JP3751963B2 - Sphericality judgment method and curved screen construction method - Google Patents

Description

  The present invention relates to a sphericity determination method and a curved screen construction method, and in particular, a sphericity determination method for determining a sphericity of a curved surface to be determined, and a sphericity determination method using the sphericity determination method. The present invention relates to a method for constructing a curved screen for finishing a screen surface having a surface layer made of the above material as a top layer so as to coincide with a predetermined spherical surface.

  In presentations such as exhibitions and events, images are often presented by projecting two-dimensional images such as photographic images and CG onto a flat screen, but the projection of a two-dimensional image onto a flat screen or the like is simply an enlarged display. Therefore, there is a disadvantage that visual presence is poor, and in order to increase visual presence, it is effective to project and display a two-dimensional image on a curved screen. However, although the curved screen is constructed with the goal of making the screen surface coincide with the spherical surface, it is difficult to make the entire screen surface coincide with the spherical surface, and a portion deviating from the spherical surface may occur. And if there is a part deviating from the spherical surface in the screen surface, a shadow is generated with the projection of the image, and the visual sense of reality is greatly hindered by visually recognizing this shadow. is there. Particularly in training simulations, which are one of the uses of curved screens, the level of demand for visual presence is extremely high, and the sphericity of the screen surface of curved screens is also required to be very high.

  Conventionally, curved screens are constructed by measuring the three-dimensional positions of a large number of measurement points set at approximately equal intervals on the screen surface with a theodolite, and obtaining the deviation between the measured three-dimensional positions and the positions on the spherical surface. The sphericity of the screen surface was confirmed, and the finishing of the screen surface was adjusted so that each measurement point on the screen surface was located on the spherical surface. In order to improve the sphericity of the screen surface with this construction method, it is conceivable to narrow the interval between measurement points. However, in order to measure the three-dimensional position with theodolite, mark the measurement point position on the screen surface. It is necessary to carry out the complicated collimation work of adjusting the theodolite direction according to the mark attached to the measurement point position, but if the interval between the measurement points is narrowed, the number of measurement points is greatly increased. The number of measurement points increases (for example, if the interval is halved, the number of measurement points increases four times), and it takes a lot of time for measurement, which is not realistic.

  In relation to the above, Patent Document 1 discloses that a pulse signal from a transmission unit is irradiated on a mirror surface to be measured (for example, an antenna), a pulse signal reflected from the mirror surface to be measured is received by a reception unit, and transmission / reception of pulse signals is performed. A technique for measuring the accuracy of the mirror surface of the surface to be measured is disclosed by repeating counting the clock pulses in between while performing spherical scanning on the surface of the mirror to be measured.

  Further, Patent Document 2 discloses a surface shape measuring apparatus configured to perform measurement of an aspheric surface by a fringe scanning shearing interference method and perform measurement of a plane / spherical surface by a fringe scanning Twiman Green type interference measurement method. It is disclosed.

In Patent Document 3, a light beam from a light source is irradiated onto a test surface via a point light source forming unit, and a measurement light beam reflected by the test surface and passed through the point light source forming unit is converted into a wavefront having a predetermined shape. In an interferometer that measures the surface shape of the test surface based on the state of interference fringes, a measurement for measuring the distance between the point light source forming means and the vertex of the test surface is performed. A configuration provided with long means is disclosed.
JP 61-230013 A JP 60-222704 A JP 2000-88548 A

  As described above, construction work is performed on the screen surface of the curved screen so that the screen surface matches the spherical surface. On the other hand, in the techniques described in Patent Documents 1 to 3, the shape of the curved surface can be measured with high accuracy, but in the construction work described above, how the curved surface is specifically determined from the result of measuring the shape of the curved surface. It is not easy to know whether the curved surface can be matched with a spherical surface if it is finished, and even if the above technique is applied, it takes time to finish the curved surface so that it matches the spherical surface. There was a problem that it was difficult to finish accurately.

  The present invention has been made in consideration of the above facts, and even when construction work is performed so that the curved surface matches a spherical surface, the sphericity of the curved surface can be determined so that the construction work can be easily performed. A first object is to obtain a sphericity determination method.

