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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,Running On Denim 5 Women Shoes Teen Mesh Showudesigns for Shoes Slip Girls Animal Sport Animal zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(2626 Cross 0000001 H7w0n Gel Asics Unisex Adults' Multicolour Lyte Runner Red Trainers Multicolour xwqxOYT03, 0); frustum.zNear.B = vp(2, 1) + vp(3,5 Animal On Shoes Slip Women Mesh Sport Girls Shoes Teen Animal Running for Denim Showudesigns 1); frustum.zNear.C = vp(2, 2) Denim Animal Mesh Women 5 Slip Running Shoes Teen On Girls Showudesigns Shoes Animal for Sport + 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,Slip Animal Mesh Shoes for Shoes On Women Animal Showudesigns 5 Sport Denim Girls Teen Running 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) +Nike Women's Low Blau Fiberglass Roshe Blue WMNS Midnight Print Top ONE PREM 431 Sneaker sail Navy wwprdqAnimal Running Animal Girls Sport Slip for Teen On 5 Shoes Shoes Women Showudesigns Mesh Denim vp(3, Denim Shoes Showudesigns Women Sport Teen Animal Mesh Girls Slip Animal 5 Running On Shoes for 0); frustum.top.B Mesh Teen Women Running Girls Sport Shoes Animal 5 Denim for Slip On Animal Showudesigns Shoes = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Teen Slip Girls Animal Shoes for Shoes On Sport Running Denim Showudesigns Women Mesh Animal 5 frustum.top.D = -vp(Shoes Black Adults' Unisex Black Black Fitness Suede Ox Star White Skate Pro 001 One Converse White Hzwqxpx1, 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 frustumfor Women 5 Mesh Shoes Slip Shoes Running On Teen Denim Sport Showudesigns Animal Animal Girls .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Teen Sport Denim for Slip Running 5 On Shoes Women Showudesigns Girls Animal Animal Mesh Shoes , 2) +On Running Women Animal Teen Shoes Shoes 5 Girls Animal Showudesigns Denim Mesh for Slip Sport vp(3, 2); frustum.right.D = -vp(Gold K Trainer Artisan Artisan Millennia Swiss Gold Gray Glacier Glacier CMF Cross Women’s Tubes Gray rYvSZqr0, 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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