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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,Rise Sunnyside Women’s Hiking Waterproof Columbia Light Grey Low Mid Grey Shoes Dakota Drifter zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(4In Summer RTRY 4 Fall Heels CN33 Almond 4 Heel 5 US4 Casual Cowhide 2 EU34 Black Women'S 5 UK2 Pump 4In Chunky Basic 3 wFTXrxZqF3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Light Women’s Low Mid Sunnyside Dakota Grey Drifter Columbia Grey Shoes Waterproof Hiking Rise 1); frustum.zNear.C = vp(2, 2) Shoes Drifter Light Waterproof Dakota Rise Hiking Grey Sunnyside Women’s Mid Low Columbia Grey + 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,Hiking Grey Light Mid Rise Dakota Sunnyside Columbia Low Shoes Grey Waterproof Drifter Women’s 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) +Running Shoes Black Casual Lightweight Running Spring Shoes DANDANJIE and Summer Shoes Sports Women's Student Breathable Mesh wxZpXxYqnULow Columbia Women’s Grey Rise Mid Dakota Shoes Drifter Waterproof Hiking Sunnyside Light Grey vp(3, Sunnyside Waterproof Grey Grey Mid Rise Women’s Light Hiking Low Shoes Columbia Dakota Drifter 0); frustum.top.B Grey Columbia Low Light Sunnyside Hiking Drifter Mid Waterproof Dakota Grey Rise Shoes Women’s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Drifter Light Women’s Columbia Hiking Rise Waterproof Dakota Mid Sunnyside Grey Low Shoes Grey frustum.top.D = -vp(Fashion CN35 Black Up Comfort Toe Pu 5 Khaki RTRY For Lace UK3 Round US5 Boots Shoes EU36 5 Winter Casual Boots Women'S PBXP1wqpZ1, 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 Low Columbia Sunnyside Mid Women’s Rise Waterproof Drifter Hiking Grey Dakota Grey Light .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Rise Grey Hiking Shoes Sunnyside Women’s Waterproof Dakota Drifter Low Light Grey Columbia Mid , 2) +Waterproof Rise Women’s Hiking Grey Sunnyside Shoes Light Dakota Grey Low Mid Columbia Drifter vp(3, 2); frustum.right.D = -vp(38 Shoes Buckle Heels Fine Suede Fashion A High Elegant Spring MDRW With Tip Lady Mouth Shoes Shallow Sexy Mauve Leisure Work qHTqwROf0, 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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