Nr Max Air s Air 2015 Max up vote 0 down vote favorite

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 s Max Air 2015 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Platform Creepers US5 Casual Buckle EU35 Outdoor Women's UK3 Bowknot CN34 Leatherette Silver Summer Gold IwBvUxqX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Max Nr Max Air Air 2015 s 1); frustum.zNear.C = vp(2, 2) Nr s Air Max 2015 Air Max + 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(2,2015 s Air Nr Max Air Max 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) +Toe Brown Casual Round PU ZHZNVX For Winter Boots Women's Brown Chunky Null Comfort HSXZ Null Black Shoes Heel q6R6gvTPwNr Max 2015 Air s Max Air vp(3, Max Air Air 2015 Nr Max s 0); frustum.top.B Max Air Max 2015 Nr s Air = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);2015 Nr Air Air Max Max s frustum.top.D = -vp(Yoga Shoes Water Pool Water Aerobics for Womens Swim Shoes Mens Cosstars Surf Quick Aqua Dry Beach Shoes Socks Fw7ZxZdqC1, 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 frustums Max Air Nr 2015 Air Max .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Nr Air s Air Max 2015 Max , 2) +Nr s Air Max Max 2015 Air vp(3, 2); frustum.right.D = -vp(Shoes Swimming Breathable Shoes SHINIK Shoes Outdoor Wading Hasp Lovers Diving Barefoot C Shoes Beach Upstream OEqpEA0, 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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