Resolution-independent surface rendering using programmable graphics hardware

A method of drawing a section of a surface, the surface defined within a tetrahedron by quadric Bézier weights, the method comprising:

• determining a quadric coefficient matrix describing the surface within the tetrahedron;
• determining vertices of a triangle which constitutes a side of the tetrahedron and which covers, at least in part, the section of the surface;
• interpolating values based on the vertices, the quadric coefficient matrix, and the tetrahedron;
• and
• drawing pixels within the section using the interpolated values.

One or more computer-readable media containing machine-executable instructions which describe a method for rendering an image containing a view of a quadric surface, the quadric surface being described by one or more Bézier tetrahedra and each of the one or more Bézier tetrahedra being composed of four triangles, the method comprising:

• for each of one or more of the triangles, choosing a series of points in the triangle;
• for each point chosen, the point lying in a viewing triangle:
• extending a ray through the point;
• computing an intersection point on the surface which is located at an intersection of the ray extended through the intersection point with the surface;
• determining if the intersection point on the surface is inside the tetrahedron containing the viewing triangle;
• computing a surface normal at the intersection to use in a lighting evaluation;
• and
• performing the lighting evaluation based on the surface normal;
• and producing the image.