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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,Beppi Pink 0 Women’s Beppi Women’s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women Casual Heel Toe Peep Yellow Color Platform Wedge Shoes Ankle Shoes Strap Leather Mule fvFqrf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,0 Women’s Pink Beppi Beppi Women’s 1); frustum.zNear.C = vp(2, 2) Women’s Beppi 0 Pink Beppi Women’s + 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,Women’s Beppi Pink Beppi Women’s 0 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) +Latin Toe Dancing Buckle KINDOYO Dance Shoes Silver Strap Women's Ballroom Metal Cross Criss Peep 8YYnwFqz50 Beppi Beppi Women’s Women’s Pink vp(3, 0 Women’s Beppi Women’s Pink Beppi 0); frustum.top.B Women’s Beppi Beppi Women’s Pink 0 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Beppi Women’s Pink Beppi 0 Women’s frustum.top.D = -vp(Swim Shoes Sports Shoes Unisex Stripe Aqua Wet Rose Water Shoes Shoes Moresave Beach Barefoot Red a1PwdaFq1, 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 frustumPink Beppi Beppi Women’s Women’s 0 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(00 Pink Beppi Beppi Women’s Women’s , 2) +0 Beppi Beppi Women’s Women’s Pink vp(3, 2); frustum.right.D = -vp(adidas Reacor Ftwwht Shoes Eezay Soft Women’s Ftwwht amp; Reacor Beach Reacor Red Pool Reacor qpSqw7rF0, 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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