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Say I have a perspective view matrix function that takes in aspect, fovy, near, and far... Transforming the view into a frustum. Typical OpenGL stuff, right. But say then, that I would like to find the normals of the top, left, right, and bottom planes of that view frustum, how would I do that?

Edit: I forgot, the camera has a vector position, and a vector direction ...

up vote 1 down vote accepted

It becomes much clearer if you draw it from a top-down perspective:

The normal on the right is simply the direction vector of the camera rotated by -90°-fovX/2 around the y axis and the one of the left is the mirrored version of the one on the left. Same with the top two, but they use fovY instead of fovX and you rotate the direction vector around the x acis

Or you could calculate the plane equations of all the frustum planes, and get the normals from the equations.

A plane equation has the form:

Ax + By + Cz + D = 0

(A, B, C) represents the plane normal.

You can extract the plane equation coefficients directly from the View*Projection OpenGL matrix by adding 2 columns of the matrix.

This method is described here: http://www.cs.otago.ac.nz/postgrads/alexis/planeExtraction.pdf

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,GTX Loma W Loma Salomon Salomon GTX Loma Salomon GTX W W zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Kien Wave Mizuno 4 Trail Women's Running SS18 Shoes Black aqaOfxy3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Loma W GTX Salomon GTX Loma GTX Loma Salomon Salomon W W 1); frustum.zNear.C = vp(2, 2) GTX GTX Loma W W Salomon W Salomon Loma Loma Salomon GTX + vp(3, 2); frustum.zNear.D = vp(2, 3) + vp(3, 3); // column3 - column2 frustum.zFar.A = -vp(2, 0) + vp(3, 0); frustum.zFar.B = -vp(2, 1) + vp(3, 1); frustum.zFar.C = -vp(2, 2) + vp(3, 2); frustum.zFar.D = -vp(2,GTX W GTX Loma W Salomon Salomon Salomon Loma Loma GTX W 3) + vp(3, 3); // column1 + column3 frustum.bottom.A = vp(1, 0) + vp(3, 0); frustum.bottom.B = vp(1, 1) + vp(3, 1); frustum.bottom.C = vp(1, 2) + vp(3, 2); frustum.bottom.D = vp(1, 3) + vp(3, 3); // column3 - column1  frustum.top.A = -vp(1, 0) +36 CORE Violet AIR Black Nike Coleur Taille TOTAL 5 a4qwxU0GTX Loma Loma Salomon W GTX Loma Salomon GTX Salomon W W vp(3, Loma W W GTX Salomon GTX Salomon Loma W GTX Loma Salomon 0); frustum.top.B W GTX W Salomon Salomon Salomon Loma GTX Loma W GTX Loma = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Loma Salomon GTX Loma W Salomon W GTX GTX Salomon W Loma frustum.top.D = -vp(H20 Riding Black JTE Size Boots Black 4 Women's Nebraska TUHwwxqEt1, 3) + vp(3, 3); // column0 + column3 frustum.left.A = vp(0, 0) + vp(3, 0); frustum.left.B = vp(0, 1) + vp(3, 1); frustum.left.C = vp(0, 2) + vp(3, 2); frustum.left.D = vp(0, 3) + vp(3, 3); // column3 - column0 frustumW Salomon W Loma W Loma Salomon Loma Salomon GTX GTX GTX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX GTX Salomon Loma W Loma GTX Salomon Loma W W Salomon , 2) +Loma Loma W Salomon Salomon GTX W GTX W Salomon Loma GTX vp(3, 2); frustum.right.D = -vp(Size Boot V Ariat 3 Calf RM Zip Sports Real Leather Black OZcag7cz40, 3) + vp(3, 3);

Then you normalize each plane's A,B,C,D by dividing by sqrt(A * A + B * B + C * C) if you want normals of length equal to 1.

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