  The second object of the present invention is to obtain a method for constructing a curved screen that can easily realize finishing so that the curved screen matches a spherical surface.

  A plane (tangential plane) that is in contact with the spherical surface at the point P on the spherical surface is orthogonal to the straight line OP that connects the center O of the spherical surface and the point P, regardless of the position of the point P on the spherical surface. The normal line (a straight line perpendicular to the tangent plane) coincides with the straight line OP. On the other hand, the normal of the curved surface at the point P ′ on the curved surface of the aspherical surface (that is, the normal of the tangent plane that touches the curved surface at the point P ′) does not necessarily coincide with the straight line OP ′, and the position of the point P ′ with respect to the spherical surface An angle deviation from the straight line OP ′ is generated according to the inclination of the curved surface at. When the inventors of the present application obtain the magnitude and direction of the angle deviation of the normal of the curved surface at a certain position on the curved surface, the direction in which the tangent plane that touches the curved surface at the position is inclined, that is, We have come up with the idea that it is possible to grasp how much the curved surface is tilted in which direction and its position. If the inventors of the present application can grasp how much the curved surface is inclined in which direction at the measurement point positions set around the curved surface and the periphery thereof, even when performing construction work to finish the curved surface to coincide with the spherical surface. The present invention has been accomplished by conceiving that the curved surface can be easily finished so as to coincide with the spherical surface.

  Based on the above, the sphericity determination method according to the first aspect of the present invention measures the three-dimensional coordinates of the measurement points set on the determination target curved surface with respect to the determination target curved surface to be finished into a predetermined spherical surface. , Irradiating the measurement point with a light beam to measure the reflection direction, and based on the measured three-dimensional coordinates and the reflection direction, the measurement with respect to the direction of the first straight line connecting the center of the predetermined spherical surface and the measurement point The determination of the magnitude and direction of the angle deviation of the normal of the curved surface to be judged at a point position is performed for each of the plurality of measurement points set on the curved surface to be judged at an arbitrary interval. Determine the sphericity of the curved surface.

  In the first aspect of the invention, a plurality of measurement points are set at arbitrary intervals on the curved surface to be determined to be finished to a predetermined spherical surface, and for each measurement point, for example, three-dimensional coordinates are measured using a theodolite or the like. Measure the reflection direction by irradiating a light beam (for example, a laser beam), and based on the measured three-dimensional coordinates and the reflection direction, the measurement point position with respect to the direction of the first straight line connecting the center of the predetermined spherical surface and the measurement point The sphericity of the curved surface to be determined is determined by obtaining the magnitude and direction of the angle deviation of the normal line of the curved surface to be determined in each of the measurement points. It is possible to grasp how much the curved surface to be judged is inclined at the position and its periphery.

  As a result, even when construction work is performed so that the determination target curved surface matches the spherical surface, in order to make the determination target curved surface coincide with the spherical surface, the determination target curved surface is positioned at and around each measurement point position. The operator performing the construction work can easily and accurately recognize how much correction is required in which direction. Therefore, according to the first aspect of the present invention, the sphericity of the curved surface is determined so that the construction work can be easily performed even when the construction work is finished so that the curved surface to be judged matches the spherical surface. be able to. In addition, by using the magnitude and direction of the angular deviation of the normal of the curved surface to be judged, the curved surface to be judged can be matched with the spherical surface more accurately than when only the three-dimensional coordinates of the measurement points are used. Can be realized without increasing the number of measurement points.

  In the first aspect of the invention, the light beam used for measuring the reflection direction is preferably visible light. Thereby, when measuring the three-dimensional coordinates of the measurement point using theodolite or the like, the light spot formed on the determination target curved surface by irradiating the measurement point on the determination target curved surface with 3 It can be used as a reference (mark) for collimation work for measurement of dimensional coordinates, and work such as marking a measurement point becomes unnecessary.

