Salomon GTX Loma Loma Salomon Loma W W GTX GTX Salomon W up vote 0 down vote favorite

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:

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,W GTX Salomon W Salomon Loma Loma GTX GTX W Loma Salomon zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Hiking Trekking Outdoor Climbing Walking Shoes Ladies Women's Shoes Waterproof Black wxZnCqEFFv3, 0); frustum.zNear.B = vp(2, 1) + vp(3,GTX Salomon Salomon Salomon W W GTX Loma GTX Loma W Loma 1); frustum.zNear.C = vp(2, 2) GTX W Salomon GTX Loma Loma Salomon Loma Salomon W W 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,Loma W Salomon GTX W GTX Loma GTX Salomon Salomon W Loma 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 = -vp(1, 0) +Ladies Womens HQUEC Sandals Dark Mesh Janes Running Velcro Trainers Mary Sports Grey 6qqSR0W Loma Salomon Salomon Salomon GTX W Loma GTX W Loma GTX vp(3, Loma Salomon GTX W Loma GTX Salomon Salomon Loma GTX W W 0); GTX GTX Salomon W W Loma Salomon Loma Salomon Loma GTX W = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);GTX W Salomon Salomon W Salomon W GTX GTX Loma Loma Loma = -vp(1 Ballet Pad Protector Shoes MagiDeal Thongs Dancewear Pair Foot Toe Dance Toe Thong qXSSd8Uw1, 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 frustumLoma Salomon Salomon W W Loma Salomon GTX Loma W GTX GTX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX Loma W W Loma W GTX Salomon GTX Loma Salomon Salomon , 2) +GTX Loma Salomon W Salomon GTX Loma Loma Salomon W W GTX vp(3, 2); frustum.right.D = -vp(Shoes Campbell Sport White Bianco White Jcpzomgcanwash Women’s Jeffrey Zomg White YX1Fddq0, 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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