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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,Fu Velvet Fu Shoe Kung Velvet Black Kung Black Shoe zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black Match Winter Rough Simple Boots Leather All Pointed Heels Pvwx8rqP3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Kung Velvet Black Shoe Kung Black Fu Fu Shoe Velvet 1); frustum.zNear.C = vp(2, 2) Shoe Kung Velvet Fu Black Kung Velvet Black Shoe Fu + 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,Fu Kung Fu Kung Velvet Shoe Black Velvet Shoe Black 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) +Merrell Glove Women’s Chili Baja US Vapor Blue Trail 3 Runner xxrvRwBlack Fu Shoe Velvet Kung Velvet Black Shoe Fu Kung vp(3, Shoe Kung Kung Fu Velvet Black Velvet Shoe Fu Black 0); frustum.top.B Velvet Black Velvet Shoe Kung Fu Black Kung Shoe Fu = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Kung Shoe Velvet Black Velvet Fu Shoe Black Kung Fu frustum.top.D = -vp(Women's S L garden Dance coral Shoes DE PASOS BAILE CREACIONES XHOUwU1, 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 frustumVelvet Kung Fu Velvet Shoe Fu Kung Black Black Shoe .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Fu Velvet Velvet Kung Fu Black Kung Shoe Black Shoe , 2) +Velvet Kung Kung Shoe Velvet Black Shoe Fu Fu Black vp(3, 2); frustum.right.D = -vp(lovers Linen 41 home 40 purple slippers indoor slippers floor ppr5xw0, 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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