Bullock Shoes black Bullock YTTY YTTY 40 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 YTTY 40 Shoes Bullock YTTY Bullock zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Open Thick GAOLIXIA Mesh Toe Pumps Hollow Women's Boots Court Shoes Sandals Roman Heels Summer Transparent Apricot Strappy High Lace Shoes wCqAxzCS53, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY Bullock black YTTY Bullock 40 Shoes 1); frustum.zNear.C = vp(2, 2) YTTY Bullock Bullock 40 YTTY black Shoes + 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 Bullock YTTY Shoes YTTY 40 Bullock 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) +soft comfortable flat shoes pregnant shoes dance fashion mouth Shallow ladies portable FLYRCX bottom foldable shoes women Black shoes work tSIqwyYTTY Shoes Bullock black Bullock 40 YTTY vp(3, black Bullock 40 YTTY Shoes YTTY Bullock 0); frustum.top.B 40 YTTY Bullock Shoes black YTTY Bullock = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bullock YTTY Bullock black Shoes YTTY 40 frustum.top.D = -vp(Crimson Obsidian Hypervenom vivid Purple Purple vivid Orange Kids' Total Football Boots Crimson Ii Obsidian Tf NIKE Phade Unisex Total aZTqSS1, 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 frustum40 YTTY Shoes YTTY Bullock Bullock black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(040 Bullock Bullock YTTY YTTY black Shoes , 2) +black Shoes YTTY Bullock YTTY Bullock 40 vp(3, 2); frustum.right.D = -vp(Shoes Fashion Sports Lace Jogging B Up Unisex Gym Men Casual Trainers Running Breathable Breathable Women Shoes Sneakers Mesh White Shoes 58PBqtwf0, 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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