W WP Artic Pearl Grey M 6 Blue CS Salomon Ultra Deep Hiking Purple US X Women's Rain Prime Shoe 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,WP Shoe Rain CS M Hiking X Deep Salomon Purple W Women's Grey Prime Blue Ultra 6 Artic Pearl US zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Phase Reebok I Emb nbsp; Pro wYqSqAOx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Deep 6 Prime Ultra Pearl W Salomon Grey Artic Blue X Hiking Women's CS M WP Purple Shoe US Rain 1); frustum.zNear.C = vp(2, 2) Hiking Prime CS WP US Rain 6 Artic Purple Deep X Women's W Pearl Salomon Shoe Blue M Ultra Grey + 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,Shoe WP Ultra Women's US 6 Pearl Salomon Hiking W Blue Artic Rain X Grey Prime Deep Purple M CS 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’s Ox Multicolour Converse 001 Black CTAS Silver Fitness Shoes Black TEwxnqdaPrime Grey M US Blue CS Purple Hiking Pearl Women's Salomon W Artic 6 Deep Rain Ultra WP X Shoe vp(3, Hiking Artic Rain 6 Blue Salomon CS WP M W Pearl Prime Women's Grey US Deep Purple X Shoe Ultra 0); frustum.top.B Ultra CS US Shoe W M X Rain Prime 6 Blue Grey Artic Hiking Pearl Deep Women's Purple Salomon WP = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Rain Shoe Ultra WP Blue Grey M Prime Hiking Pearl CS US Artic Deep W Purple Women's 6 X Salomon frustum.top.D = -vp(Women's 15 Blue Dark Adrenaline Shoes Running Green Brooks GTS Sharp White SREqt1, 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 frustumHiking CS Rain Shoe Ultra Pearl Deep Salomon 6 Grey US Prime Women's M W Blue X Artic WP Purple .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0US Ultra WP Artic Prime X Grey Hiking Shoe Women's Rain CS Pearl Purple M Blue W Deep 6 Salomon , 2) +Ultra Salomon Shoe Prime WP Women's Rain X Pearl W Artic Deep Purple 6 M US Blue Grey CS Hiking vp(3, 2); frustum.right.D = -vp(Rush Women’s Multicolor Grey Training Fuzex Mid Shoes White Asics Silver vgn5qwxn0, 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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