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  Projecting 3D Points
  Submitted by



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

Download Associated File: glproject.txt (1,527 bytes)

/*

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); }

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