Patent ID: 7924278

Claim:
A computer-readable storage medium that does not consist of a signal, said computer-readable storage medium storing computer-executable instructions that, when executed by a computer, cause the computer to perform steps for generating a visual representation of a three-dimensional surface, the surface being described by reference to one or more polynomials bounded by one or more Bézier tetrahedra, the computer-executable instructions directed to steps comprising: defining a bounding Bézier tetrahedron as a set of coordinates and a symmetric weight tensor containing Bézier weights which define a shape of the surface within the bounding Bézier tetrahedron; projecting the bounding Bézier tetrahedron onto a planar screen space; dividing the projected bounding Bézier tetrahedron into triangles having three vertices; associating with each vertex of a triangle in the projected bounding Bézier tetrahedron a minimum and maximum height value as vertex attribute data; computing a partially collapsed symmetric tensor at each vertex of the triangle, the partially collapsed symmetric tensor having a lower rank than the symmetric weight tensor and representing a common factor in coefficients of a univariate polynomial bounded by the bounding Bézier tetrahedron; associating with each vertex of the triangle unique elements of the partially collapsed tensor as vertex attribute data to be interpolated when rasterizing the triangle; providing the vertices and vertex attribute data for interpolation across the triangle; reconstructing the partially collapsed symmetric tensor for a pixel within the triangle using the vertex attribute data; computing the coefficients of the univariate polynomial bounded by the bounding Bézier tetrahedron; and determining if the three-dimensional surface is visible at the pixel within the triangle in the projected bounding Bézier tetrahedron based on the computed coefficients of the univariate polynomial.