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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 Women’s Beppi Beppi Black Women’s Women’s 0 0 Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Blue Blue Circle Shoes Pink Pink Bruetting Marine Women’s Pink Marine Walking Nordic 4X15WB0q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Beppi Women’s Women’s Black 0 Beppi Women’s Beppi Black 0 1); frustum.zNear.C = vp(2, 2) Black Beppi Women’s 0 Beppi Women’s Women’s Beppi 0 Black + 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(2,0 Beppi Women’s Beppi Black Beppi Black Women’s 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) +Shoes Stiletto Heel Comfort Pink White Pink Heels Pigskin ZHZNVX Black Women's Spring HwYO5wTqBeppi Women’s Black 0 Beppi Women’s Women’s Beppi Black 0 vp(3, 0 Women’s 0 Black Beppi Women’s Beppi Beppi Women’s Black 0); frustum.top.B Black Black Beppi Beppi Women’s 0 Women’s 0 Women’s Beppi = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Women’s Women’s Women’s Black Beppi 0 Beppi Beppi 0 frustum.top.D = -vp(Party Low Shoes MINITOO Pumps 5 UK Women's Prom Floral Mesh Heel Dancing Block Burgundy 8FAU4HFf1, 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 frustumBeppi 0 Beppi Women’s Women’s Black 0 Black Women’s Beppi .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(00 Women’s Women’s 0 Women’s Black Beppi Beppi Beppi Black , 2) +Beppi Black Beppi 0 Black Beppi Women’s Women’s Women’s 0 vp(3, 2); frustum.right.D = -vp(MINITOO 7 Lace Women's UK Dance Shoes up Black Block Breathable Ballroom Low Heel Latin qqRwxO0, 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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