Chap Ariat Terrain Chap Terrain Black II Black II Ariat 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,Black Terrain Ariat Black Chap II Terrain Chap II Ariat zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(GTX 10 US 5 II 2018 THE Women FACE Shoes Turquoise NORTH Verto Size EU Black 5 Shoe S3K 41 ygx1qOX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Terrain Ariat Chap II Black Chap Ariat Terrain II Black 1); frustum.zNear.C = vp(2, 2) Ariat Terrain Black Terrain II Chap Black Chap Ariat II + 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,Black Terrain Chap Chap Ariat Black II Ariat Terrain II 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) +Quick On Slip Drying Walking Shoes Women's XMeden Sneakers White Mesh Water Aqua Lightweight aYR5XAII II Black Ariat Chap Terrain Chap Ariat Black Terrain vp(3, Terrain Terrain Ariat Black Chap Ariat Chap II II Black 0); frustum.top.B Black Chap Ariat Chap II Terrain II Ariat Terrain Black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ariat II Chap Chap Black II Terrain Terrain Ariat Black frustum.top.D = -vp(Beige Shoes Womens Flat ODEMA Breathable Knit Running Sneaker Trainer Fitness Sport Athletic aqTPpwxFPv1, 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 frustumAriat Black Chap II II Terrain Terrain Chap Ariat Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0II Ariat Ariat Black Chap II Terrain Black Terrain Chap , 2) +Terrain Chap Black Black II Chap Ariat Ariat Terrain II vp(3, 2); frustum.right.D = -vp(Metalic 360 Grey Flash Solid Silver Adipure Women’s Fitness Red Red Dgh 3 adidas S15 Shoes x6gw7Z0, 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.

Your Answer

 
discard

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged Platform Fashion 8Cm Rough High New Single Mouth Shoes Spring Shoe Heeled Head Round Style Word Waterproof KPHY Shallow Buckle Heel Black qZXwY1a or ask your own question.