figure 13f).
  • bottleneck joints are a subset of the gooseneck joints. The distinction is made since all bilateral symmetric bottleneck joints are capable of stable and solid spatial interlocking. Gooseneck joints that do not belong to the set of bottleneck joints cannot have bilateral symmetry and, therefore, are incapable of forming stable and solid three-dimensional coupling.
  • a male or a female edge is generally referred to as an coupling edge.
  • a non-interlocking edge is a plain edge. All the edges of every general-purpose pixel are coupling edges. Special- purpose pixels may have plain normalized edges, e.g., a framing pixel may have a straight or curved edge or two or more straight or curved adjacent edges. Pixels with a single interlocking edge are also useful. For instance, each of the three framing triangular pixels at each of the corners of a triangular image has only a single coupling edge. To maximize the usefulness of pixels, it is preferable, but not necessary, to have an equal number of male and female edges, unless, of course, the pixel has an odd number of edges. In this case, one gender of edges necessarily has at least one more edge than the other gender. Of course, non-gender edges may be combined with male and/or female edges.
  • Friction fit provides stability to every interlocked pair of pixels against a disjointing force(s) that act on them along a line(s) or a curve(s) that is perpendicular their common plane. Friction fit is accomplished by a combination of precise manufacturing technologies, achieving precise tolerances, and a careful selection of materials. Perfect matching between bays and peninsulas of the same species regardless to the product edition, the age and the amount of previous use of the pixels.
  • the design of the interlocking scheme must take into consideration the tessellating property of the normalized body of the pixel. For, if the geometric shape of the body of the pixel is tessellating, reshaping it with the addition of one or more peninsulas and the subtraction of one or more bays, may or may not render it non-tessellating. Similarly, one must consider the effect of the shape of the coupling edge on the reversibility of the pixel, i.e., on the ability to interlock the pixel with another which is shaped precisely as its mirror image.
  • coloring and patterning schemes facilitate its visual creation.
  • the two processes that of the construction of the image support and that of the image creation
  • Each surface of every opaque picture element is provided with a homogeneous (not necessarily uniform) color, shade, hue or tone of color.
  • coloring scheme refers to any of the finite, but quite large, number of combinations of colors, color graduations, analog and digitals, monochromatic and spectral, in various ranges, number of gradations, pattern combinations, etc.
  • the gradation scale may be digital or analog; it may be monochromatic or it may be spectral.
  • textural gradation and the gradation of geometric patterns both with respect to the density of the textures and the patterns and with respect to their colors, may be facilitated by the pixels. Combinations of any of such gradations are also possible.
  • the color scales are designed to facilitate both variations in color intensities, densities, shades, tones and hues.
  • the color scales may vary in the number of gradations per scale to accommodate different applications. They may also vary in the incremental (or decremental) changes between the different gradations of the same scale or of similar scales. For example, non-professionals, such as children, may be satisfied with a small number of gradations per scale while professionals and serious artists may require much finer details. This invention does not impose any limit in this respect, one way or the other.
  • Color Contours In addition to providing pixels with coloring schemes to satisfy a large spectrum of needs, it is also an objective of this invention to utilize the shape of the pixels to affect the perception of the color contours in the produced images.
  • the pixels can facilitate either well defined color contours, or blending of colors along their contours, or displaced colors.
  • Rotationally asymmetry facilitates flexibility and versatility in the approximation of curves and of color contours. Therefore, it is another objective of this invention to provide pixels that can be interlocked (whether or not they tessellate) with their rotational asymmetric counterparts. Tessellating sets of pixels may be composed of rotationally symmetric pixels. In such a case, some collective shapes that are formed by interconnecting some or all of the pixels of the set is rotationally asymmetric.
  • Dual Imaging It is an objective of this invention to provide opaque pixels which facilitate for the simultaneous production of more than a single image. That is, since every opaque sheet of pixels has two surfaces, an image may be created on each surface. If only a single image is produced at a time, it is by the user's choice, not a necessary result of the design of the picture element. No symmetry is necessary in order to provide for dual imaging. Three- dimensional picture elements facilitate for the simultaneous production of at least four images.
  • Each of the two surfaces of opaque pixels is colored.
  • every opaque sheet has a single monochromatic or spectral, digital or analog color scale on each of its surfaces.
  • the combination of the two color scales, one per surface of the opaque pixels is designed to further maximize the effectiveness of the pixels. Having a different color per surface, facilitates the simultaneous creation and display of two images, one per surface.
  • one image may be the mirror image of the other.
  • opposing color scales are selected, then one image may be the "negative" of the image on the opposing side. That is, images with the same contour lines but with different coloring are "automatically” formed. Or, given "unrelated" color combinations, it is possible to create an image on one surface and, totally disregarding the other surface, end up with a random mosaic.
  • a sheet of transparent or light emitting pixels has a single either digital or analog, either monochromatic or spectral color scale. So, a transparent or light emitting image (note that light emitting pixels may have the properties of either opaque or transparent pixels) may be viewed from either side. Transparent images can be formed and be displayed with rear illumination. Dual imaging has further significance when this imaging system is used to create three-dimensional images.
  • dual imagining requires special support system or is out right impractical.
  • a cut-and-paste imaging may be used for dual imaging. But the pasting must be done onto both surfaces of the paper, the adhesive on one surface must not interfere with the image on the opposite surface, the artwork must be hung to dry so nothing else adheres to any of its surfaces, and no "automatic" dual -imaging is possible.
  • the front surface of one pixel may be interconnected with the back surface of another identical pixel.
  • Bilateral symmetry is a sufficient but not necessary condition for complete interchangeability of the front and the back surfaces of pixels. That is, the front surface of one pixel can be interconnected with either the front or the back surface of another pixel.
  • Using bilateral symmetry and asymmetry it is possible to design pixels that interconnect with either their own duplicates (i.e., translated images) or with their mirror images or with both.
  • both surfaces of a pixel are of the same species, the pixel is said to have left-right symmetry.
  • a pixel that has no left-right symmetry is said to have one left-hand surface and one right-hand surface.
  • the choice of which surface is the right-hand and which is the left- hand is arbitrary.
  • Left-right symmetry exists if and only if bilateral symmetry exists. That is, a pixel is left-right symmetric if and only if each of its surfaces has at least one line of reflection which is the axis of this surface's bilateral symmetry.
  • Left-right symmetry is desirable; both surfaces of a left-right symmetric pixel can be used in the creation of an image. Namely, a left- right symmetric pixel can contribute either of its colored surfaces to the image, not only one of them, as is otherwise the case.
  • the interlocking of surfaces provides for the production of multi-surface visual images and/or other three-dimensional structures.
  • a flat sheet that is constructed from coplanar picture elements is structurally stable so that forces can be applied on it so it becomes a three-dimensional curved surface.
  • the edges of the sheet In order to preserve such a contorted shape of a flat sheet, the edges of the sheet must be affixed in their relative position in space. That can be achieved with additional picture elements.
  • the primitives of painting are the paints, the paint diluting materials, the paint mixing tools, the brushes and the canvas, if the primitives of drawing are the pencils, the paper and the eraser, if the primitives of mosaic are the stones, the stone dying materials and tools, the chisels, the cement and its application tools and the floor or wall onto which the mosaic is applied, then the one and only primitive of the image producing system according to the invention is its picture element.
  • a further objective of this invention is to readily facilitate any size and shape image (larger than a single pixel and within the constraints of the shape of the picture elements). For example, to produce a single painting in the shape of the letter "A" requires a customized canvas; this invention readily provides for an A-shaped self-supporting image.
  • Another objective of this invention is that at any time, during the production of an image and after its completion, any part of the image may be modified. Any individual pixel or a group of pixels can be separated from the structure of the image and replaced by another or others without adversely effecting the rest of the image. The replaced pixel(s) may be reused immediately or at any time in the future in the same image at any place or in any other image. This invention is thereby tolerant to errors and facilitates trial-and-error experimentation. Furthermore, a completely formed image can always be disassembled down to its individual picture elements so they may be reused to produce a variation of the disassembled image or another totally different image.
  • the durability of the pixels is substantially independent of and is unaffected by their use. Unlike using paint pigments and paper, mosaic stones on walls, and other such imaging methods, using pixels does not substantially alter their properties or significantly increase their wear and tear.
  • the pixels require no maintenance and are resistant to the normal conditions that exist in the normal household, office and studio environments. The pixels attract no foreign elements as, for instance, adhesive or static electricity attract dust.
  • this invention provides for a predetermined safe environment where images can be produced. For example, parents can therefore be satisfied that in such an environment children are safe. The additional safety needs of very young children can be addressed by especially designed picture elements.
  • a complete environment for the use of this invention is provided at any location that contains a user of this invention, some picture elements and nothing else.
  • a further objective of this invention is to provide the gamut of users, from the professional artist to the lay child, with a choice of pixels and sets of pixels for the gamut of applications.
  • this imaging method compensates for the lack of the mechanical skill that is so often a prerequisite for other imaging methods.
  • the professional artist on the other hand, will find very few restriction to his or her imagination. For instance, this invention provides a wide range of resolutions both in pixel size, color definition and curve approximation.
  • Tessellation is not a necessary condition for the development of any picture element or any set of picture elements for this imaging construction system.
  • An image created by this imaging system may contain gaps between picture elements and/or overlapping picture elements.
  • the acceptance or rejection of gaps and/or overlapping, depending on a particular implementation of this invention, is the choice of the user ( Figures 12d, 12g and 12i).
  • Tessella ⁇ tion is used only as a guideline in designing picture elements. For example, a circular pixel (as pixel 17a in Figures lla-b) can be used quite effectively; true, a planar image will have one gapl ⁇ a between every three interlocked pixels 17a, shaped as a triangle with concave sides.
