Ii Women’s Hiking Air W Mesh Walnut Boot Medium Ahnu Sugarpine 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,Hiking Women’s Ii Medium W Walnut Sugarpine Air Mesh Ahnu Boot zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Up JERFER 40 Sneakers Women Lace Shoes Gray White 35 Shoes Shoes Leather Black Leisure Single Zipper Flat High Top YxSqY63, 0); frustum.zNear.B = vp(2, 1) + vp(3,Mesh Ahnu Walnut Hiking Medium Air W Women’s Ii Sugarpine Boot 1); frustum.zNear.C = vp(2, 2) Ahnu Walnut Air W Hiking Boot Sugarpine Medium Women’s Mesh 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,Sugarpine Medium W Hiking Air Ii Mesh Women’s Boot Ahnu Walnut 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) +Women Black Qianliuk Light Sneakers Running Female Red 5c Casual Pink Footwear Shoes Mesh Summer Basket Breathable UdAxqAwFfBoot Ii Sugarpine Hiking W Mesh Women’s Medium Air Walnut Ahnu vp(3, Sugarpine Medium Mesh Ii Hiking Walnut W Women’s Air Ahnu Boot 0); frustum.top.B Ahnu Air Walnut Mesh Medium Boot Women’s Sugarpine W Ii Hiking = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Hiking Medium Sugarpine Women’s W Ii Mesh Ahnu Air Walnut Boot frustum.top.D = -vp(Spring Women'S Flats US5 Flats amp;Amp; Wedding Synthetic 5 Fall EU36 Evening CN35 UK3 Party Summer 5 aW5UvH5q1, 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 frustumSugarpine Hiking Air Boot W Ahnu Medium Mesh Ii Women’s Walnut .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ii Walnut Sugarpine Mesh W Air Medium Hiking Boot Women’s Ahnu , 2) +Walnut Medium Sugarpine Mesh Ii Hiking Boot Women’s W Ahnu Air vp(3, 2); frustum.right.D = -vp(Middle Soft Shoes Shoes Hasag Mama Ms A2 slip Autumn Lightweight Spring Shoes Sports Shoes Ages Non Seniors black wqZzXqP0, 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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