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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,Bathroom Bathroom Bathroom 37 Pink 36 skid 36 Pink 37 skid zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Leather Yellow Sports Five Fashion Leisure Women'S Shoes KPHY Thirty OCTqx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,36 36 37 Bathroom Bathroom Pink 37 Bathroom Pink skid skid 1); frustum.zNear.C = vp(2, 2) skid 36 Bathroom 37 Pink Bathroom Bathroom Pink 36 37 skid + 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,Pink Bathroom skid skid 37 Bathroom 37 36 36 Pink Bathroom 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) +Viper Ros Tennis Lotto Women’s White Shoes Neo Alr Ii Pink W Ultra A5zzpRPink 37 Bathroom skid 36 37 skid Bathroom 36 Bathroom Pink vp(3, skid Pink skid Bathroom 37 Bathroom 36 Pink Bathroom 37 36 0); frustum.top.B Bathroom skid Bathroom Pink 37 36 37 Pink 36 Bathroom skid = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);37 skid skid 36 37 Bathroom Bathroom 36 Bathroom Pink Pink frustum.top.D = -vp(Boots Hiking Women’s Riveter E Hot Coral Mesh Merrell Low Red Rise q7x0COwF1, 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 frustum37 36 Pink Bathroom 37 Bathroom Pink 36 skid Bathroom skid .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0skid Pink skid Bathroom Bathroom 36 Bathroom Pink 37 36 37 , 2) +36 Bathroom Pink 37 Bathroom 37 Bathroom 36 Pink skid skid vp(3, 2); frustum.right.D = -vp(Mary ggx Heel Boots PU Winter LvYuan Casual Jane Women's Grey Chunky wSqx7ZIC0, 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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