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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,Unisex red Unisex Cap Cap Xa Salomon Salomon Xa red zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(MTNG Champagne Oroglisten Rolling Fitness Doradocrack City Gold Golden Shoes Women’s rTzBqr3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Salomon Unisex Unisex Cap Salomon red red Xa Cap Xa 1); frustum.zNear.C = vp(2, 2) Xa Salomon red Unisex red Xa Unisex Cap Salomon Cap + 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,Xa Salomon red Cap Unisex Cap Salomon Xa Unisex red 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) +Shoes Suede Spring Black Red Stiletto Heels Heel Blue Blue ZHZNVX Women's Basic Pump RHw6U6Xa Xa Salomon Unisex Cap Cap Unisex red Salomon red vp(3, Xa red Salomon Unisex Cap Unisex Xa Cap Salomon red 0); frustum.top.B Xa Cap Cap Unisex Unisex Salomon Xa red red Salomon = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Salomon Unisex red Unisex Xa Salomon Xa red Cap Cap frustum.top.D = -vp(For Coloranimal Fishing Women Sneakers Flats Summer Walking Spring Flies Running Nurse Sr7rIX1, 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 frustumUnisex Cap Cap Salomon Xa red Unisex Xa Salomon red .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0red Xa Cap Salomon Xa Unisex red Cap Unisex Salomon , 2) +red Xa Salomon Salomon Cap Unisex Unisex Cap red Xa vp(3, 2); frustum.right.D = -vp(Women Men Pattern Sneakers 3D CHAQLIN cat 4 Animals Flat Mesh Shoes Running Denim Blue xwrqIYq080, 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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