  • a picture element that has some planar asymmetry may be placed at the same lattice point in different orientations. Two cases are described as follows:
  • This imaging construction system facilitates more then the reorientation of the whole lattice. Since it imposes no restriction on the overall shape of the image, it provides the freedom to maintain the orientation of the shape of the image while its underlying lattice is reoriented. In other words, the overall shape of the image - say, a vertical rectangle such as in a portrait - can be maintained regardless to the orientation of the lattice that forms it. Note that this is not the case for imaging systems that depend on a support platform. To reorient the lattice of such a system (e.g., those described by Patent No. 4,398,890 and 3,987,558) means to reorient the support platform.
  • edge picture elements must be significantly altered (e.g., reorienting the lattice of tiles which has matched a floor perfectly, will require breaking some of the tiles where the floor meets the walls.)
  • the outer edges of the image are also reoriented; or the image must be sufficiently smaller than its supporting platform so it is possible to avoid the limitations the platform imposes on its size and overall shape. This invention imposes no such limitation.
  • the invention as described here is a general purpose visual imaging system. Like any other imaging system, it has many and versatile applications such as artistic, decorative, educational and practical applications.
  • a sheet may be composed of at least a single group of pixels, each of which is interlocked with its adjacent pixels. If the sheet is framed, then the frame is interlocked to the outer pixels. Such a frame is an integral part of the sheet of pixels. If a sheet contains several groups of pixels, then within each group, the pixels are interlocked with their adjacent pixels. Further, if an integral frame is part of such a sheet, then the outer pixels of each group can also be interlocked with the frame that surrounds them.
  • the coloring scheme of the picture elements and their sheets may be of two types.
  • a solid coloring scheme is one in which the resolution of the color applied to the surfaces (or, in the case of transparent picture elements, to the body picture elements themselves) is sufficiently high to allow no discernible patterns of any sort, random or otherwise.
  • a patterned coloring scheme is one in which the resolution is sufficiently low to permit clearly visible patterns, random, geometric or of any other kind. Patterning may be produced in one color-gradation scale on the background of another color or another color scale. This invention does not impose any limit with respect to patterning, one way or the other. By mixing pixels having different patterns or by mixing pixels having pattern with pixels having no pattern, it is possible to create new patterns which are of coarser resolution than the size of the pixels themselves. Indeed, this imaging system leaves the artist or creator in charge; given sufficient demand for a particular pattern design, it can be manufactured (by the individual who desires it or by anyone else).
  • a pixel may be designed such that its body and the arrangement of its male and female edge facilitate the coupling of it with its mirror image. In other words, such a pixel may be turned over to be interlocked with its clone that has not been turned over. The functionality of each pixel is thereby doubled. The result is that, if N is the number of desired color scales, then if N is even, then it is necessary to produce only N/2 sheets of pixels and, if N is odd, then it is necessary to produce only N/2 + 1 sheets.
  • Multi-Layered Image Construction Given sufficient thickness and/or sufficiently high friction coefficient for the friction fit, then it is possible to couple regular picture elements in a staggered arrangement, with respect to their thickness, thereby generating multi-layered images.
  • a step further will be to provide picture elements especially designed for such construction. Such picture elements can be created as if two picture elements were cemented to each other along their flat surfaced. These picture elements, in combination with the simple single-layer picture elements, open a new realm of multi-layered imaging ( Figure 24a-g).
  • double layered pixel may be designed as such, it is simpler to describe its design and behavior as if it is composed of two single-layered pixels "sandwiched" together.
  • Such two single-layered pixels may or may not be identically shaped or even of the same species. If they are identical, then they most likely be positioned in a non-congruent orientation with respect to each other; otherwise they form a single double-layered pixel having an identical shape.
  • the most common design of double-layered pixels is to combine two single-layered pixels having the same normalized body shape and being of the same species but not being identically shaped.
  • Multi-level imaging is the most obvious goal of these double-layer pixel.
  • the combination of reflecting, transparent and light emitting pixels with other pixels having same or similar optical properties is a most powerful application. Such a combination can generate new color combinations and visual effects.
  • the first is the image resolution. Clearly, the smaller the picture element, the greater is the resolution. Dexterity and the user's capability to manipulate the picture elements is the second consideration. Some users, such as young children or physiologically disabled, may be limited in their ability to manipulate small objects. Thirdly, manufacturing constraints, including tooling, manufacturing precision, material limitations, etc. limit the smallness of the pixels or the smallness of the bays and peninsulas. Fourthly, is safety. For instance, pixels to be used by very young children and infants, are required by law to be sufficiently large so they cannot be swallowed. The first constraints conflicts with the second and with the third ones.
  • pixels which have peninsulas and no bays. These special peninsulas, called islands, are removable such that, when a peninsula is removed, a bay is left in its place. This lets the user determine the interlocking scheme of each pixel so constructed. If sufficiently high friction coefficient is provided between the islands and the bodies of the pixels, then an island may be reinserted into a pixel from which it has been removed. In a sense, such island become "Sub-pixels" - they are atomic image elements which contain no bay or peninsula. However, independent use of islands does not provide for the strength and stability of ordinary pixels.
  • picture elements include special purpose pixels for framing or constructing three-dimensional images. Framing strips are only one pixel wide. They have one long edge that is made of only convertible pixel edges. The other long edge is straight or in the shape of any curve, such as a sinusoid, that forms a finished edge. Pixels from such a strip can be fitted to the jagged edge of a completed image in order to provide the image with a finished edge. Corner pixels are also possible. These are picture elements with two adjacent finished, i.e., non-interlocking, edges. The designs of corner picture elements match the designs of the available framing strips. Pictorial pixel are also possible. As M.C. Escher has demonstrated, it is possible to design tiles that have pictorial images other than pure geometric shapes. For various reasons (e.g., educational promotional and artistic) it is, therefore, possible to design pictorial pixels or sets of pixels.
  • three-dimensional structures from the flat two-dimensional picture elements.
  • six flat square pixels of the same species can form a cubical pixel; and four triangular picture elements of the same species (not necessarily the same as that of the squares') will generate a pyramidal picture element.
  • Such picture elements can then be interlocked with others of the same three-dimensional species.
  • these pixels can be interlocked along every edge of every surface. For example, only two of the surfaces of every "LEGO" piece can be used for coupling.
  • a cubical picture element made of six flat square pixels (the type shown in Figure 22c) can be interlocked along each and every one of its surfaces (as shown in Figure 24h); moreover, coupling is possible along the four edges of each and every surface. Since the three-dimensional pixels are actually a composition of flat two-dimensional ones, whenever a corner is created by an arrangement of such cube cubes in all three axes, it is sufficient to use only three additional flat square pixels to "fill" the corner, as if an additional cubical pixel is used.
  • Two equilateral right angle triangular pixels a first pixel with a female edge along its hypotenuse and a second pixel with a male edge along its hypotenuse, can generate a single square pixel.
  • 270 and 360 degree (see Figure 20e-f) - the set of right angle pixels mentioned here facilitates polygons with four additional angles: 45, 135, 225 and 315 degrees.
  • the hypotenuse is of an odd length. Although a male edge of the hypotenuse length may be interlocked with a female side edge of the triangle, and vice versa, gaps or an irregular edge may occur.
  • a set of two equilateral triangular picture elements (Figure 20b-c) having two female edges and one male edge, or two male edges and one female edge. Further, it is possible to generate any regular hexagonal picture element from some combination of these two triangular picture elements ( Figure 23a-j.) The value of the hexagonal picture element is in its close approximation of a circle.
  • the set of square pixels and the set of equilateral triangular picture elements is enough to generate a complete imaging system.
  • an imaging system that combines both of them, that is, both being of the same species, will be more versatile; it will provide a greater accuracy approximating curves and angles.
  • a square picture element and an equilateral triangular pixel facilitate 11 angles: 0, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360 degrees.
  • the square is replaced with a set of two isosceles right- angle triangular picture elements then it is possible to generate ten additional angles: 45, 105, 135, 165, 195, 225, 255, 285, 315 and 345 degrees.
  • Figures la-b show various designs for square picture elements of the invention.
  • Figures 2a-d show various designs for triangular picture elements of the invention.
  • Figures 3a-c show various shapes for hexagonal picture elements of the invention.
  • Figure 4a shows a picture element of the invention and its back side, being the mirror image thereof, and figure 4b shows an assembly of the picture elements of Figure 3a.
  • Figure 5a shows another picture element of the invention and Figure 5b shows an assembly thereof.
  • Figure 6a shows a picture element of the invention and its back side, being the mirror image thereof, and figure 6b shows an assembly of the picture elements of Figure 6a.
  • Figure 7a shows another embodiment of the picture element of the invention and Figure 7b shows an assembly thereof.
  • Figure 8a shows another embodiment of the picture element of the invention and Figure 8b shows an assembly thereof.
  • Figures 9a-c show a set of picture elements according to the invention wherein the picture elements have different shapes as shown in Figures 9a and 9b, respectively and their assembly.
  • Figure 10a shows a picture element of the invention, having a single bay and a single peninsula along each edge, and its back side, being the mirror image thereof, and 10b shows a staggered assembly of the pixels in Figure 10a.
  • Figure 11a shows another picture element of the invention and Figure lib shows an assembly thereof in a non-tessellating arrangement.
  • Figures llc-e show a set of picture elements according to the invention which are arranged in a tessellating arrangement as shown in Figure lie the set of picture elements including the respective shapes shown in Figure lie and Figure lid, respectively.
  • Figure llh shows an assembly of four pixels shown in Figure llf and a gap that is formed within said assembly may or may not be filled with a pixel shown in figure llg.
  • Figures 12a-i show various shapes of peninsulas and bays of the bottleneck type according to the invention.
  • Figures 13a-f show various shapes of peninsulas and bays of the gooseneck type according to the invention.
  • Figures 13f shows a peninsula and a bay having an S shape.
  • Figures 14a-c show arrangements for peninsulas and bays which are outside the scope of the invention.
