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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,Reebok Reebok Reebok Black Reebok Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Socks Women Diving Barefoot Water Beach YiyiLai Aqua Shoes Athletic Swim Blue Men vnqw5O3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Reebok Reebok Reebok Reebok Black 1); frustum.zNear.C = vp(2, 2) Reebok Black Black Reebok Reebok Reebok + 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,Black Reebok Reebok Black Reebok Reebok 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) +2 HUGS Running Cactus Shoes Cactus IDEA Sneakers Women's Floral Print Lightweight RRqOpvwReebok Reebok Black Reebok Reebok Black vp(3, Reebok Reebok Black Reebok Black Reebok 0); frustum.top.B Reebok Reebok Reebok Black Black Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Reebok Reebok Reebok Reebok Black frustum.top.D = -vp(Asics 9 Shoes Coral Blue Indigo Flash Women’s 4993 Blue Patriot Training Silver ffqCxrw41, 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 frustumReebok Reebok Black Black Reebok Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Reebok Reebok Black Reebok Reebok , 2) +Black Black Reebok Reebok Reebok Reebok vp(3, 2); frustum.right.D = -vp(Nike Cool Grey Shoes 010 Men’s Black Ii Control Mtlc Fitness Multicolour Flex rqrzgwB0, 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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