  In the first aspect of the present invention, the measurement of the reflection direction by irradiating the measurement point with the light beam means that, for example, the reflection surface is a tangent plane of the curved surface to be determined at the measurement point. A plane mirror is arranged at the measurement point so as to be parallel to the light source, a light source is arranged at the approximate center of a predetermined spherical surface, the light beam emitted from the light source is reflected by the plane mirror, and along the direction of the first straight line This can be realized by detecting the irradiation position of the reflected light beam on the detection surface whose position is substantially equal to the light emitting point of the light source. By arranging the light source at the approximate center of a predetermined spherical surface, the trajectory of the light beam reflected by the plane mirror arranged at the measurement point substantially coincides with the normal of the curved surface to be determined at the measurement point position. The magnitude and direction of the angle deviation of the normal line of the curved surface to be determined at the measurement point position can be easily obtained from the irradiation position of the reflected light beam on the detection surface.

  Further, in the invention described in claim 2, for example, as described in claim 3, the flat mirror has a circular outer shape, and the peripheral portion is arranged so as to be in contact with the curved surface to be determined over the entire circumference. The reflecting surface is preferably arranged so as to be parallel to the tangential plane. Thereby, it can be realized very simply that the reflecting surface of the plane mirror is arranged in parallel with the tangential plane.

In addition, in the invention described in claim 2, the magnitude and direction of the angle deviation of the normal line of the curved surface to be determined can be obtained by, for example, irradiating the reflected light beam on the detection surface as described in claim 4. The distance between the position and the light emitting point of the light source is E1, the distance between the center of the predetermined spherical surface obtained from the three-dimensional coordinates of the measuring point and the measuring point is R, the thickness of the plane mirror is D1, the center of the predetermined spherical surface and the light source When the distance from the light emitting point is D2, the magnitude of the angle deviation Δθ of the normal of the curved surface to be determined is
Δθ = [sin ⁻¹ (E1 ÷ (R−D1−D2))] ÷ 2
And calculating the direction of the second straight line connecting the irradiation position and the light emitting point as the direction of the angle deviation Δθ.

  The method for constructing a curved screen according to the invention described in claim 5 is a method for constructing a curved screen for finishing a screen surface having a surface layer made of a predetermined material as the uppermost layer so as to coincide with a predetermined spherical surface. The screen surface is the curved surface to be determined, and the sphericity determination method according to any one of claims 1 to 4 is applied, so that a plurality of measurement points set on the screen surface are measured. The three-dimensional coordinates and the magnitude and direction of the angle deviation of the normal of the screen surface at each measurement point position with respect to the direction of the first straight line are respectively obtained, Each screen surface is measured by applying the predetermined material or grinding the surface layer at and around each measurement point position based on the magnitude and direction of the angle deviation of the surface normal. After finishing so as to coincide with the predetermined spherical surface at the position and its periphery, in accordance with the position of each measurement point on the screen surface and the curvature at the periphery thereof, in the range corresponding to the measurement point on the screen surface. On the other hand, by applying the predetermined material or grinding the surface layer, a corresponding range between the measurement points is finished to coincide with the predetermined spherical surface.

  According to the fifth aspect of the present invention, in finishing the screen surface having the surface layer made of the predetermined material as the uppermost layer so as to coincide with the predetermined spherical surface, the sphericity determination method according to the present invention is applied. Then, the three-dimensional coordinates at each measurement point set on the screen surface and the magnitude and direction of the angle deviation of the normal of the screen surface at each measurement point position with respect to the direction of the first straight line are obtained, respectively. Based on the three-dimensional coordinates of each measurement point and the magnitude and direction of the angle deviation of the normal of the screen surface, by applying a predetermined material or grinding the surface layer at each measurement point position and its periphery, the screen surface Each measurement point position and its periphery are finished so as to coincide with a predetermined spherical surface.

  As described above, if the three-dimensional coordinates at each measurement point and the magnitude and direction of the normal deviation of the screen surface are known, each measurement point position and Since it is possible to easily and accurately recognize how much and in what direction the curved surface to be judged should be corrected in the periphery, by applying a predetermined material or grinding a surface layer at each measurement point position and its periphery, It is possible to easily finish the screen surface at each measurement point position and its periphery so as to exactly match a predetermined spherical surface.