  • Figures 15a-c show how the peninsulas and bays are interconnected in a vertical direction.
  • Figure 16a shows a picture element according to the invention and Figure 16b shows a "LEGO" building block according to the prior art.
  • FIGS 17a-c show how prior art "LEGO" type blocks are assembled.
  • Figure 18a shows a pixel arrangement having blending color contours.
  • Figure 18b shows a pixel with well defined color contour, the pixel having peninsulas and bays with an area ratio similar to the area ratio of the pixel in Figure 18a and the area of said bays and peninsulas is displaced close to the edges thereof.
  • Figure 18c and 18d show pixels with well defined color contour, the pixel having peninsulas and bays with a small area ratio and the area of said bays and peninsulas of pixel 18c being displaced far from the edges thereof and the area of said bays and peninsulas of pixel 18d being displaced close to the edges thereof.
  • Figure 18e shows blending color contours wherein the bays and peninsulas having moderately sized area ratio.
  • Figures 18f shows well defined color contours wherein the bays and peninsulas having small area ratio.
  • Figures 19a-h show a sequence of eight assemblies of square pixels illustrating the gradual change from displaced color contour through a range of blending color contours to well defined color contours.
  • Figures 20a-i show different sets of pixels capable of constructing different angles, approximating curves to different degrees, and their assemblies.
  • Figures 21a-b show the effect of shifting the lattice or grid of an image with respect to its model.
  • Figures 21c-d show the effect of reorienting a lattice of square pixels on the capability to cover an area enclosed between two curves with said pixels.
  • Figures 21e-f show the effect of lattice orientation using triangular shaped picture elements according to the invention on the capability to approximate a fixed set of circles and curves.
  • Figures 22a-p show various shapes and arrangements of picture elements having a square basic shape.
  • Figures 23a-j show how two picture elements having triangular basic shapes can be used to construct every possible hexagonal picture element.
  • Figures 24a-c show different arrangements of double-thickness pixels having single- and double-thickness peninsulas and bays.
  • Figures 24d-e show how the picture elements of Figure 24a-c can be arranged in a two- dimensional structure as shown in Figure 24d or a three-dimensional structure as shown in Figures 24e.
  • Figure 24f shows an assembly of pixels most of which are transparent and some of which may be opaque, five of the pixels shown having a double-thickness and one having single- thickness pixel.
  • Figure 24g shows an assembly of a single-thickness pixel and a multi-thickness pixel.
  • Figure 24h shows how flat picture elements according to the invention can be arranged in a three-dimensional structure.
  • Figures 25 shows a visual image produced by interconnecting picture elements according to the invention.
  • Figures 26a-c show a single sheet of square pixels having a digital gradation of either monochromatic or spectral color scheme and including a frame which encloses each group of pixels having a common color scheme separating it from the adjacent group(s) of pixels.
  • Figure 26a shows one side of said sheet.
  • Figure 26b shows a section of the other side of the same sheet shown in Figure 26a having the color but with the gradation scale changing in the reverse order thereof.
  • Figure 26c shows a section of the other side of the same sheet shown in Figure 26a having a different color and with the gradation scale changing in the same order thereof.
  • Figure 27 shows a sheet of square pixels having a continuous gradation of either a monochromatic or spectral color scheme.
  • Figure 28 shows a triangular sheet of triangular pixels having a continuous spectral color scheme which is based on the chromaticity diagram of the CIE triangle.
  • Figures 29a-b show assemblies illustrating two color schemes having color contours that are independent of the coupling schemes thereof. Black and white patterns are used to represent solid color schemes or, alternatively, patterned color schemes.
  • Figures 30a-b show pixels which are of different species and have different overall size and pixels of the same species and having different overall size.
  • Figure 31 shows an assembly which incorporates pixels of two different species with a special type of pixel called a transition pixel bridging between the two species.
  • Figures 32 show a pixel having the shape of a winged horse.
  • Figures 33a-e show special pixels having non-interlocking edges, the purpose of such pixels being to terminate the edges of a work of art.
  • Figure 34 shows an assembly of complex coupling of the first level wherein a bay is formed by two bay segments each of which is part of a separate pixel.
  • Figure 35 shows an assembly of coupling of the second level wherein bays are embedded in peninsulas and peninsulas are embedded in bays.
  • Figure 36 shows a sheet of picture elements, the picture elements including square basic shapes and islands in the shape of double peninsulas.
  • Figure 37 shows an assembly composed of set of especially designed pixels displaying the image of a car, and the assembly may include different numbers of general purpose pixels.
  • an object of the present invention is to provide a picture element for simultaneously constructing a support structure while creating a work of art.
  • the pixel comprises a substantially flat piece of material having different color schemes on opposite faces thereof and includes means for connecting the pixel to other pixels having the same or a different basic shape with the same or different coloring schemes on opposite faces thereof.
  • the connecting means permits detachment of the pixel from the other pixels in a vertical direction perpendicular to the faces of the pixel and prevents detachment of the pixel from the other pixels when the pixel is pulled away from the other pixels in any direction that lies within the plane of the faces of the pixel.
  • the pixel preferably, but not necessarily, has bilateral symmetry or rotational symmetry.
  • the pixel has a basic shape which affects visual perception of color contours of a visual image produced by connecting a plurality of pixels having the same or different basic shapes as the basic shape of the pixel.
  • the basic shape can provide well defined color contours or blending of colors along contours thereof.
  • the pixel can further include means for approximating curves in the visual image produced by connecting a plurality of pixels having the same or different basic shapes as the shape of the pixel, the curve approximating means comprising the basic shape of the pixel being asymmetric, such that rotation of the pixel to different angular positions at which the pixel can be connected with at least one other pixel changes color contours between the pixel and an adjacent pixel.
  • the connecting means can comprise at least one peninsula which protrudes from at least one edge of the pixel and at least one bay extending through the opposite faces of the pixel, which intrudes from at least one edge thereof.
  • the connecting means thus provides interlocking and a friction fit between the pixel and another pixel.
  • the connecting means comprises a first bay extending part way into but not through one face of the picture element and a second bay extending part way into but not through an opposite face of the pixel.
  • the connecting means can also comprise first and second peninsulas having thicknesses less than that of the pixel, the first peninsula protruding from one edge of the pixel and having one surface thereof coplanar with one face of the pixel.
  • the second peninsula protruding from another edge of the pixel, and has one surface thereof coplanar with an opposite face of the pixel.
  • the pixel includes a plurality of edges extending between the opposite faces, at least one of the edges comprising either a male edge which includes a peninsula protruding therefrom or a female edge which includes a bay intruding therefrom.
  • one of the edges can comprise a male edge which includes a peninsula protruding therefrom and a second one of the edges can comprise a female edge which includes a bay intruding therefrom.
  • the peninsula can include first and second sections lying in the same plane, the first section being closer to the one edge than the second section and the first section having a width which is more narrow than that of the second section.
  • opposite side edges of the first section can be concave in shape and opposite side edges of the second section can be convex in shape.
  • the first section can have a straight side edge which intersects with a straight side edge of the second section at an angle between 0 degrees and 180 degrees.
  • the peninsula and the bay can have various shapes such as a keystone, a rhomboid, a T-shape, a C-shape, a nipple-like shape or a mushroom-like shape.
  • the peninsula has three sections, one side edge of the first section is concave in shape and an opposite side edge thereof is substantially rectilinear, one edge of the second section is convex in shape and joins the concave shaped side edge of the first section at an inflection point, an opposite edge of the second section is substantially rectilinear and coincident with the rectilinear side edge of the first section, and the third section is dome- shaped and one side edge of the third section is coterminous with the rectilinear side edge of the second section.
  • the peninsula can comprise a single section having two opposite side edges which are concave in shape and a third side edge which is concave in shape and extending between the two concave side edges.
  • the first section can be rectangular in shape and the second section can be triangular in shape, one side edge of the triangular shaped second section being joined to an outermost side edge of the first section such that the first section and second sections form an arrow- shaped peninsula.
  • the peninsula can also include two spaced-apart concentric, arc-shaped side edges, the arc- shaped side edges forming segments of a circle, the center of which is located either inside or outside an outer periphery of the pixel.
  • the picture element can have many different basic shapes.
  • the pixel can include four rectilinearly extending edges, the edges forming a square basic shape or the pixel can include six rectilinearly extending edges, the edges forming a hexagon basic shape.
  • the pixel can also include three rectilinearly extending edges, the edges forming a triangular basic shape.
  • Another possibility is for the pixel to have a generally quadrilateral shape with one inner angle being greater than 180 degrees.
  • the picture element could also include four rectilinearly extending edges of unequal lengths, at least one pair of the edges forming an obtuse angle therebetween and at least one other pair of the edges forming an acute angle therebetween.
  • the pixel also can include four rectilinearly extending edges of unequal lengths, at least one pair of the edges forming a right angle therebetween.
  • Another picture element includes eleven rectilinearly extending edges with at least one pair of the edges forming a V-shaped recess in the pixel.
  • the pixel can also include a plurality of non-rectilinear edges, each edge including a concave portion and a convex portion joined to the concave portion at an inflection point.
  • the pixel can also include a plurality of non- rectilinear edges, two of the edges being convex in shape and one of the edges being concave in shape, the concave edge extending between one end of each of the convex edges and an opposite end of each of the convex edges being joined together.
  • the pixel in another embodiment, includes a plurality of non-rectilinear edges, two of the edges being concave in shape and one of the edges being convex in shape, the convex edge extending between one end of each of the concave edges and an opposite end of each of the concave edges being joined together.
  • the pixel can also include a single edge so as to provide a circular pixel.
  • the pixel can also include three edges, each of which is concave in shape and is formed by an arc having a constant radius for each of the edges.
  • the locking means can comprise at least one bottleneck joint and/or at least one gooseneck joint.
