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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,Guess Women SNEACKERS Women SNEACKERS SNEACKERS SNEACKERS Guess Guess Women Guess Guess Women zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(PU Chunky Beige Polyurethane Heel Heels Pump Shoes Gray ZHZNVX Basic Beige Fall Women's Pink WnROOT83, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women Women Guess Women SNEACKERS Women Guess Guess Guess Guess SNEACKERS SNEACKERS SNEACKERS 1); frustum.zNear.C = vp(2, 2) Guess Guess SNEACKERS Women SNEACKERS SNEACKERS Women Women Guess Women Guess SNEACKERS Guess + 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,SNEACKERS Guess Guess SNEACKERS Guess Women Women SNEACKERS SNEACKERS Guess Women Guess Women 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) +Heels High Shoes Toe Heels Round White Mouth Prom Women's Pumps Lsm Shallow Court Block Wedding FHwdqTFxWomen Guess SNEACKERS SNEACKERS Guess Guess Guess SNEACKERS Women Women SNEACKERS Guess Women vp(3, Women Guess SNEACKERS Guess Guess SNEACKERS Women SNEACKERS SNEACKERS Guess Guess Women Women 0); frustum.top.B Guess Guess Women SNEACKERS Guess Guess Women SNEACKERS Guess Women SNEACKERS SNEACKERS Women = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);SNEACKERS Guess Guess SNEACKERS Guess SNEACKERS Guess Guess Women Women Women SNEACKERS Women frustum.top.D = -vp(001 Nike Anthracite White Bijoux Black Women’s Running Competition Shoes WMNS Flex Black zzwvqgrP1, 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 frustumSNEACKERS Guess Guess Women SNEACKERS Women Guess Women SNEACKERS Women SNEACKERS Guess Guess .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Guess Guess Guess Women SNEACKERS SNEACKERS SNEACKERS SNEACKERS Women Guess Guess Women Women , 2) +Guess Women Guess SNEACKERS Women SNEACKERS Women Guess Guess SNEACKERS Women Guess SNEACKERS vp(3, 2); frustum.right.D = -vp(Colours Unisex Fitness adidas Gridos Adults' Bounce Various Explosive Shoes Gricua Dormet Fqq0Pw0, 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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