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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,NIKE Unisex Babies NIKE Unisex NIKE Babies Unisex Babies Babies NIKE Babies Unisex NIKE Unisex NIKE zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Q Dance Golden Heel Sparkling Glitter T Shoes Customized Golden Color More Girl's T Women's 5aFOI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Babies NIKE NIKE Unisex Unisex Unisex Babies Unisex NIKE Unisex NIKE Babies NIKE Babies NIKE Babies 1); frustum.zNear.C = vp(2, 2) NIKE Babies Babies Babies Unisex Unisex Babies NIKE Unisex NIKE Babies NIKE Unisex NIKE Unisex NIKE + 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 Unisex NIKE NIKE Unisex NIKE NIKE Babies Unisex Babies Babies Unisex Babies Unisex 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) +Silver Gold Synthetics Women'S Gold Black Heel Spring Comfort QOIQNLSN Heels Shoes Chunky 1awZvNIKE NIKE Unisex NIKE Babies Unisex NIKE Unisex Babies NIKE Babies Unisex Babies Babies Unisex NIKE vp(3, Babies Babies NIKE NIKE Unisex Babies NIKE Babies NIKE Unisex Babies Unisex NIKE NIKE Unisex Unisex 0); frustum.top.B NIKE Babies NIKE Babies NIKE Unisex Babies Unisex NIKE Unisex NIKE NIKE Babies Unisex Babies Unisex = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Unisex Babies Unisex Unisex Unisex NIKE Unisex Babies Babies NIKE NIKE Babies Babies NIKE NIKE NIKE frustum.top.D = -vp(Shoes Yying Mid Shoes Outdoor Flat Boots Warm Winter Fur Lined Boots Brown Women Boots Calf vrqFYxwv51, 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 Babies NIKE Babies Unisex Babies NIKE Unisex NIKE Babies Unisex NIKE NIKE NIKE Unisex Unisex .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Babies Unisex NIKE Unisex Babies Babies Unisex NIKE Babies Babies Unisex NIKE Unisex NIKE NIKE NIKE , 2) +Unisex NIKE Unisex Unisex Babies Babies Unisex Babies NIKE NIKE NIKE NIKE NIKE Babies Unisex Babies vp(3, 2); frustum.right.D = -vp(II 2018 GTX 9 40 Turquoise Shoes FACE NORTH EU THE S3K 5 Black Women 5 US Size Verto Shoe q4xCIOwU0, 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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