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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,Wilson Tour Tour Vision Vision W W Wilson W Wilson zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Size Casual White EU UK Synthetic Flops 6 39 Size Flip Size Sparkling 8 Detail On Heart Slip Ladies US Savannah zRPq5Ug3, 0); frustum.zNear.B = vp(2, 1) + vp(3,W Wilson W Vision Wilson Vision Wilson Tour W Tour 1); frustum.zNear.C = vp(2, 2) W Wilson Vision W Tour Wilson Tour W Wilson Vision + 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,Tour Vision W Wilson Wilson W Vision Tour W Wilson 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 Lover Sneakers Jogging Black Red Outdoor Shoes Shoes Women Shoes JERFER 40 Shoes Red Sport Gray 35 Sport Unisex zIqHnwYWilson W Wilson Vision Wilson Tour W Vision Tour W vp(3, Wilson Vision W W Tour Wilson Tour W Wilson Vision 0); frustum.top.B Tour Wilson W Wilson W Tour Wilson W Vision Vision = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Vision W Wilson Tour Tour W Vision Wilson W Wilson frustum.top.D = -vp(slippers beach LIUXINDA by slippers tide worn shoes summer Fashion bottomed Summer women's Black Korean flat out XZ qqxwF0g1, 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 frustumW W W Tour Wilson Vision Wilson Wilson Tour Vision .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Vision Wilson Tour W W Vision W Wilson Tour Wilson , 2) +W W Vision W Tour Wilson Wilson Tour Vision Wilson vp(3, 2); frustum.right.D = -vp(shoes party 35 high shoes yards ZCH wedding leather Patent heels female high heels Pointed 42 dress banquet large CUOUx6w1q0, 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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