/*
It is occasionally necessary to project points from 3D to 2D in software. A
sample application is the rendering HUD effects like targeting boxes and
character names in a game. The following code transforms and projects a 3D
point or vector by the current OpenGL matrices and returns a 2D vector with
associated depth value. The 2D vector is in the screen coordinate frame, where
y increases from 0 at the top of the screen to height - 1 at the bottom and x
increases from 0 at the left to width - 1 at the right.
Morgan McGuire
matrix@graphics3d.com
*/
Vector3 glProject(const Vector4& v) {
// Get the matrices
double modelView[16];
double projection[16];
glGetDoublev(GL_MODELVIEW_MATRIX, modelView);
glGetDoublev(GL_PROJECTION_MATRIX, projection);
// Compose the matrices into a net row-major transformation
Vector4 transformation[4];
for (int r = 0; r < 4; ++r) {
for (int c = 0; c < 4; ++c) {
transformation[r][c] = 0;
for (int i = 0; i < 4; ++i) {
// OpenGL matrices are column major
transformation[r][c] += projection[r + i * 4] * modelView[i + c * 4];
}
}
}
// Transform the vertex
Vector4 result;
for (r = 0; r < 4; ++r) {
result[r] = transformation[r].dot(v);
}
// Homogeneous division
const double rhw = 1 / result.w;
return Vector3((result.x * rhw + 1) * width / 2,
(1 - result.y * rhw) * height / 2,
rhw);
} |