  • the bottleneck joint can have bilateral symmetry.
  • the pixel can also include at least one plain edge which is a non-coupling edge.
  • the pixel can include an even number of interlocking edges or an odd number of coupling edges.
  • Another objective of this invention is to provide the imaging system with a choice of pixels based on the perceptual eifect of the bays and peninsulas on the constructed image. From perceptual viewpoint, the bays and peninsulas are nothing but deviations from the normalized edges of the basic shape of the body of the pixel. The perceptual effect of such a deviation is directly proportional to the extent of such a deviation.
  • the area ratio is defined as the ratio between the area displaced from a pixel by a single deviation from the normalized edge thereof and the area of the normalized body thereof and can be expressed by B/A.
  • B the limit of the area ratio
  • the components of the pixels which facilitate the construction of the supporting structure for the image leave the color contours well defined. Their existence has no significant perceptual effect on the basic shape of the pixel.
  • the pixels have small area ratio or, if the area ratio is large, then the areas of the bays and peninsulas are distributed as close as possible to the coupling edge of said bays and peninsulas.
  • the range of sizes of bays and peninsulas from the very small ones in Case 1 and the maximum possible size in Case 2 forms a continuum. Between these two extremes lies a range of perceptual ambiguity. That is, when the proportion of the size of the bay(s) and of the peninsula(s) with respect to the size of the basic body of the pixel is in this range, some people perceive well-defined contour lines (as in Case 1) while others no longer perceive the basic shape of the pixel (as in Case 2). For most people, the effect is as if the colors along the color contours simply blend into each other. This is the range of ambiguity.
  • the perceptual effect is similar to that of such famous optical illusions of alternating images as the old lady and young maiden or the vase and the two facial profiles.
  • the invention provides for mixing of colors using areas that are indeed smaller than the size of an individual pixel. As a result, it is possible with this embodiment to fine tune the color contours more than it is possible with the resolution of a single pixel.
  • the color scheme of each pixel has a composition of several areas each of which has its own coloring scheme.
  • This coloring scheme facilitates color contours which are independent of the edges of the pixels and their coupling schemes.
  • the basic area of the pixel has one color scheme and each of the peninsulas has another.
  • pixels are provided in either colors each of which is divided into an eight-gradation color scale.
  • This embodiment provides for color contours, well defined, displaced or blending, which for perceptual considerations, are completely independent of the interlocking scheme. Depending only on the color schemes of the pixels, the user is free to generate color contours as desired.
  • the pixel can have a shape which provides tessellation such that an image created with the pixel does not include gaps between the pixel and other pixels.
  • the pixel can have a shape which provides non-tessellation such that an image created with the pixel includes at least one gap between the pixel and other pixels.
  • the pixel can have a thickness which is large enough to provide a friction fit between a peninsula or bay of the pixel and a corresponding bay or peninsula of another pixel in a staggered arrangement which generates a multi-layered three-dimensional image.
  • the pixel can also have a first basic shape excluding peninsulas and bays on one side thereof which is different from a second basic shape excluding peninsulas and bays on an opposite side thereof, the first basic shape having a thickness equal to about one half the thickness of the pixel and the second basic shape having a thickness equal to about one-half the thickness of the pixel.
  • the first basic shape can have a small area ratio of the total area of the bays and peninsulas thereof to the overall area of the first basic shape excluding peninsulas and bays and the second basic shape can have a large area ratio of the total area of the bays and peninsulas thereof to the overall area of the second basic shape excluding peninsulas and bays.
  • the picture element can be a convertible pixel having convertible means called an island for selectively providing a male or female edge.
  • the convertible means can comprise a removable double peninsula which when removed from the pixel forms a bay in the pixel.
  • the pixel can include a peninsula and a perforation in the shape of the bay, the perforation being adjacent the peninsula and being a mirror image thereof.
  • Another object of the invention is to provide a set of pixels comprising a plurality of first and a plurality of second pixels for simultaneously constructing a support structure while creating a work of art, each of the pixels comprising a substantially flat piece of material having different color schemes on opposite faces thereof and means for connecting the set of pixels together, the connecting means permitting detachment of two of the pixels from each other in a vertical direction perpendicular to the opposite faces and preventing detachment of the two pixels in a direction parallel to the opposite faces.
  • the first pixel has a basic shape of a square and the second pixel has a basic shape of a right isosceles triangle, the hypotenuse of the triangle being equal in length to the diagonal of the square.
  • the first and second pixels can have tessellating shapes and each surface of the first and second pixels can be completely covered with a single homogeneous color.
  • the first pixel can include at least one bay or peninsula and the second pixel can include at least one bay or peninsula, a total area of all bays and peninsulas of the first pixel being equal to a total area of all bays and peninsulas of the second pixel, each of bays of the first pixel having a different shape than each of the bays of the second pixel and each of the peninsulas of the first pixel having a different shape than each of the peninsulas of the second pixel.
  • At least one of the picture elements can be transparent.
  • One of the pixels can be a framing pixel having one edge which is a male or female edge or both and other edge which is not a male edge or a female edge.
  • the other edge can be straight, or curved.
  • one of the pixels can be a corner pixel having two adjacent finished edges which are not male or female edges.
  • the pixels can be provided in the form of a sheet of pixels for simultaneously constructing a support structure while creating a work of art, the sheet of pixels including at least a first group of identical pixels, each of which has different coloring schemes on opposite faces thereof and including connecting means for connecting one of the pixels to another one of the pixels having the same or different coloring schemes on opposite faces thereof.
  • the sheet can include a frame having at least one plain edge, the frame including connecting means connecting the frame with the pixels.
  • the sheet can include at least one second group of identical pixels, each of the second group of pixels having a shape which is different from a shape of each of the first group of pixels, each of the second group of pixels having different coloring schemes on opposite faces thereof and including connecting means for connecting one of the pixels to another one of the pixels having the same or different coloring schemes on opposite faces thereof.
  • a first color scale can be provided on one face of the sheet and a second color scale can be provided on an opposite face of the sheet. For instance, one face of the pixel can be covered with a dark color and an opposite face of the pixel can be covered with a light color thereby creating an image on one side of the work of art and a negative of the image on an opposite side of the work of art.
  • Another object of the invention is to provide a method of picturing and sculpturing with pixels which are interconnected to form a two-dimensional or a three-dimensional self- supporting visual image, the method being carried out without the use of tools, devices and/or materials other than the pixels, comprising: (a) interconnecting a plurality of pixels having different color schemes on faces thereof such that a peninsula protruding from an edge of one of the pixels extends into a bay intruding from an edge of an adjacent one of the pixels and the color scheme of the one pixel is different from the color scheme on the adjacent pixel on faces thereof visually observable from a first direction thereby creating an area of confusion along the adjoining edges of the pixels to a person visually observing an image created by the connection between the one pixel and the adjacent pixel; (b) repeating step (a) until a desired visual image is produced.
  • the pixels can include the male and female edges having a first color scheme and facing certain directions with respect to male and female edges of other pixels having a second color scheme so as to create different perceptual effects.
  • male edges of a group of pixels can be oriented in the same direction so as to create a perceptual effect with respect to another group of adjacent pixels having different color schemes.
  • the method can comprise a step of orienting all of the pixel such that each of the male edges extend in only two directions such as +X and +Y.
  • a first pixel can be fitted in the bay of a second pixel by aligning a wider section of the peninsula with a length of the bay and an opening formed by the bay, inserting the peninsula through the bay, rotating the first pixel about a bilateral axis thereof until the wide section is aligned with a narrow section of the bay and the first pixel cannot be pulled away from the second pixel.
  • a set of pixels can comprise first and second types of equilateral triangular shaped pixels, the first type having two female edges and one male edge and the second type having two male edges and one female edge, the image being created by connecting six of the pixels including at least one each of the first and second types so as to form a hexagonal shape, forming additional hexagonal shapes in the same manner and connecting the hexagonal shapes together to form the desired image.
  • the method of the invention can be carried out by mapping the visual image to be produced by determining a pattern of the color schemes of the pixels which will correspond to a visual image of an original subject whereby a two-dimensional self-supporting image is formed or a three- dimensional self-supporting image is formed.
  • the method can include a first step of mapping the visual image to be produced when the pixels are viewed by a person from the first direction by determining a first pattern of the color schemes of the pixels which will correspond to a visual image of a first original subject and a second step of mapping a visual image to be produced when the pixels are viewed by a person from a second direction which is opposite to the first direction, the second mapping step being performed by determining a second pattern of the color schemes of the pixels which will correspond to a visual image of a second original subject which is different from the first original subject.
  • the pixels can be interconnected with gaps therebetween or without any unfilled gaps therebetween.
  • Step (a) can be repeated until the pixels form a self-supporting structure which has an overall shape in two-dimensions other than a quadrilateral or a parallelogram. Also, one or more of said pixels can be replaced with pixels having different color schemes on opposite sides thereof without disturbing remaining ones of the pixels forming the desired visual image.
  • Figure la shows one configuration of a picture element 1 having peninsulas 2 and bays 3 according to the invention.
  • the picture element la has a square basic shape and has bilateral symmetry about the axis A.
  • the picture element la also has two male edges 4 which are adjacent each other and two female edges 5 which are adjacent each other.
  • the square picture element lb shown in Figure lb has bilateral symmetry about two axes, that is about axis B and about axis C.
  • the picture element lb includes two male edges 4 which are opposite to each other and two female edges 5 which are opposite to each other.
  • the picture element shown in Figure la does not have any rotational symmetry whereas the picture element shown in Figure lb has two 180-degrees rotational symmetries.
  • Figures 2a-d show another form of a picture element 6 having a triangular basic shape.
  • the picture element 6a shown in Figure 2a includes two male edges 4 and one female edge 5 having one axis of bilateral symmetry D.
