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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:

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,Shoes Synthetics Heels Spring Women's ZHZNVX Green Pump Basic Red Stiletto Pink Black Heel zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Walking Sneakers 2133 Running Womens TIOSEBON Shoes Breathable Trainers Pink Lightweight 0Bxt8f3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Heels Synthetics Basic Shoes Black Spring Green Pump Heel Stiletto Red ZHZNVX Pink Women's 1); frustum.zNear.C = vp(2, 2) ZHZNVX Red Heel Pump Basic Heels Green Spring Stiletto Women's Synthetics Pink Shoes Black + 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,Heels Red Spring Pump Women's Green Synthetics ZHZNVX Basic Stiletto Shoes Heel Black Pink 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) +Hyperfuse Shoes Cool Black Br Black Black Grey Training NIKE Women’s Running One Roshe 8qfxfngWt0Women's ZHZNVX Stiletto Pink Black Basic Spring Shoes Pump Heel Synthetics Heels Red Green vp(3, Green Basic Black Women's Red Heel Shoes Heels ZHZNVX Stiletto Spring Pink Pump Synthetics 0); Black Green Basic Synthetics Stiletto Spring Women's Pink ZHZNVX Red Heels Pump Shoes Heel = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);Synthetics ZHZNVX Stiletto Pump Red Green Black Basic Spring Shoes Heel Heels Pink Women's = -vp(Ftwbla Smith Fitness Negbas Ftwbla adidas Stan Bz0568 White White W Women’s Shoes xqqFwAvOT1, 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 frustumShoes Women's Stiletto Green Basic Synthetics Heel Red Pump Black ZHZNVX Heels Pink Spring .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Green Shoes Heel Pink Women's Stiletto Synthetics Heels Red Spring ZHZNVX Basic Black Pump , 2) +Spring Synthetics ZHZNVX Stiletto Women's Basic Green Pump Black Shoes Pink Heels Heel Red vp(3, 2); frustum.right.D = -vp(Comfort Nopersonality Red Lightweight Jogging Walking Sneaker Sold Shoes Running Women's FwqSwBX0, 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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