TW200723160A - Mapping and drawing method for a tetrahedron - Google Patents

Abstract

This invention provides a drawing method for a tetrahedron mapping in which a tetrahedron map consisting of four equilateral triangles is used to calculate the relative positions of two dimensional planar image and three dimensional object. Each object in the three dimensional space is projected onto the two dimensional planar tetrahedron map from the center of the tetrahedron wherein the image and pattern may be reflected thereon with elements of color, transparency, and reflective material. The method of the invention comprises two major steps: first, generating a tetrahedron map, the tetrahedron being disposed on a local coordinates of the tetrahedron with a fixed angle, the rest of the angles may be located at any position on the coordinates, the tetrahedron being consisting of four equilateral triangles, each of which is rendered once from the center of the tetrahedron and the result being saved in a texture so as to obtain the tetrahedron map; second, corresponding data is retrieved to combine each corresponding observation matrix, projection matrix, and texture coordinates matrix to form a four-triangle complex matrix, the center of the tetrahedron corresponding to the center of the triangles to form four central vectors, the inner product of the apexes of the local coordinates and the four central vectors being calculated, from which the maximal reveals that the apexes is located at the maximal triangle; then the apical coordinate is multiplied by the corresponding triangle complex matrix so as to proceed with computational calculation to convert it into planar mapping coordinates and obtain the corresponding data of a three dimensional object from the planar mapping coordinates.