  • the picture element 6b shown in Figure 2b includes two female edges 5 and one male edge 4 having one axis of bilateral symmetry E.
  • the picture element 6c shown in Figure 2c includes three male edges 4 having three axes of bilateral symmetry F, G and H.
  • the picture element 6d shown in Figure 2d includes three female edges 5 having three axes of bilateral symmetry I, J and K.
  • the triangular picture elements shown in Figures 2a and 2b have no rotational symmetry whereas the triangular picture elements shown in Figures 2c and 2d have three 60-degree rotational symmetries.
  • Figure 3a shows a form of a picture element 7 having a hexagonal basic shape.
  • the picture element 7a includes three male edges 4 and three female edges 5, each of the male edges 4 being between two of the female edges 5.
  • the picture element 7a has bilateral symmetry about three axes, that is about axis L, about axis M and about axis N.
  • the hexagonal picture element 7b shown in Figure 3b includes six male edges 4 whereas the hexagonal picture element 7c shown in Figure 3c includes six female edges 5.
  • the pixel 7b has six axes of bilateral symmetry O, P, Q, R, S and T and the pixel 7b has six axes of bilateral symmetry U, V, W, X, Y and Z.
  • the picture element shown in Figure 3a has three 120-degree rotational symmetries.
  • the pixels shown in Figures 3b and 3c have six 60-degree rotational symmetries.
  • Figure 4a shows a picture element 8 having a substantially triangular basic shape with a male edge 4, a female edge 5 and a combination edge 9 which includes a male and female edge in a non-linear arrangement.
  • the picture element 8b shown in dashed lines in Figure 4a being the mirror image of the picture element 8a, is the reverse side of pixel 8a.
  • An assembly of the picture elements 8a and 8b in the form of a sheet is shown in Figure 4b. It can be seen that this arrangement is a tessellating arrangement, that is, neither gaps nor overlaps are provided between the picture elements.
  • Figure 5a shows a picture element 10 having four rectilinear combination edges 9. The combination edge 9 shown is linear.
  • Figure 5b shows an assembly of the picture elements 10, this arrangement being a tessellating arrangement.
  • Pixel 11 is an example of having a peninsula lie protruding from a vertex of the edges of the basic shape of the picture element, rather than from somewhere along an edge.
  • Pixel 11a interlocks with pixel lib which, being the reverse side thereof, has the shape that is the mirror image of the shape of pixel 11a.
  • peninsula lie of pixel 11a interlocks with bay llg of pixel lib and peninsula llj of pixel lib interlocks with bay lid of pixel 11a.
  • Each pixel 11a and lib also has two vertices without a protruding peninsula. These vertices, lie, llf, llh and Hi are notched so that no overlap occurs when several pixels are interlocked in an assembly of as shown in Figure 6b.
  • Figure 7a shows an 11 sided picture element 12. Seven of these sides are plain edges meaning they do not have a peninsula or bay therein. Two of the edges are female edges 5 and two of the edges are male edges 4. The edges of the picture element 12 are rectilinear and five pairs of these edges are parallel to each other. Pixel 12 is a variation of pixel la ( Figure la) having the square edges thereof bent and their bays and peninsulas shifted from their central locations along said edges. As shown in Figure 7b, the picture elements 12 can be arranged in a tessellating arrangement.
  • Figure 8a shows a picture element 13 having four curved edges, that is, two curved male edges 4a and two female edges 5a. These curved edges each comprise a convex part and a concave part which meet at an inflection point.
  • Figure 8b shows a tessellating assembly of pixel 13.
  • Figure 9a shows a picture element 14 having three curved edges, two of the edges being concave male edges 4b and the other edge being a convex female edge 5b.
  • Figure 9b shows a mating picture element 15 which also includes three edges, two of the edges being concave male edges 4c and the other edge being a convex female edge 5c.
  • Figure 9c shows how the picture elements 14 and 15 can be assembled in a tessellating arrangement. As shown in Figure 9c, the picture elements 14 can include an optional peninsula 2a and a corresponding bay 3a.
  • Figure 10a shows a picture element 16a having combination edge 9 which includes a a bay and a peninsula in a linear arrangement.
  • Figure 10a being the mirror image of the picture element 16a, is the reverse side of pixel 16a.
  • FIG. 10b A tessellating staggered "brick-layered" assembly of the picture elements 16a and 16b is shown in Figure 10b. Pixel 16a alone can in its plurality form a tessellating arrangement.
  • Figure 11a shows a picture element 17 having a single edge.
  • the picture element 17a shown in Figure 5a includes alternating bays and peninsulas, there being three bays 3 and three peninsulas 2.
  • Figure lib shows an assembly of the picture elements 17a which provides a non-tessellating arrangement with gaps 18a between adjacent picture elements 17a.
  • Figure lie shows another form of the picture element 17.
  • a picture element 17b includes six bays 3.
  • Figure lid shows a picture element 19 which interconnects the picture elements 17b.
  • the picture element 19 includes three concave male edges 4c.
  • Figure He shows how the picture elements 17b and 19 can be arranged in a tessellating arrangement.
  • Pixel 17c in Figure llf can be interlocked in its plurality to construct images.
  • Figure llh shows an assembly constructed of six pixels 17c. Between these size pixels two gaps 18b are formed. Hence, pixel 17c alone, in its plurality is not tessellating.
  • Pixel 20 in Figure llg has the precise shape to fill the gap 18b in Figure llf without overlapping. Therefore, the set of pixels 17c and 20 a is tessellating.
  • Figures 12a-i show various configuration for the peninsulas and bays, the connection therebetween being a bottleneck type connection.
  • the various shapes of the peninsulas are shown at 3b-j and the various shapes of the bays are shown at 2b-j.
  • FIGs 13a-f show various arrangement of a gooseneck type connection according to the invention.
  • each of the peninsulas 2k-p and bays 3k-p respectively, includes a first section 21 and a second section 22, the first section having a particular relationship to the second section.
  • Figure 13b shows how an interior angle xl on one side of the bay or peninsula and the exterior angle yl on the other side of said bay or peninsula both have their vertices pointed in the same direction.
  • Figure 13c shows a modified version of the arrangement shown in Figure 13b.
  • Figure 13d-e shows an arrangement wherein the peninsula and bay are formed by curved edges having different radii, the center of which is at a point 26 located within one picture element or the other.
  • the picture elements will not separate in the X-Y plane whereas the picture elements shown in Figure 14c could separate in the X-Y plane since the center of the arcs 27 is located at abutting corners of the picture elements.
  • Figure 13d shows an arrangement wherein the center of the arcs of the bay are located within the same picture element whereas Figure 13e shows the center of the arcs located outside the picture element.
  • the center of the arcs 26 for the peninsula in Figure 13d is located outside the picture element having the peninsula whereas Figure 13e shows the center of the arcs 26 being located within the same picture element having the peninsula.
  • Figure 13f shows a first curved section 21' and a second curved section 22', the curved edges of the first section 21' meeting the curved edges of the second section 22' at an inflection point 23.
  • Figure 13f shows a first curved section 21' and a second curved section 22', such that an angle x2 is formed between an interior tangent to the curved edge of section 21' and an interior tangent to the curved edge of section 22'.
  • an angle y2 is formed between an exterior tangent to the opposite curved edge of section 21' and the exterior tangent to the opposite curved edge of section 22', both angles having their vertices pointed in the same direction.
  • Figures 14a and 14b show arrangements wherein the peninsulas and bays are capable of separating in the X-Y plane.
  • the pairs of angles x3 and y3 and xl and y2 violate the requirement set the description of Figure 13b. Accordingly, peninsulas 2q-r and corresponding bays 3q-r are outside the scope of the present invention.
  • Figures 15a-c show how the picture elements are connected together by moving them along the Z axis.
  • Figure 15b shows how the picture elements cannot be separated in the X-Y plane.
  • Figure 8c shows how the picture elements are separated by applying a force F in the Z direction and applying a rotational component of the force F2 or F3 which separates the picture elements.
  • Figure 16a shows a picture element 1 according to the invention compared to a "LEGO" block shown in Figure 16b according to the prior art.
  • Figures 17a-c show how the "LEGO" blocks are assembled.
  • the blocks 28 are assembled by pressing them together in the Z direction but unlike the picture elements of the invention, the blocks 28 cannot be connected together in the same X-Y plane.
  • the blocks 24 must be assembled in a layered arrangement in order to connect the blocks 28 together in the X-Y plane.
  • Figures 18a through 18f show how color contours are affected by the area ratios and the distances of displacement of bays and peninsulas.
  • the bays 3 and the peninsulas 2 have a moderate area ratio and their displacement is far from the edge thereof resulting with blending color contours.
  • Some viewers perceive pixels 29a and 29b having well-defined color contours while other viewers perceive these two pixels as blending one into the other. Or the same viewer may alternately perceive well-defined color contours between pixels 29a and 29b at some times and blending color contours between pixels 29a and 29b at other times.
  • Figure 18b shows that if the area ratio remains the same as in Figure 18a but the displacement of the area of the peninsula is not far enough from the edge thereof, the color contour appears well defined.
  • Figure 18c shows that when the area ratio is small and the displacement of the area of the peninsula is far, the color contours appear well defined.
  • Figure 18d shows that when the area ratio is smaller than that which is shown in Figure 18b and the displacement of the area of the peninsula is the same as shown in Figure 18b, the color contour appears even more well defined. Having differently shaped bays and peninsulas, Figures 18e and 18f are equivalent to Figures 18a and 18d, respectively.
  • Figures 19a-h show eight identical assemblies of nine square pixels, having a shape that is a variation of pixel lb ( Figure lb), four of which are gray and four of which are black.
  • the normalized bodies of all pixels in all eight figures are of exactly the same size and shape.
  • the bays and peninsulas in Figure 19a are of a first size, the largest within said set of figures, and the bays and peninsulas in Figure 19h are of an eighth size, the smallest within said set of figures.
