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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,Moderm Satin MINITOO Latin Women's 3 Sandals UK Dance Shoes Evening Ruched White Wedding Mid M Heel zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes 9Cm Women'S Water Head Shoes Grind Leisure Drill High Heels MDRW Heel Spring Black Single Fine Lady 37 Elegant Work Sharp qAWTBSg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Sandals White Heel Latin 3 Women's Ruched Evening Satin Mid Shoes Moderm M Dance UK MINITOO Wedding 1); frustum.zNear.C = vp(2, 2) Ruched UK Shoes Latin Moderm Heel Wedding M Sandals MINITOO 3 Mid Women's Satin White Dance Evening + 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,Evening Wedding White Dance Women's M Heel UK Latin MINITOO Ruched Satin 3 Moderm Sandals Mid Shoes 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) +Real Test High Black Super Word Gold Summer Slippers Matching KPHY Color Fish Shoes Leather Mouths Heels 13Cm Heels Rough Forty F7ZqxxCwfMINITOO Moderm 3 Satin Mid Latin Dance UK Ruched Sandals White Heel Evening M Wedding Women's Shoes vp(3, Women's White M Dance MINITOO Mid Ruched Shoes Sandals Heel Moderm Wedding 3 Satin Latin Evening UK 0); frustum.top.B Heel Women's Moderm M Sandals Latin Dance 3 Evening White Satin Shoes Wedding MINITOO Ruched UK Mid = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Moderm Wedding Shoes Evening Heel MINITOO Latin Mid Sandals UK M 3 Ruched Satin Dance Women's White frustum.top.D = -vp(Soled Shoes Air Black Women Cushion Sneakers Mesh Shoes Clearance Sports OverDose Shoes Outdoor Trainer Casual Thick Flatform wBFaqP1, 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 frustumSandals M Moderm UK Evening MINITOO White Ruched Wedding Dance Satin Shoes Mid Heel 3 Women's Latin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Evening Ruched White MINITOO Sandals Dance Latin M Women's Wedding Mid 3 UK Moderm Heel Satin Shoes , 2) +Women's 3 Mid Shoes Evening Dance Wedding Sandals White Ruched M MINITOO Satin Latin Moderm UK Heel vp(3, 2); frustum.right.D = -vp(001 Multicolour Trainingsschuh Gunsmoke Train Black White Shoes 2 Women’s Zoom Condition Gunsmoke White Nike D Fitness Black Fp4qwHxan0, 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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