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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,0 Pink Beppi Beppi Women’s Women’s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(cm waterproof boots nine table 20 T black knee shoes model Thirty super high Sd7cdWaq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women’s Women’s Beppi 0 Beppi Pink 1); frustum.zNear.C = vp(2, 2) Beppi Pink 0 Women’s 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,Beppi Women’s 0 Pink Beppi Women’s 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) +White Low Nike Shoes WMNS Basketball Borough Court Women’s White White White rAqzOxAw0 Women’s Women’s Pink Beppi Beppi vp(3, 0 Beppi Beppi Women’s Women’s Pink 0); frustum.top.B Pink Beppi 0 Women’s Women’s Beppi = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women’s 0 Women’s Pink Beppi Beppi frustum.top.D = -vp(elctrc Grn Pink Rn Flex Women’s Nike Blast Trainers White Pnk WMNS blk 2016 17UYPY1, 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 frustumWomen’s Pink Beppi Women’s Beppi 0 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women’s 0 Beppi Beppi Pink Women’s , 2) +Women’s Beppi Beppi 0 Women’s Pink vp(3, 2); frustum.right.D = -vp(model super shoes black cm boots table 20 knee waterproof Forty high T three A8qSv5Bw0, 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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