  • Each consecutive figure in the sequence from Figure 19a through 19h shows a discrete and uniform decrease in the size of the bays and peninsulas thereof with respect to the size of the bays and peninsulas in the preceding figure.
  • Figures 19a-b show a displaced color contour.
  • Figure 19c through 19f show blending color contours.
  • Figures 19g-h show well defined color contours.
  • Figure 20a shows a square pixel with a side "a” and a diagonal "c".
  • Figures 20b and 20c show equilateral triangular pixels with a side "a”. Forming a set, the three pixels in Figures 20a-20c, in their plurality, can be combined to form a wider range of angles as illustrated, for example, in Figure 20d.
  • Figures 20e and 20f show isosceles right-angle triangles with the side "a" and the hypotenuse "c”.
  • a gap may be filed with overlapping as shown by the dashed line representing the pixel of Figure 20h.
  • Figure 20h illustrates that since the edge of the size of hypotenuse "c" is longer than edge "a", a gap the length of "d” may be created if an edge of length "a” is interlocked with an edge of length "c". The gap cannot be filed without overlapping.
  • the pixel shown in Figure 20i being rectangular and having a first side of length "a” and having a second side of length "c", can be added to the aforementioned set to avoid this latter problem.
  • having a side of length "c” the pixel of Figure 20i only pushes the problem toward the edge of the image.
  • FIG. 21a shows how an area below a curved line was digitized with dark square pixels and the area above said curved line was digitized with light square pixels.
  • Figure 21b the grid of the image from Figure 21a was first shifted downward with respect to said curved line by a distance that is equal to approximately half the length of a single edge of the square pixel thereof.
  • Figures 21c and 21d show how the orientations of the picture element affect the color contours and their ability to approximate curved lines in the original model.
  • the model is outline 33 of a figure-8.
  • the image is digitized with a plurality of gray square pixels 34.
  • Creating the image in Figure 21d the first pixel to be placed in the image was rotated by 45 degrees with respect to its orientation in Figure 21c.
  • the whole lattice of pixels in Figure 21d has been rotated with respect to the lattice of Figure 21c and more pixels are necessary to approximate the same model.
  • the judgement which image better resembles the original model is subjective for each viewer.
  • Figure 21e-f show how the orientation of the picture elements affect other picture elements in the lattice.
  • the picture elements 35 and Figure 21e are triangular in shape and are arranged such that at least one edge thereof is horizontal.
  • the pixels 36 shown in Figure 21 f are arranged such that at least one edge thereof is parallel to the vertical direction.
  • Figures 21e-f show two digitizations of a face using curved lines. The effects of rotating the pixels in Figure 21 f by 30 degrees with respect to the picture elements in Figure 21e can be easily appreciated from these figures.
  • the eyes are spaced wider apart, the nose is angled and the mouth is comprised of two pixels instead of three pixels as in Figure 21e.
  • Figures 14a-f show six variations of a square basic shape picture element 1.
  • picture element lc includes four male edges
  • picture element Id includes three male edges and one female edge
  • picture element la includes two male edges which are adjacent each other and two female edges which are adjacent each other
  • picture element lb includes two female edges which are opposite each other and two male edges which are opposite each other
  • picture element le includes three female edges and one male edge and picture element If includes four female edges.
  • Figures 22g-j show how picture element la can be oriented in four different positions, that is laa, lab, lac and lad.
  • Figures 22k-p show how the picture elements 1 can be assembled with various orientations.
  • Figures 22k-l include only picture elements in orientation laa
  • Figure 22m includes two picture elements in orientation laa and two picture elements in orientation lad.
  • Figure 22n shows one picture element in orientation laa and another in orientation lab.
  • Figure 22o includes two picture elements in orientation laa and two picture elements in orientation lab.
  • Figure 22p includes a picture element in each orientation laa-ad.
  • Figures 23a-k show various arrangements for triangular shaped basic pixel 7.
  • the picture elements 6a and 6b shown in Figures 23a and 23b, respectively can be arranged in various combinations to form various hexagonal picture elements 7.
  • Figures 23c-k show how the triangular shaped picture elements 6a and 6b can be arranged in the hexagonal picture elements 7a-i.
  • Figure 24a shows a pixel 37 having a double thickness compared to the earlier described pixels.
  • the pixel 37 includes peninsulas 2 having a thickness one-half that of the pixel 37.
  • the bays 3 are formed by recesses in the pixel 37, the recesses extending to a depth one-half the thickness of the pixel 37.
  • the pixel 37 can be assembled as shown in Figures 24d- e.
  • Figure 24d shows a single layer whereas Figure 24e shows a staggered layer.
  • Figure 24e shows a cross section of a multi-layer assembly wherein the upper and middle pixels 37a, 37b, 37c and 37d are transparent and the lower pixels 37e and 45 f each is either transparent or opaque.
  • Pixel 37f is of a first thickness, called single thickness.
  • Pixels 37a through 37e are of a second thickness, called double thickness, which is twice the size of the first thickness.
  • Pixel 37f is used if it is desired for the bottom face of the image to have a single coplanar surface. (Note that in these figures hatching is used only to illustrate cross sections. No particular material is suggested by any choice of the hatching pattern.)
  • pixel 38 in Figure 24b is a double-layer pixel, having bays and peninsulas which are single-layer. Unlike the bays and peninsulas of pixel 38 which are aligned above each other, the bay and peninsulas of pixel 38 are independent of each other. In particular, two edges have one peninsula 2 each with no bay, two edges have only one bay 3 each with no peninsulas.
  • Pixel 39 in Figure 24c is of a double-layer. Its edges 5 and 4 have single thickness peninsulas and double-thickness bays respectively.
  • Figure 24g shows an assembly of a single- thickness pixel 40a with a multi-thickness pixel 40b. A single layer peninsula and a multi-layer bay form coupling 41 with sufficient space for another pixel layer.
  • Figure 24h shows how picture elements la can be assembled in a three-dimensional arrangement forming a cube.
  • Figure 25 shows show a visual image produced by interconnecting pixels la.
  • Figure 26a shows one face of a sheet of square picture elements and Figure 26b and 26c show the opposite face of said sheet.
  • the color scheme of each surface of said sheet has several discrete colors or discrete shades of the same colors, each of which is represented by a different density of dot patterns.
  • Figure 26b the reverse order of the dot densities on the opposite faces of said sheet represents the fact that if both sides have the same color scales, then these scales are reversed in order.
  • Figure 26c the same order of the dot densities on the opposite faces of said sheet represents the fact that both sides have the same color scales whether said surfaces have the same colors or not.
  • the pixels are enclosed within a frame 42 having the same color scheme as the pixels therein.
  • a segment of the frame 44 extends from one side of the sheet and across the sheet to the other side to separate each set of pixels 43 having the same color scheme from the pixels around it having different color schemes thereof.
  • the color scheme of each set of pixels having the same color scheme extends half way width-wise into said extensions 44 of the frame. This frame can be used to restore unused pixels and as a color-scale indicator.
  • Figure 27 shows an example of a sheet of square picture elements.
  • the continuous gradation of the density of the random pattern represents a continuous gradation in a monochromatic or spectral color scheme.
  • a triangular sheet of triangular picture elements is shown in Figure 28.
  • the color of pixel 45a is yellow-green having a wavelength at its top vertex of approximately 520 millimicron.
  • the color of pixel 45b is purple having a wavelength at its left vertex of approxi ⁇ mately 400 millimicron.
  • the color of pixel 45c is red having a wavelength at its right vertex of approximately 770 millimicron.
  • the color around point 46 is white.
  • This spectral sheet of pic ⁇ ture elements approximates the chromaticity diagram as shown in a standard CIE triangle of colors.
  • the color graduation between individual pixels in this sheet may be either discrete or continuous along both the X and the Y axes.
  • Figures 29a-b show assemblies illustrating two color schemes having color contours that are independent of the coupling schemes thereof.
  • Black and white patterns are used to represent different solid color schemes or, alternatively, different patterned color schemes. This color scheme generates color contours that are independent of the interlocking scheme of said pixels.
  • the rectilinearly extending edges of the normalized bodies of pixel la-xl in Figure 30a and of pixel 47 in Figure 30b are three times as large as the rectilinearly extending edges of pixel la in Figure 30b.
  • the bay and peninsulas of pixel la-xl were enlarged with respect to the bays and peninsulas of pixels la by the same proportion in which the normalized body of pixel la-xl is larger than the normalized body of pixel la.
  • Pixels la-xl and la are of different species as they cannot be interlocked.
  • Pixel 47 has an arrangement of bays and peninsulas along the edges thereof such that it can be interlocked with pixel la. Pixels 47 and la are of the same species.
  • Pixel la is of a first species having well-defined color contours.
  • Pixel 50 is of a second species having displaced color contours.
  • Pixels 48 and 49 have at least one edge of the first species and at least one edge of the second species. Pixels 48 and 49 facilitate an assembly which may include pixels of both the first and the second species.
  • Figure 32 shows an asymmetric pixel having various a symmetric peninsulas and bays.
  • peninsula 2z and bay 3z are of the gooseneck type.
  • Figures 33a-e Variants of edge or framing picture elements are shown in Figures 33a-e.
  • the pixels in Figure 33a through 33d terminate in a work of art with a straight edge.
  • Figure 30a-30c show pixels 51-57 each of which has one non interlocking edge.
  • Figure 33d shows an L-shape pixel having a length of several pixels and a width of a single pixel.
  • Figure 33e shows a similar pixel as in 33d but it terminates a work of art with a sinuous line.
  • Pixel 51 of Figure 33a is a corner pixel having a beveled corner.
  • Figure 34 shows a set of three pixels that illustrates a complex coupling scheme of a first level.
  • Two Pixel 58 together form a bay that interlocks with the peninsula of pixel la.
