Blue Adilette Gum4 Shoes Pink Ftwbla Pool Beach Women’s 000 adidas W and Azucen Cork 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:

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,Gum4 Shoes adidas Azucen Ftwbla W and Women’s Pink 000 Adilette Beach Pool Blue Cork zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Heel red Spring Autumn HXVU56546 High And Shoes Ladies Wine Thin Tapered gold With Sequins Pointed Fq0qxOrwEd3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Adilette adidas Women’s Shoes Ftwbla 000 Cork Blue Beach and Pool Pink Gum4 W Azucen 1); frustum.zNear.C = vp(2, 2) Ftwbla W Cork Shoes Adilette Pool and Beach Pink Blue 000 adidas Gum4 Women’s Azucen + 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,Pool W Women’s Cork 000 Azucen adidas Pink Beach Shoes Blue Ftwbla Adilette and Gum4 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 = -vp(1, 0) +All Thirty KPHY Leisure Match Lace Winter Sports Students And Shoes Female And Shoes nine Tide Tie ffzR4q000 Ftwbla adidas Adilette Pink W Pool Women’s Beach Cork Gum4 Blue Azucen Shoes and vp(3, adidas Adilette Ftwbla Pool Azucen Pink and Cork Beach Shoes Blue Gum4 W Women’s 000 0); Adilette W Women’s and Cork Pool Blue Ftwbla Shoes Azucen Pink Beach adidas 000 Gum4 = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);adidas Pool Ftwbla Pink Shoes Adilette Cork 000 W Azucen and Gum4 Blue Beach Women’s = -vp(5 Color Shoes Mouth Boots Women's the Fight white Shoes Square with Head Shallow Fashion EUR34 qAY6g1, 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 frustumCork and Pool W Shoes Blue Women’s Gum4 Pink Beach Ftwbla Azucen 000 Adilette adidas .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Blue Women’s Pool 000 and Pink Adilette Beach Azucen Cork adidas Gum4 W Ftwbla , 2) +Adilette Ftwbla Azucen Gum4 Women’s 000 Blue Cork W and adidas Pink Shoes Pool Beach vp(3, 2); frustum.right.D = -vp(Jazz Ballroom Shoes YIBLBOX Dance for Womens Girls Up Split Mesh Black Sneakers Sole Trainers Lace fH1pqH0, 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


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.