Method and system for evaluating derivatives in screen space using perspective corrected barycentric coordinates

A computer system capable of computing the level of detail (LOD) at a pixel in a triangle during texture mapping, the computer system comprising:

• a processor for issuing commands;
• a memory sub-system coupled to the processor for storing information including graphics data;
• and
• a graphics sub-system coupled to the processor and operations according to the commands from the processor, wherein the graphics sub-system is configured to determine screen coordinates of the pixel and derivatives of the texture coordinates at the vertices of the triangles;
• the graphics sub-system is also configured to evaluate derivatives of texture coordinates at the pixel with respect to screen space by interpolation of the derivatives of the texture coordinates at the vertices using barycentric coordinates of the pixel;
• and the graphics sub-system is further configured to computer the LOD at the pixel using the derivatives of the texture coordinates at the pixel, the LOD of the pixel being computed independent of texture coordinates of neighboring pixels;
• such that the LOD as computed is unbiased in any particular direction.

In a graphics computer system, a method for computing derivatives of a function with respect to screen space, the function capable of being interpolated in eye space by perspective corrected barycentric coordinates for a point in screen space, the method comprising the steps of:

• a) identifying coordinates of vertices of a triangle in screen space, the triangle including the point at which the derivatives are to be evaluated;
• b) determining barycentric coordinates of the point, the barycentric coordinates specifying a location of the point relative to the vertices of the triangle;
• c) generating perspective correction factors for the point based on the coordinates of the vertices;
• d) expressing the derivatives of the function in interpolated form using the perspective correction factors, the barycentric coordinates of the point and values of the derivatives at the vertices;
• and
• e) evaluating the derivatives at the point wherein the derivatives can be computed independently without relying on data from neighboring points.