  • Each pixel la can interlocked in this manner with up to six picture elements that surround it (not shown), four are pixel 58 and two are pixel la.
  • Each pixel 58 interlocks with six pixels that sur ⁇ round it, four are pixel la and two are pixel 58.
  • Figure 35 shows picture element 60 having a basic square shape 61 which illustrates a complex interlocking scheme of a second level.
  • interlocking is established by peninsulas 2 that protrude from second level bays 59 and are coupled with bays 3 which intrude into second level peninsulas 62.
  • Second level bays 59 are formed by horizontally adjacent pixels 60a.
  • Figure 36 shows a sheet of picture elements including square picture elements 63 that is composed of a body 64 and double peninsula 65.
  • the double-peninsulas 65 are islands in the sense that they can be separated from the body 64 on both sides, becoming independent pixels, or remain attached to a particular pixel thus forming a peninsula on the picture element.
  • the island 65 are connected to the bodies 64 by perforated material providing easy detachment.
  • Figure 37 shows a special purpose set of picture elements 66-73 that is designed to gener ⁇ ate images of cars. Using different numbers of pixels la, the car may be stretched or shrunk.
  • the imaging system should be able to produce opaque images (reflecting light), transparent images (transmitting light), and light emitting images.
  • the imaging system must be inexpensive, within the financial reach of all (except, perhaps, for light radiating imaging systems).
  • the imaging system may be used to produce works of art, or images, for a large variety of utilitarian, recreational, educational and decorative applications. Further, provided the proper material is used in the fabrication of the pixels, it should be possible to put the images into the use to which they were designed while the creation work is still in progress. For example, if one is creating a place mat, a mat for hot pots, a coaster, or a tiled counter top or a floor, it should be possible to use these assembled objects as intended even before the design has been finalized (not while actual work is performed).
  • Another object of the invention is to provide an imaging system which includes a substantially flat picture element, in one embodiment, or a small, finite set of substantially flat picture elements, in another embodiment, for simultaneously constructing a supporting structure while creating a work of art.
  • These picture elements are to provide the user with a choice of the following features:
  • the pixel may have a tessellating shape (e.g., square) or it may have a non- tessellating shape (e.g., square with rounded corners or circle). If a set of pixels is used, it may be a tessellating or a non-tessellating set.
  • a first pixel can be combined with a second pixel having the mirror image shape of the first pixel. (See Figures la-b; 2a-d; 34; 35).
  • a first pixel must be capable of coupling with a second pixel having the mirror image of the first pixel (See Figures 4a-b, 6a-b; lOa-b). Yet in another embodiment, it is not possible to combine a first pixel with a second pixel having the mirror image shape of the first pixel. (See Figures 32; 37).
  • the model for the image can be shifted with respect to the lattice (or grid) of the art work along one or more of the grid's X, Y and Z axes, the X and Y axes being in the grid's plane and the Z axis being perpendicular to the grid's plane, such that, following said shift, no pixel's new position in the image precisely overlaps any pixel's position in the image prior to said shift. (See Figures 21a-b).
  • the basic, normalized shape of the pixel may have at most a small finite number of rotational symmetry axes, such that rotating a single picture element in its position within any constructed work of art to an angle that is rotationally asymmetric with its original orientation, necessitates an identical rotation of all other pixels in said image without altering the overall shape of the image. (See Figures 21c-f). Also, rotating a pixel into one of the rotationally symmetric orientations of its basic shape may affect its color contours.
  • any picture element within a constructed image may be disengaged from its surrounding pixels with no adverse effect on itself, on its surrounding pixels or on the overall image.
  • the picture elements having different normalized shapes can be combined to improve the approximation of curves by the color contours (when compared to such curves as produced by pixels having a single overall shape).
  • a further aspect is that there are no intrinsic restrictions on the size and shape of the picture elements except as dictated by the material that is used for manufacturing the pixels and by the fabrication and manufacturing technology.
  • the picture elements may be manufactured from a variety of materials such as but not limited to cardboard, chipboard, plastic, wood, particle board, clay, ceramic, glass, metal, or from some compositions or lamentations of such materials. (See Figs 15a-c).
  • the normalized shape of the picture element(s) may be geometric (e.g., triangle, quadrilateral, hexagon for tessellating pixels or circle, ellipse, pentagon for non-tessellating pixels) with straight or curved (e.g., sinusoid) edges.
  • the basic shape of the pixel(s) may be in some artistic form (See Figures la-llc; 30a-b; 32; 33d-e; and 34, 35, 37).
  • the property of symmetry or, conversely, the property of asymmetry may be used in the design of a picture element.
  • symmetry or asymmetry it is done with reference to any one of the following four elements of the picture-element design or it is done with reference to any combination of these four elements, including all four of them together:
  • the normalized body of the picture element may be symmetric or asymmet ⁇ ric.
  • Each edge of a pixel may be symmetric or asymmetric.
  • the symmetric edges of an eleven edged pixel Figure 7b
  • the asymmetric edges of a four edged pixel Figure 5b.
  • Each bay and peninsula may be symmetric ( Figures 12a, c, e, f, h, i) or asymmetric ( Figures 12b, d, g).
  • the overall shape of the picture element that is, the pixel's normalized body as affected by its edges and their bays and peninsulas, may be symmetric ( Figures la; 8a, 9a,
  • picture elements are designed to couple with each other. If the interlocking scheme of two picture elements, regardless to their basic (normalized) shape, facilitates the interlocking of the one with the other, then the two pixels are said to be of the same species. If the two pixels cannot be interlocked, then they are said to be of different species. For all practical purposes, any pair of pixels of the same species can be interlocked with each other regardless to manufacturing batch, generation, etc. Further, interlocking is a transitive property: If edge A interlocks with both edge B and edge C, and if edge D interlocks with edge C, then edge D also interlocks with edge B.
  • the pixels of a given imaging system provide for the construction of a substantially flat work of art, or image, in a single planar surface and/or of artworks in a curved surface.
  • the bays and peninsulas which provide for the pixel interlocking extend thickness-wise from one surface of the pixel all the way to the other surface.
  • These type of pixels are very versatile; they provide for the construction of images on a planar sheet, of images on a curved sheet, and, if they are sufficiently thick, they provide for the construction of images that are composed of multi-layered intersecting sheets.
  • the thickness of the pixel is sufficient to provide for staggered, layered coupling. That is, two pixels, not necessarily of the same basic shape but necessarily of the same species, may be arranged such that (a) one surface of a first pixel butts against one surface of a second pixel; and (b) one bay of a first pixel is perfectly aligned with one bay of a second pixel such that the two bays couple with a single peninsula of a third pixel. Then, each bay has half of its outer thickness (the portion away from the abutted pixel) free from being interlocked with the peninsula; thereby, a fourth pixel with a peninsula may be aligned with the first peninsula of the third pixel on either side thereof. In this manner pixels may form a staggered interlock to form a multi-layered work of art. ( Figures 24a-g).
  • the bay and peninsula which provide for the pixel coupling, extend from one surface toward the other surface only partially. That is, the bay and peninsula have the thickness of an ordinary picture element, called single thickness, while the thickness of the normalized body of the pixel is twice as thick, called double-thickness.
  • the thickness of the peninsula is identical to the thickness of the bay.
  • the peninsula is of a single thickness while the bay is of a double thickness. This embodiment provides for two pixels with butting surfaces, each of which has such a peninsula, to be interlocked with a single pixel with such a bay. ( Figures 24a-g).
  • both bays and peninsulas are of a single thickness and the positioning of a bay along the edge of the pixel is independent of the positioning of the peninsula along the edge of the pixel.
  • the bay and peninsula, both of a single thickness are aligned "on top of each other" along the edge of the pixel.
  • each interlocking edge of a picture element has either a single protruding peninsula or a single intruding bay but not both.
  • each interlocking edge may have two or more protruding peninsulas or two or more intruding bays.
  • an interlocking edge may include both one or more protruding peninsulas with one or more intruding bays.
  • Some embodiments which utilize pixels with multiple bays and/or peninsulas along some edges can provide for the staggering of pixels within the plane of construction in a "brick-laying" fashion. ( Figures 5a-b; 6a-b; lOa-b; 24a; 32; 33D). In case of a circular or an ellipsoidal picture element the whole circumference is taken into account. For instance, Figures llc-d show female pixels whereas the pixels shown in Figures lla-b, f and h, have no gender.
  • the bay and peninsula are centered along their edges.
  • the bay and peninsula are displaced from the center of their edges in an equal distance such that they can be interlocked.
  • two interlocked pixels may be aligned or they may be staggered in a brick-laying fashion.
  • the peninsula or bay may be located at a vertex where two edges of the normalized body of the picture element intersection. ( Figure 6a).
  • a portion of a bay or only a portion of a peninsula exists along an edge of a picture element. More than a single pixel is necessary to form a whole bay or a whole peninsula. To provide a stable coupling, the picture elements that together form such a composite bay must interlock with each other and their composite bay must couple with a single peninsula. ( Figure 34). Conversely, such a composite peninsula must couple with a single bay.
  • the peninsula of a first design is sufficiently large to accommodate one or more bays of a second design and the bay of the first design is sufficiently large to accommodate one or more peninsulas of the sec- ond design. ( Figure 35).
  • Another objective of this invention is to provide the imaging system with substantially flat picture elements for the creation of visual images, such that:
  • the coloring scheme of one surface may be dependent on the coloring scheme of the opposite surface. While creating an image on one surface, another image that has the same general design but with different colors (e.g., negative or inverse colors) is being generated simultaneously on the opposite surface. ( Figures 26a-c).
  • the coloring scheme of one surface may be independent of the coloring scheme of the opposite surface. A user of this embodiment can simultaneously create two independent images, one on each surface. ( Figures 26a-c).
  • the pixel may be transparent. ( Figure 24f).