  According to the invention described in claim 5, according to the position of each measurement point on the screen surface and the curvature at the periphery thereof, the application of a predetermined material or the surface layer is applied to the range corresponding to the area between the measurement points on the screen surface. By performing grinding, a range corresponding to each measurement point is finished so as to coincide with a predetermined spherical surface. At this time, since the screen surface is exactly coincident with a predetermined spherical surface at each measurement point position and its periphery, by following the curvature at each measurement point position and its periphery, between each measurement point on the screen surface. It is possible to easily finish the corresponding range so as to exactly match a predetermined spherical surface. Therefore, according to the fifth aspect of the present invention, it is possible to easily realize finishing so that the curved screen matches the spherical surface.

  As described above, the present invention measures three-dimensional coordinates and measures the reflection direction by irradiating a light beam at each measurement point set on a curved surface to be determined at an arbitrary interval. Based on the reflection direction, the magnitude and direction of the angle deviation of the normal line of the curved surface to be determined at the measurement point position with respect to the direction of the first straight line connecting the center of the predetermined spherical surface and the measurement point are respectively determined. Therefore, even when construction work is performed so that the curved surface matches the spherical surface, the sphericity of the curved surface can be determined so that the construction work can be easily performed.

  In addition, the present invention applies the sphericity determination method according to the present invention, so that a plurality of three-dimensional coordinates and screens at each measurement point set on a screen surface on which a surface layer made of a predetermined material is formed as the uppermost layer. Determine the magnitude and direction of the angle deviation of the normal of the surface, and determine the measurement point position and its surroundings based on the three-dimensional coordinates of each measured point and the magnitude and direction of the angle deviation of the normal of the screen surface. After finishing the screen surface so that it coincides with a predetermined spherical surface at each measurement point position and its periphery by applying the material or grinding the surface layer, the curvature at each measurement point position and its periphery on the screen surface is adjusted. Then, by applying a predetermined material or grinding the surface layer to a range corresponding to each measurement point on the screen surface, the corresponding range between each measurement point matches a predetermined spherical surface. To finish Can be easily realized that the finish so curved screen matches the spherical surface, has an excellent effect that.

  Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 shows a curved screen 10 that can be used as a screen of a wide viewing angle visual simulator.

  Although not shown, the wide viewing angle visual simulator includes a plurality of projection apparatuses (for example, liquid crystal projectors), a blending unit to which these projection apparatuses are connected, and an image processing apparatus connected to the blending unit. It is configured to include. The image processing apparatus stores image data of a reference image that is a basis of an image (simulation image) to be projected on the screen surface of the curved screen 10 (inner wall surface of the curved screen), and performs predetermined image processing on the image data. And output to the blending unit. The blending unit converts the image data input from the image processing device into image data for each projection device (image data to be synthesized on the curved screen 10), and then outputs the image data to each projection device. As a result, an image obtained by synthesizing images from a plurality of projection devices is projected onto the curved screen 10, and a simulation with a high visual presence is provided over a relatively wide range of the screen surface of the curved screen 10. An image can be displayed.

  The curved screen 10 has a shape in which a lower part of a true sphere is removed, and includes a substantially spherical inner wall surface used as a screen surface. The curved screen 10 includes a base portion 10A and a surface layer 10B. The base portion 10A is divided into a plurality of curved parts for easy transportation and assembly. The curved screen 10 is transported to the installation location in a state of being divided into a plurality of curved parts, and the base part 10A is assembled by connecting the transported curved parts to each other. When the base portion 10A is assembled, a surface layer 10B is formed by applying a predetermined material to the inner peripheral surface of the base portion 10A, and then the screen surface of the curved screen 10 (the curved surface to be judged according to the present invention). Spherical finishing construction work is performed to finish so as to match a predetermined spherical surface (for example, the surface of a true sphere having a radius of about 5 to 10 m).

