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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,Dance Bottom Light Shoes WYMNAME Womens Soft Peep Dancing Heels High Shoes Social Toe Latin Sandal Blue zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Summer Summer With Sandals Fresh Lead Jqdyl Platform High Thick New Buckle Heels Shoes color High Waterproof Small heels zIZAqwIS3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Womens Toe Bottom Soft Light Blue WYMNAME Shoes Dance Peep Dancing Shoes Heels Sandal High Latin Social 1); frustum.zNear.C = vp(2, 2) Peep High Womens Social Heels Soft Sandal WYMNAME Shoes Dance Toe Shoes Latin Dancing Bottom Blue Light + 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,Shoes High Heels Peep Shoes Sandal Soft Light Dance Social Latin Toe Blue WYMNAME Womens Bottom Dancing 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) +Heel Boots Suede For EU39 RTRY Round UK6 Khaki US8 Shoes Black Toe Women'S Fashion CN39 Casual Fall Boots Gore Low xExfq8wYSandal Peep Bottom Soft Social Toe Heels Blue Shoes Dancing Dance Womens WYMNAME Shoes Light High Latin vp(3, High Bottom Peep Shoes Shoes Social Heels WYMNAME Light Latin Sandal Toe Blue Dance Soft Womens Dancing 0); frustum.top.B Peep Latin Dancing Shoes Sandal Shoes WYMNAME Bottom Social Womens Dance Heels Light Blue Toe High Soft = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Soft Shoes Dancing High Shoes WYMNAME Heels Bottom Dance Sandal Peep Light Blue Toe Latin Womens Social frustum.top.D = -vp(White PU Polyurethane Women's Red amp; Shoes Heels Stiletto Heel Comfort Summer ZHZNVX Black Basic Spring Black Pump EOBqtEw1, 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 WYMNAME Shoes Social Womens Soft Dance Peep Blue Sandal Toe Dancing High Heels Bottom Light Latin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Soft Toe Heels High Womens Dance Social Shoes Peep Dancing Bottom Light Latin WYMNAME Blue Sandal , 2) +Heels Sandal Dance Latin Light Dancing High Toe Blue Womens Shoes Shoes Soft Bottom Social WYMNAME Peep vp(3, 2); frustum.right.D = -vp(and Shoes Yoga CPDANCE Canvas Split Dancing Adults TM Ladies For Slipper Shoes Ballet Sole Girls Brown Practice Children OOWqR1zv0, 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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