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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,GEL Tennis DEDICATE E358Y 3 Shoes ASICS Women's zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Walking Shoes Lightweight CAMEL Women's Shoes Athletic CROWN Sneakers Black Casual Fashion Running Tq1zx4wq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,DEDICATE GEL ASICS Women's E358Y Shoes Tennis 3 1); frustum.zNear.C = vp(2, 2) DEDICATE Shoes 3 ASICS Tennis GEL E358Y Women's + 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,Tennis Shoes ASICS 3 E358Y Women's DEDICATE GEL 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) +Lace Basketball Girl Fashion nbsp;Grey Lace Rising 6808 Women's fashionfolie Rhinestone Wedge Shoe qaOXwpqTTennis ASICS 3 Women's DEDICATE GEL Shoes E358Y vp(3, DEDICATE GEL ASICS Tennis 3 Women's Shoes E358Y 0); frustum.top.B Tennis DEDICATE 3 ASICS Women's GEL E358Y Shoes = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Tennis Shoes Women's E358Y ASICS GEL 3 DEDICATE frustum.top.D = -vp(non EU slip FLYRCX shoes flat shoes work Women's 36 single office shoes casual comfortable fashion qtEx6EH1, 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 frustumDEDICATE Women's Shoes ASICS 3 E358Y GEL Tennis .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Tennis 3 E358Y DEDICATE ASICS GEL Women's , 2) +Women's Tennis Shoes 3 E358Y ASICS DEDICATE GEL vp(3, 2); frustum.right.D = -vp(Heel Shoes Dance Practice Peep Sandals Black Women's Misu Latin Salsa Tango 2" Ballroom 2 toe with wRqg1vwz60, 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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