  Next, a laser theodolite used for measuring and determining the sphericity of the screen surface of the curved screen 10 in carrying out the spherical finishing work will be described. As shown in FIG. 2, the laser theodolite 12 includes a laser unit 14 that emits a visible laser beam. The laser unit 14 is pivotally supported on the support plate 16 via a rotation shaft 18 spanned between a pair of support plates 16 arranged substantially in parallel. It can be rotated in the direction of arrow A. The pair of support plates 16 are attached to the turning base 20, and the turning base 20 is supported by the base member 22 so as to be rotatable about an axis perpendicular to the longitudinal direction of the turning shaft 18 (in the direction of arrow B in FIG. 2). ing.

  When measuring and determining the sphericity of the screen surface, the laser theodolite 12 is arranged at a position corresponding to the center of a predetermined spherical surface (position C shown in FIG. 1) so that the base member 22 is substantially horizontal. Therefore, the laser beam emitted from the laser theodolite 12 changes the horizontal angle in the emission direction by rotating the swivel base 20 in the direction of arrow B in FIG. By rotating in the A direction, the vertical angle in the injection direction changes. When measuring / determining the sphericity of the screen surface, a predetermined measurement point on the screen surface is located at a position (position D shown in FIG. 1) separated by a predetermined distance across the center of the predetermined spherical surface. Theodolites (not shown) for measuring three-dimensional coordinates are respectively arranged.

  A circular light receiving plate 24 is attached to the tip of the laser unit 14 (near the light emitting point). The measurement / determination of the sphericity by the laser theodolite 12 is performed by arranging the plane mirror 26 shown in FIG. 4 at a predetermined measurement point position on the screen surface, emitting a laser beam toward the plane mirror 26, and reflecting by the plane mirror 26. This is done by reading the irradiation position of the laser beam on the light receiving plate 24 and determining the reflection angle of the laser beam. As shown in FIG. 3, the light receiving plate 24 has a concentric scale for reading a distance E 1 between the center of the light receiving plate 24 and the irradiation position of the laser beam on the light receiving plate 24, and the center of the light receiving plate 24. A radial scale for reading the angle ψ of the irradiation position of the laser beam on the light receiving plate 24 is recorded. Note that the plane mirror 26 according to the present embodiment has a cylindrical shape (for example, about 3 cm in diameter), a reflection surface is formed on the upper surface 26A, and the periphery of the bottom surface 26B is disposed so as to be in contact with the screen surface over the entire circumference.

  Next, as an operation of the present embodiment, the spherical finishing work according to the present embodiment will be described with reference to the flowchart of FIG. As described above, this spherical finishing work is performed in a state where the laser theodolite 12 is arranged at the position C shown in FIG. 1 and the theodolite is arranged at the position D shown in FIG.

  In the spherical finishing construction work, first, a measurement point to be measured is selected from a plurality of measurement points set on the screen surface of the curved screen 10, and the laser beam emitted from the laser theodolite 12 is applied to the screen surface of the curved screen 10. The laser unit 14 of the laser theodolite 12 is rotated in the direction of arrow A in FIG. 2 to adjust the vertical angle of the laser beam emission direction and the laser theodolite 12 is rotated so that the measurement point position of the measurement target is irradiated. A collimation operation for adjusting the horizontal angle in the laser beam emission direction by rotating the base 20 in the direction of arrow B in FIG. 2 is performed (step 100). In this embodiment, the measurement points are set on the screen surface so that the interval between the individual measurement points is about 1 m. When the radius of the predetermined spherical surface is about 5 to 10 m, the number of measurement points is about 100 to several hundreds.

  When collimation work of the laser theodolite 12 is completed, the laser theodolite 12 is turned on and a laser beam is emitted from the laser unit 14 (step 102). Thereby, a light spot is formed at the measurement point position of the measurement target on the screen surface. Next, using this light spot as a reference, collimation work is performed to adjust the horizontal angle and the vertical angle so that the two theodolites arranged respectively at the position D shown in FIG. (Step 104). As described above, by forming a light spot at the measurement point position of the measurement target by the laser beam emitted from the laser theodolite 12, a work for attaching a mark or the like to the measurement point position of the measurement target when collimating the theodolite There is no need to do.