  • the pixel may be light emitting. That is, it may be fluorescent or contain the necessary modular circuitry (including power source) and light emitting devices. Some pixels are light emitting (e.g., fluorescent) on both of their surfaces while others (e.g., electric) emit light from only one surface.
  • any color scheme may be composed of either a solid color (26a-c); or some geometric pattern, peri ⁇ odic or non-periodic, having one color scheme for said pattern and another color scheme for the background of the pattern; or some combination of solid colors or of geometric patterns. ( Figures 29a-b).
  • the graduation scale between the two surfaces or the graduation scale between the two pixels is: either digital ( Figures 26a-c, 28) or analog ( Figures 27, 28); and either monochromatic ( Figure 25) or spectral ( Figures 26a-c, 27, 28).
  • Another objective of this invention is to provide the imaging system with a choice of pixels based on the perceptual effect of the bays and peninsulas on the constructed image.
  • the bays and peninsulas are nothing but deviations from the normalized edges of the basic shape of the body of the pixel.
  • the perceptual effect of such a deviation is directly proportional to the extent of such a deviation.
  • the area ratio is defined as the ratio between the area displaced from a pixel by a single deviation from the normalized edge thereof and the area of the normalized body thereof and can be expressed by B/A.
  • B the limit of the area ratio
  • the limit of the area ratio is zero. Namely, as the size of the deviation is reduced, so does its visual effect on the color contour. When the area shrinks to nothing, its visual effect on the color contour is nil.
  • the limit of the area ratio approaches infinity.
  • the components of the picture elements which facilitate the construction of the supporting structure for the image leave the color contours well defined. Their existence do not significantly perceptually alter the basic shape of the pixel.
  • the picture elements have small area ratio or, if the area ratio is large, then the areas of the bays and peninsulas are distributed as close as possible to the coupling edge of said bays and peninsulas. ( Figures 18b-d; 19g-h; 20b; 25).
  • the color of one pixel is almost completely displaced by the colors if the peninsula(s) which intrude into it from some adjacent pixel(s) while the color of its own peninsula(s) intrude into other adjoining pixels. Perceptually, the basic shape of the pixel is no longer discernable. The color contours are said to be displaced. In this embodiment, the pixel must have both large area ratio and the area of the bays and peninsulas are distributed significantly away from their respective interlocking edges. ( Figures 19a-b).
  • the invention provides for mixing of colors using areas that are indeed smaller than the size of an individual picture element. As a result, it is possible with this embodiment to fine tune the color contours more than it is possible with the resolution of a single pixel. ( Figures 18a; 19c- f).
  • the various coloring schemes in all three cases are independent of the coupling schemes.
  • the color scheme of each pixel has a composition of several areas each of which has its own coloring scheme.
  • This coloring scheme facilitates color contours which are independent of the edges of the picture elements and their coupling schemes.
  • the basic area of the pixel has one color scheme and each of the peninsulas has another.
  • pixels are provided in eight colors each of which is divided into an eight-gradation color scale.
  • This embodiment provides for color contours, well defined, displaced or blending, which, for perceptual considerations, are completely independent of the interlocking scheme. Depending only on the color schemes of the pixels the user is free to generate color contours as desired. ( Figures 29a-b).
  • Another objective of this invention is to provide an imaging system with transition picture elements.
  • a picture element has at least one interlocking edge of one species and at least one interlocking edge of another species.
  • the use of a transition pixel provides for the change from one coupling scheme into another. For example, in one section of the constructed image, the coupling provides for well defined color contours and in another section of the constructed image the interlocking provides for blending color contours. Transition pixels are used in order to connect the two sections. (Fig. 31).
  • Another objective of the invention is to provide the imaging system with finishing picture elements. That is, picture elements with one straight edge or with two adjacent straight edges, forming a comer, without any peninsula and without any bay, may be generated to form the outmost edge of a triangular, quadrilateral, hexagonal (etc.) image. Similarly, pixels which form an outer curved edge, such as sinusoid, (with comers, if needed, to match) should also be possible. ( Figures 33a-e).
  • Another objective of this invention is to provide the imaging system with convertible picture elements. These picture elements have only peninsulas and for each peninsula, where a bay would have been present, penetrating the main body of the pixel, a perforation, outlining of the bay is present. The user, at his or her choice may leave the peninsula undisturbed or punch out the perforation, leaving a bay in its place. (Fig. 36).
  • Another objective of this invention is to provide a plurality of picture elements in the form of sheets.
  • the sheets may be framed, such that: (1) regardless to the color scheme, monochromatic or spectral, and regardless to its gradation, digital or analog, the frame can be used as a color gradation scale, or (2) the frame may be used repeatedly to store unused pixels.
  • Figures 26a-c use digital variations in the dot densities. They may represent, for illustrating some aspects of this invention, a monochromatic color scale or, for illustrating other aspects of this invention, these different dot densities represent different colors or patterned colors.
  • the analog variation in the density of the pattern represents a monochromatic color gradation; for other embodiments, it represents spectral color gradation.
  • Fig. 28 represents either an analog or digital spectral color scale.
  • Yet another objective of this invention is to provide picture elements of different overall sizes.
  • the larger picture elements have proportionally enlarged bays and peninsulas.
  • Such size variation render the pixels of different sizes to belong to different species. For instance, compare pixel la-xl in Figure 30a to pixel la in Figure 30b.
  • Another objective of this invention is to provide special purpose picture elements.
  • Such pixels are designed to better approximate specific shapes.
  • a kit that is designed for imaging cars may include pixels in the basic shape of car wheels, bumpers, etc. ( Figure 37).
  • Another objective of this invention is to provide a method of creating works of art from such an imaging system as described above.
  • An image is assembled from individual picture elements. At any time any individual pixel or set of pixels may be disengaged from the assembled work of art and replaced by another without adverse effect on it, on its adjacent pixels or on the whole image.
  • Examples of a method include the use of various coupling schemes which utilize the bottleneck, or the gooseneck, or the S-shape, interlocking edges.
  • the method also includes the use of symmetric and asymmetric coupling schemes, utilizing the symmetry or asymmetry of the coupling shape, or the symmetry or asymmetry of the interlock ⁇ ing edge.
  • the method also includes the use of a single bay or peninsula per interlocking edge, or the use of multiple bays or peninsulas per coupling edge, such edges including male/female edge or bay and peninsula combination.
  • various coloring schemes are possible including digital or analog, monochromatic, or spectral with changes along one or two axes.
  • the method also includes the use of well-defined color contours, or blending color contours or displaced color contours.
  • the method can further include pattern making schemes.
  • Another objective of this invention is to provide a method for generating new picture elements or small finite sets of picture elements each of which can facilitate an imaging system that have all the features enumerated above.
  • Another objective of this invention is to provide a method for producing motion pictures animation.

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Abstract

Classe de dispositifs, appelés éléments d'image, ou pixels, permettant la production d'images visuelles bidimensionnelles (planes) et tridimensionnelles (spatiales) à la fois dans la représentation par image et la sculpture, et procédés par lesquels lesdites images visuelles peuvent être construites à partir desdits éléments d'image. La conception des éléments d'image facilite simultanément la construction des deux éléments nécessaires de chaque image visuelle, l'image elle-même et son support. De configuration sensiblement plane, les éléments d'image sont façonnés pour présenter un support solide et stable se présentant sous la forme d'une feuille individuelle, plane, opaque ou transparente à double surface, ou une structure tridimensionnelle composée d'une ou de plusieurs desdites feuilles. La conception des pixels facilite également des contours de couleur bien définis ou le mélange de couleurs sur leurs contours. Dans le cas d'une feuille ou de feuilles opaques présentant deux surfaces sur lesquelles se trouvent deux agencements de couleurs différentes, les éléments d'image sont conçus pour faciliter la création simultanée de deux images, une sur chaque surface de la feuille construite. Certaines règles sont prévues afin de produire de nouvelles conceptions desdits éléments d'image.
PCT/US1991/006618 1990-09-12 1991-09-12 Systeme de construction d'images visuelles WO1992004701A1 (fr)

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US581,565 1990-09-12

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CN103002078A (zh) * 2011-09-08 2013-03-27 Lg电子株式会社 移动终端以及制造其外壳的方法
EP2732980A1 (fr) * 2012-11-14 2014-05-21 Thomas Kostulski Jeu de carreaux
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GB2531575A (en) * 2014-10-22 2016-04-27 Simbrix Ltd Beads and bead assemblies
EP2734682A4 (fr) * 2010-09-15 2016-08-10 Adám Bálint Bloc de construction, unité de pavage, carreau ou élément ludique autobloquants et procédé de construction associé
RU205392U1 (ru) * 2021-04-06 2021-07-13 Общество с ограниченной ответственностью «ИНТЕРСТРОЙ» Интерьерное мозаичное зеркальное панно (варианты)

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Cited By (11)

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EP2734682A4 (fr) * 2010-09-15 2016-08-10 Adám Bálint Bloc de construction, unité de pavage, carreau ou élément ludique autobloquants et procédé de construction associé
WO2012106797A1 (fr) * 2011-02-11 2012-08-16 Canadian Space Agency Procédé et système d'augmentation de la résolution spatiale d'une imagerie optique multidimensionnelle au moyen d'un trapèze intrinsèque du capteur
US9041822B2 (en) 2011-02-11 2015-05-26 Canadian Space Agency Method and system of increasing spatial resolution of multi-dimensional optical imagery using sensor's intrinsic keystone
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GB2531575A (en) * 2014-10-22 2016-04-27 Simbrix Ltd Beads and bead assemblies
GB2531575B (en) * 2014-10-22 2016-09-14 Simbrix Ltd Beads and bead assemblies
RU205392U1 (ru) * 2021-04-06 2021-07-13 Общество с ограниченной ответственностью «ИНТЕРСТРОЙ» Интерьерное мозаичное зеркальное панно (варианты)

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