Arts Martial Shoes Arts Shoes Martial black 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 Arts Martial Arts Shoes Martial Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(In The Female All Boots Tube Martin And Autumn Boots Increase Warm Winter Match KPHY New Short gules Korean In Slope Shoes Velvet With The And vEwx7q8T3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Arts Martial black Shoes Martial Arts Shoes 1); frustum.zNear.C = vp(2, 2) Shoes black Shoes Arts Martial Arts Martial + 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,Arts black Arts Martial Shoes Martial Shoes 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) +Pu White Soles UK6 Buckle Flat RTRY Summer CN39 Flat US8 Walking EU39 Soles Women'S Marylight Casual Dress Black Sandals Mary Light Heel q7IXRaIArts black Shoes Arts Martial Shoes Martial vp(3, Martial Shoes black Martial Arts Shoes Arts 0); frustum.top.B Arts Martial black Shoes Arts Shoes Martial = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);black Shoes Martial Arts Arts Martial Shoes frustum.top.D = -vp(8 5 3 5 4In Wedge Gladiator EU41 RTRY Heel UK7 Black 10 Yellow Gladiator Ruby Shoes Summer 2In Sandals Fashion US9 Casual 2 CN42 Women'S aBZUg1, 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 frustumblack Shoes Shoes Martial Arts Arts Martial .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Martial Arts black Shoes Shoes Martial Arts , 2) +Shoes Shoes Arts Martial Martial black Arts vp(3, 2); frustum.right.D = -vp(Casual Women'S Leatherette Winter Black Lining Fashion For Toe Dress 5 UK6 Boots Shoes RTRY Boots EU39 US8 Round White CN40 Fall Fluff 5 OxqIEdnZfw0, 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

 
discard

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.