  When the collimation work for the theodolite is completed, the horizontal and vertical angles of each theodolite after the collimation work are read, and the 3D coordinates of the measurement point to be measured are calculated based on the read horizontal and vertical angles. Derived by (three-point survey) (step 106). In addition, if the theodolite provided with the function which measures distance is used, it is also possible to measure the three-dimensional coordinate of the measurement point of a measuring object with a single theodolite.

  Next, the angle deviation of the normal of the screen surface at the measurement point position to be measured is measured. That is, first, the plane mirror 26 is arranged at the measurement point position of the measurement target on the screen surface (step 108). This can be performed, for example, by the operator holding the plane mirror 26 and pressing the bottom surface 26B of the plane mirror 26 against the screen surface so that the periphery of the bottom surface 26B of the plane mirror 26 is in contact with the screen surface over the entire circumference. . Thereby, the reflection surface (upper surface) 26A of the plane mirror 26 is substantially parallel to a virtual tangent plane that is in contact with the screen surface at the measurement point position to be measured. Next, the laser theodolite 12 is turned on (step 110).

  Since collimation work on the laser theodolite 12 has already been completed, the laser beam emitted from the laser theodolite 12 is emitted along a first straight line connecting the center of a predetermined spherical surface and the measurement point. Then, the light is reflected at the approximate center of the reflection surface (upper surface) 26A of the plane mirror 26 located at the measurement point position to be measured. Here, if the inclination of the screen surface with respect to a predetermined spherical surface is zero at the measurement point position to be measured, the laser beam incident on the plane mirror 26 is regularly reflected along the first straight line, and the laser theodolite 12 emits light. The incident angle of the laser beam reflected by the plane mirror 26 from the plane mirror 26 (the reflection angle of the laser beam) is actually a screen with respect to a predetermined spherical surface at the measurement point position to be measured. The laser beam reflected by the plane mirror 26 is incident on the light receiving plate 24 of the laser theodolite 12 by changing according to the inclination of the surface and causing an angle deviation in the reflection direction of the laser beam with respect to the direction of the first straight line. The

Subsequently, the irradiation position of the laser beam on the light receiving plate 24 (the position of the light spot formed by the laser beam irradiation) is confirmed, and based on the scale recorded on the light receiving plate 24, the center ( The distance E1 between the light emitting point of the laser unit 14 and the irradiation position of the laser beam on the light receiving plate 24 and the angle ψ of the irradiation position of the laser beam on the light receiving plate 24 with respect to the center of the light receiving plate 24 are visually read (step) 112). Then, as shown in FIG. 5, the distance R between the center of the predetermined spherical surface and the measurement point is calculated from the three-dimensional coordinates of the measurement point to be measured, the thickness of the plane mirror 26 is D1, the center of the predetermined spherical surface and the laser unit When the distance from the light emitting point 14 is D2, the angle deviation Δθ of the normal of the screen surface at the measurement point to be measured (the normal perpendicular to the virtual tangent plane that touches the screen surface at the measurement point of the measurement target) The size is calculated according to the following equation (1) (step 114). Further, the angle ψ is the direction of the angle deviation Δθ.
Δθ = [sin ⁻¹ (E1 ÷ (R−D1−D2))] ÷ 2 (1)
When the three-dimensional coordinates of the measurement point to be measured and the size and direction of the angle deviation Δθ of the screen surface at the measurement point position are obtained as described above, the difference between the distance R and the radius of the predetermined spherical surface is within the allowable range. And whether or not the size of the angle deviation Δθ is within an allowable range, thereby determining whether or not the screen surface coincides with a predetermined spherical surface at the measurement point position to be measured (step 116). ). If the determination is negative, based on the three-dimensional coordinates of the measurement point to be measured and the magnitude and direction of the angle deviation Δθ at the measurement point position, the measurement target is measured for the worker who performs the spherical finishing work. A spherical finishing work is instructed at the point and its surroundings (step 118), and the spherical finishing work is performed by the operator according to the instruction (step 120).

