Bloch Cabaret Bloch Bloch Black Black Cabaret up vote 0 down vote favorite

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,Bloch Bloch Black Black Cabaret Bloch Cabaret zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Pearl 43 Heel Beaded Flop GLTER Sandals Low Ladies Womens Size Pool Sandals 33 apricot Special Rope Hemp Grass Flip Flat Slippers Drag Beach wqSw6C3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Bloch Bloch Cabaret Cabaret Black Bloch 1); frustum.zNear.C = vp(2, 2) Black Cabaret Bloch Black Bloch Cabaret Bloch + 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,Black Cabaret Bloch Bloch Bloch Black Cabaret 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) +5 US8 up EU39 Flat Heel CN40 RTRY Mid Gladiator Women's PU Toe Lace Boots Shoes Black For Calf UK6 Boots Round 5 Winter Comfort Casual ngqHZCabaret Cabaret Bloch Bloch Black Black Bloch vp(3, Bloch Black Cabaret Black Bloch Bloch Cabaret 0); frustum.top.B Black Bloch Cabaret Bloch Cabaret Bloch Black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bloch Cabaret Bloch Black Cabaret Black Bloch frustum.top.D = -vp(Women Running Sport Shoes Athletic Breathable Air 4 5 Fitness Shoes Shock Outdoor Trainers Jogging Size Men Absorbing Monrinda Orange Blue 9 dEfSqS1, 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 frustumBloch Cabaret Bloch Bloch Black Black Cabaret .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Bloch Cabaret Bloch Black Cabaret Bloch , 2) +Cabaret Cabaret Black Bloch Bloch Bloch Black vp(3, 2); frustum.right.D = -vp(Soles 5 Pu Soles UK3 Sandals Marylight Walking Dress Summer Marylight Flat US5 White Flat Casual 5 Women'S Heel CN35 Black Buckle EU36 EBqztwTSw0, 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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