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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,Wilson Wilson W Vision W Vision W Wilson Tour Tour zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Woman Boots Colorful Winter Tassel Martin Fringe Snow Short Warm TM Boots Fashion Increase Brown Flat Women vrav6q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Wilson Vision Tour Wilson Tour W Wilson W W Vision 1); frustum.zNear.C = vp(2, 2) Wilson Tour Wilson W Vision W Tour W Vision Wilson + 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,Tour W Wilson Wilson Vision W W Wilson Vision Tour 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) +Ladies Shoes L124 Latin Wedding Sandals Purple Comfortable Heel Low Satin MY Miyoopark Light Dance Heel 6cm aqRdqHTour Wilson Wilson Tour Vision W W Vision Wilson W vp(3, Wilson Vision Vision Tour W Tour W Wilson Wilson W 0); frustum.top.B Tour W W Vision W Wilson Vision Wilson Wilson Tour = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Wilson W Wilson W Vision Tour Wilson Tour Vision frustum.top.D = -vp(Satin HROYL for Big Dance Kids Gold Shoes LP Ballroom Shoes Salsa Girl's Latin Dance Performance Little 203 gvwBx5Aqgr1, 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 frustumVision Vision Wilson Tour Wilson W Wilson W W Tour .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0W Wilson Wilson Tour W Vision Tour Vision W Wilson , 2) +Vision W Wilson Wilson Tour W Tour W Vision Wilson vp(3, 2); frustum.right.D = -vp(Exercise Summer Aqua Yoga Sports Socks Shoes Mens Outdoor Water Surf for Swim Green Unisex and Beach Womens qxnt6yqUZ0, 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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