  Specifically, for example, when the distance R is smaller than the radius of a predetermined spherical surface and the difference exceeds the allowable range, the screen surface is closer to the front side than the predetermined spherical surface at the measurement point position to be measured. To the operator. In the present embodiment, a material that can be easily ground by application or sander is used as a material for forming the surface layer 10B of the curved screen 10, and the screen surface is predetermined at the measurement point position of the measurement target as described above. If the operator is positioned on the near side of the spherical surface, the operator grounds the measurement point position of the measurement target and the surrounding surface layer 10B with a sander or the like, so that the three-dimensional coordinates (distance of the measurement target measurement point) An operation of matching R) with a predetermined spherical surface is performed. Further, for example, when the distance R is larger than the radius of the predetermined spherical surface and the difference exceeds the allowable range, the screen surface is located on the back side of the predetermined spherical surface at the measurement point position to be measured. Communicate to the workers. In this case, the operator applies a predetermined material to the measurement point position of the measurement target and the surrounding surface layer 10B so that the three-dimensional coordinates (distance R) of the measurement point of the measurement target coincide with the predetermined spherical surface. Do work.

  Further, for example, when the magnitude of the angle deviation Δθ of the screen surface at the measurement point position of the measurement object exceeds the allowable range, the screen surface is inclined with respect to a predetermined spherical surface at the measurement point position of the measurement object. This is transmitted to the operator together with the direction of inclination (direction of angle deviation Δθ). In this case, according to the direction of the inclination of the screen surface, the operator grinds the measurement point position of the measurement target and the surrounding surface layer 10B or applies a predetermined material, thereby measuring the measurement point of the measurement target and the periphery thereof. An operation is performed to match the sphere with a predetermined spherical surface.

  Thus, in this embodiment, in addition to the three-dimensional coordinates of the measurement point on the screen surface, the magnitude and direction of the angle deviation of the normal of the screen surface at the measurement point position are measured. Even when the screen is tilted, the operator can easily and accurately recognize in which direction and how much the screen surface is tilted. Further, since the surface layer 10B of the curved screen 10 is roughly finished in advance so that the curvature becomes substantially constant, the magnitude and direction of the normal deviation of the screen surface at the measurement point position are measured. By doing so, it is possible to grasp how much the screen surface is tilted in which direction and over a relatively wide range of the measurement point position and its surroundings, and match the relatively wide range of the screen surface to a predetermined spherical surface. Can be made.

  When the spherical finishing work is performed by the operator, the measurement of the three-dimensional coordinates of the measurement point to be measured and the measurement of the magnitude and direction of the angle deviation of the normal of the screen surface at the measurement point position are performed again. Performed (Step 100 to Step 114). If it is determined that the screen surface does not coincide with the predetermined spherical surface at the measurement point position to be measured as a result of measuring the three-dimensional coordinates and the magnitude and direction of the angular deviation again, the spherical finishing work described above is performed again. If it is determined that the screen surface coincides with a predetermined spherical surface at the measurement point position to be measured (the difference is within the allowable range) (if the determination in step 116 is affirmative), It is determined whether or not spherical finishing construction work has been performed on all the measurement points set in (Step 122). When the determination is negative, the above-described work (step 100 to step 120) is repeated for the measurement points for which the spherical finishing work is not performed. As a result, the screen surface coincides with a predetermined spherical surface at all measurement points set on the screen surface and the periphery thereof.

  When the spherical finishing work for each measurement point and its surroundings is completed (when the determination in step 122 is affirmative), the operator uses the measurement points on the screen surface and their surroundings as a reference, and screens at the measurement points and their surroundings. Following the curvature of the surface, a spherical finishing work is performed to finish so that the corresponding range between the measurement points on the screen surface has the same curvature (step 124). At this time, since the screen surface coincides with a predetermined spherical surface at and around each measurement point position, it is easy to finish the corresponding range between the measurement points on the screen surface so as to coincide with the predetermined spherical surface. Can be done. Thereby, it can finish so that the whole screen surface of the curved screen 10 may correspond to a predetermined spherical surface.

