Matrix transformations and gluLookAt in Cg

OpenGL has some nice helper functions for matrix manipulation: glTranslate, glRotate, and glScale.

GlRotate is especially involved, so I made a version in Cg (based on the matrix in the spec):

float4x4 getRotateMatrix(float theta, float3 axis) {
float x = axis.x, y = axis.y, z = axis.z, c = cos(theta), s = sin(theta);
float4x4 matrix = float4x4(
x*x*(1-c)+c, x*y*(1-c)-z*s, x*z*(1-c)+y*s, 0,
y*x*(1-c)+z*s, y*y*(1-c)+c, y*z*(1-c)-x*s, 0,
x*z*(1-c)-y*s, y*z*(1-c)+x*s, z*z*(1-c)+c, 0,
0, 0, 0, 1
);
return matrix;
}


Another especially useful function is gluLookAt, which lets you specify camera position and tell it to look at a specific point. I downloaded the Mesa3D code and made the following Cg function based on it:

float4x4 getLookAt(float3 eye, float3 center, float3 up) {
float3 forward = normalize(center - eye);
float3 side = normalize(cross(forward, up)); /* Side = forward x up */
up = cross(side, forward); /* Recompute up as: up = side x forward */

return float4x4(
side.x, up.x, -forward.x, -eye.x,
side.y, up.y, -forward.y, -eye.y,
side.z, up.z, -forward.z, -eye.z,
0, 0, 0, 1
);
}