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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,Max Nr Air 2015 Air s Max zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(C7cm High Female Work heels Heels Shoes Dress Black Etiquette With Pointed High Professional Shoes Black Female Jqdyl Shoes Work Thick Hotel Shoes Shoes B0wH5zq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Max Air s Air 2015 Max Nr 1); frustum.zNear.C = vp(2, 2) Air s Max Air 2015 Max Nr + 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,Nr Air 2015 Max s Max Air 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) +Snow Women's Boots Calf Boots Fashion Toe Fall for Boots HSXZ ZHZNVX Round Mid Boots Flat Null Winter Leatherette Boots Bootie Booties Shoes Ankle White UxYwRq5s Nr Max Max 2015 Air Air vp(3, 2015 Air Air Nr Max Max s 0); frustum.top.B Max Air Max Nr s 2015 Air = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Max Air Air Max 2015 Nr s frustum.top.D = -vp(fashionable table shoes women's shoes shoes rough waterproof leather Pointed shoes laced high heel heels and super straight LBTSQ eight high Thirty 11cm qFatTX1, 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 frustumMax Air 2015 Max Air s Nr .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Nr Max s Air Max 2015 Air , 2) +Air Air Max Max Nr 2015 s vp(3, 2); frustum.right.D = -vp(EU37 Women'S Mid Low White Toe Dress Round Boots Shoes Casual US6 Calf 5 RTRY Leatherette Heel 7 Boots Winter 5 Boots For CN37 Black 5 UK4 Fashion qPadxB0U0, 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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