  In the above description, the mode in which the irradiation position of the laser beam on the light receiving plate 24 is visually read based on the scale recorded on the light receiving plate 24 has been described. However, the present invention is not limited to this. The irradiation position of the laser beam on the light receiving plate 24 may be automatically detected by arranging light receiving elements for detecting the laser beam in two dimensions.

It is the schematic which shows arrangement | positioning of a curved screen and theodolite. (A) is a schematic diagram of a laser theodolite, and (B) is an explanatory diagram for explaining reading of a light spot irradiation position on a light receiving plate. It is a top view which shows an example of a light-receiving plate. It is a perspective view which shows an example of a plane mirror. It is explanatory drawing explaining the measurement of the angle deviation of the normal line by a laser theodolite. It is a flowchart which shows the procedure of spherical surface finishing construction work.

Explanation of symbols

10 curved screen 10B surface layer 12 laser theodolite 14 laser unit 24 light receiving plate 26 plane mirror

Claims (5)

  Measure the three-dimensional coordinates of the measurement point set on the determination target curved surface to be finished to a predetermined spherical surface, and measure the reflection direction by irradiating the measurement point with a light beam. Based on the three-dimensional coordinates and the reflection direction, the magnitude of the angle deviation of the normal line of the curved surface to be determined at the measurement point position with respect to the direction of the first straight line connecting the center of the predetermined sphere and the measurement point; A sphericity determination method for determining the sphericity of a determination target curved surface by performing a direction determination for each of a plurality of measurement points set on the determination target curved surface at arbitrary intervals.   In the measurement of the reflection direction, a plane mirror is arranged at the measurement point so that the reflection surface is parallel to the tangent plane of the curved surface to be determined at the measurement point, and a light source is arranged at the approximate center of the predetermined spherical surface, The light beam emitted from the light source is reflected by the plane mirror, and the irradiation position of the reflected light beam on the detection surface where the position along the direction of the first straight line is substantially equal to the light emission point of the light source The sphericity determination method according to claim 1, wherein the sphericity determination method is performed by detecting.   The flat mirror has a circular outer shape, and is arranged so that a peripheral surface thereof is in contact with a curved surface to be determined over the entire circumference so that a reflection surface is parallel to the tangential plane. The sphericity determination method according to claim 2. The distance between the irradiation position of the reflected light beam on the detection surface and the light emission point of the light source is E1, the distance between the center of the predetermined spherical surface obtained from the three-dimensional coordinates of the measurement point and the measurement point is R, and the plane mirror The thickness of the predetermined spherical surface is D1, and the distance between the center of the predetermined spherical surface and the light emitting point of the light source is D2, and the magnitude of the angle deviation Δθ of the normal of the curved surface to be determined is
Δθ = [sin ⁻¹ (E1 ÷ (R−D1−D2))] ÷ 2
3. The sphericity determination method according to claim 2, further comprising: calculating a direction of a second straight line connecting the irradiation position and the light emitting point as a direction of the angle deviation Δθ. A method for constructing a curved screen for finishing a screen surface having a surface layer made of a predetermined material as a top layer so as to substantially match a predetermined spherical surface,
The screen surface is set as the curved surface to be determined, and the sphericity determination method according to any one of claims 1 to 4 is applied, so that a three-dimensional measurement point is set at a plurality of measurement points set on the screen surface. Obtain the coordinates and the magnitude and direction of the angle deviation of the normal of the screen surface at each measurement point position with respect to the direction of the first straight line,
Based on the three-dimensional coordinates of each measurement point on the screen surface and the magnitude and direction of the angle deviation of the normal of the screen surface, the predetermined material is applied or the surface layer is ground at and around each measurement point position. After finishing the screen surface to match the predetermined spherical surface at each measurement point position and its periphery,
By applying the predetermined material or grinding the surface layer to a range corresponding to each measurement point position on the screen surface in accordance with the curvature at each measurement point position on the screen surface and the periphery thereof. A method for constructing a curved screen, wherein a range corresponding to each of the measurement points is finished so as to coincide with the predetermined spherical surface.

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