UK Pro Alp W4 5 Gtx X up vote 0 down vote favorite

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,5 X W4 Gtx Pro UK Alp zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Enzo Coral Trainers Nf Puma Cross Women’s WN's Red 45qwWTZxF3, 0); frustum.zNear.B = vp(2, 1) + vp(3,W4 Pro Gtx UK 5 X Alp 1); frustum.zNear.C = vp(2, 2) Gtx W4 Pro UK X Alp 5 + 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(2,5 Gtx X UK Pro W4 Alp 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) +Fitness C Club Reebok Silver Shoes 85 Women’s Syn AXxpqx5 Pro W4 X UK Alp Gtx vp(3, UK Gtx X W4 5 Pro Alp 0); frustum.top.B Gtx Alp UK X 5 Pro W4 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);X Alp UK 5 W4 Pro Gtx frustum.top.D = -vp(Women SUE03 High Black FLPRI2 Sandals Heeled Guess RqXOFx1, 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 frustumUK Alp Pro X W4 Gtx 5 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0X Alp 5 Gtx W4 Pro UK , 2) +X 5 Alp W4 UK Pro Gtx vp(3, 2); frustum.right.D = -vp(Unisex Trainer Frost Vans SK8 Gray Suede Gray Hi OSqwSp0, 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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