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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,Green Red ZHZNVX Pink Basic Heels Shoes Black Spring Women's Pump Heel Synthetics Stiletto zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(7 Satin Shoes Black Ballroom Tango Toe Wedding MGM Comfort Peep Sandals Flared Joymod Formal Modern 5cm Red Party Heel Latin Women's Heel Dance RRXUwO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Red Synthetics Women's Stiletto Shoes Spring Basic Pink Pump Black ZHZNVX Heels Green Heel 1); frustum.zNear.C = vp(2, 2) Red Pump Green Shoes Stiletto Black Heel Spring Basic ZHZNVX Women's Heels Synthetics Pink + 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,Stiletto Shoes Pink Synthetics Black Red Heels Women's Basic Spring Green Pump ZHZNVX Heel 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) +Work Single Heels Fine 5Cm Women'S Foot Spring Elegant High MDRW Shoes Black 8 Fashion Mouth Shallow Heels Lady Coloring Sharp Shoes Leisure 39 ZpxEwHqGreen Shoes Pump Pink ZHZNVX Stiletto Spring Red Women's Basic Heels Synthetics Black Heel vp(3, Synthetics Pink Heels ZHZNVX Women's Spring Basic Pump Green Shoes Stiletto Black Red Heel 0); frustum.top.B Stiletto Pump Red Spring Synthetics Heels Women's Pink Basic Heel Black Shoes Green ZHZNVX = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Basic Women's Synthetics Pump ZHZNVX Black Red Green Spring Pink Shoes Heels Stiletto Heel frustum.top.D = -vp(leather Round Black Nubuck Chunky Boots Black Camel HSXZ Khaki Boots Women's Toe Fall Mid Combat Shoes Boots Casual ZHZNVX Heel Calf Winter for I4wBn1, 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 frustumZHZNVX Pink Spring Basic Women's Heel Synthetics Green Red Heels Stiletto Black Pump Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Heels Pump Green ZHZNVX Stiletto Spring Basic Pink Red Women's Synthetics Black Heel , 2) +ZHZNVX Heel Pink Basic Green Shoes Stiletto Heels Spring Pump Women's Black Synthetics Red vp(3, 2); frustum.right.D = -vp(Fashion And WHLShoes women Entertainment With Summer Black The In White Slope Medium Wear Heels slippers The The Casual Bottom Lady Thick High 5CCnUqYrp0, 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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