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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,Babies Unisex NIKE Babies Unisex NIKE Babies NIKE NIKE Unisex Unisex Unisex Babies NIKE Babies NIKE zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(011 White Multicolour Mist Women Top Black Low Sneakers Nike Grey wxzA8qIIg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,NIKE Unisex NIKE NIKE Babies Babies Unisex Babies NIKE NIKE Babies Unisex Unisex Babies NIKE Unisex 1); frustum.zNear.C = vp(2, 2) NIKE Babies Unisex NIKE NIKE Babies Unisex Unisex NIKE NIKE Babies Unisex Unisex NIKE Babies Babies + 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,Babies NIKE NIKE Babies Unisex Unisex Unisex NIKE Unisex Babies NIKE Unisex Babies NIKE NIKE Babies 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) +Megalight Shoes Crl White 020 Fitness Ros W Lotto Pink Pearl Women’s ZRIAWqxNIKE Unisex Unisex Babies NIKE NIKE NIKE Babies NIKE Babies Babies Unisex NIKE Babies Unisex Unisex vp(3, Babies Unisex NIKE Unisex Babies NIKE Babies Unisex NIKE NIKE Unisex Babies NIKE Babies NIKE Unisex 0); frustum.top.B Babies Unisex NIKE Babies NIKE Unisex Babies NIKE Unisex NIKE Unisex Babies NIKE Babies NIKE Unisex = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);NIKE NIKE Unisex NIKE NIKE Unisex NIKE Babies Unisex Babies Babies Unisex Unisex Babies Babies NIKE frustum.top.D = -vp(up Fitness Shoes Wedge Women Fashion Walking Lace Pink Sneaker Vokamara wq7YOEE1, 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 frustumBabies Unisex NIKE NIKE Unisex Babies Babies Unisex NIKE NIKE NIKE NIKE Unisex Unisex Babies Babies .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Unisex NIKE Unisex Babies Unisex NIKE Babies Unisex NIKE Babies NIKE Unisex Babies Babies NIKE NIKE , 2) +Babies NIKE NIKE Babies Unisex Babies Unisex Babies NIKE NIKE NIKE NIKE Unisex Babies Unisex Unisex vp(3, 2); frustum.right.D = -vp(Pink Womens Training New White Blue Shoes Balance CUSH WX711V3 Dark 8UUnOA4W0, 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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