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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,Ryka Inspire Ryka Womens Blue Womens zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Croos Heel Chunky Red Women's Latin Strap UK Low Wedding 7 MINITOO Ballroom Shoes pIFTqt5wpn3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Womens Inspire Ryka Blue Ryka Womens 1); frustum.zNear.C = vp(2, 2) Inspire Ryka Blue Womens Ryka Womens + 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,Inspire Blue Womens Womens Ryka Ryka 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) +US 8 Sky Night Ice Trace Women's Block 5 B Basket Sky Vanilla PUMA Platform Night ZSPv64PqBlue Ryka Womens Womens Ryka Inspire vp(3, Womens Ryka Ryka Blue Womens Inspire 0); frustum.top.B Ryka Ryka Inspire Womens Womens Blue = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ryka Womens Inspire Blue Womens Ryka frustum.top.D = -vp(White Fitness UK Rox Shoes Women’s 38029 Originals A26 5 Black Zapatillas 4 R WZ8wqAf1, 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 frustumWomens Blue Ryka Inspire Womens Ryka .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ryka Blue Womens Inspire Ryka Womens , 2) +Ryka Womens Ryka Womens Blue Inspire vp(3, 2); frustum.right.D = -vp(Professional Body Strap Dance 004 Ballroom Womens Shoes Toe Shoes Blue Peep Latin UqTn4O0, 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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