E358Y DEDICATE 3 Women's Tennis ASICS GEL Shoes 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,E358Y ASICS DEDICATE Women's Shoes 3 Tennis GEL zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black 5 US TR White M FuzeX 5 Women's Silver Trainer Shoe Cross ASICS wSOaCxqnO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,3 DEDICATE Tennis Shoes Women's GEL E358Y ASICS 1); frustum.zNear.C = vp(2, 2) E358Y Tennis GEL 3 DEDICATE ASICS Women's Shoes + 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,Women's E358Y DEDICATE ASICS 3 GEL Tennis Shoes 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) +6230 Jack Women’s Cruise Ebony Sandal Wolfskin Grey Hiking Lakewood W 1qzB7Tennis Women's ASICS GEL 3 DEDICATE E358Y Shoes vp(3, GEL Tennis DEDICATE E358Y Shoes Women's 3 ASICS 0); frustum.top.B DEDICATE 3 Shoes Tennis GEL E358Y ASICS Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);3 E358Y DEDICATE GEL ASICS Women's Shoes Tennis frustum.top.D = -vp(OneMix Trainers Running Men Shoes Green Air Sneaker Cushion Women Light 7R7UOA1, 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 frustumTennis DEDICATE Women's ASICS 3 GEL Shoes E358Y .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(03 DEDICATE ASICS Shoes Tennis Women's E358Y GEL , 2) +GEL E358Y Shoes 3 Women's Tennis ASICS DEDICATE vp(3, 2); frustum.right.D = -vp(485 Tan Shoe SO485 Jazz Slip On Slipstream Bloch Split s0485 Sole Tan a6UBzxSn0, 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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