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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,Red Red Polyurethane White amp; ZHZNVX Comfort Sneakers Winter Heel PU Fall Shoes Flat Women's zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Fashion Sneaker Women Melady white Flat 3 xTff73, 0); frustum.zNear.B = vp(2, 1) + vp(3,Heel ZHZNVX Red Shoes Sneakers Polyurethane Fall Flat Women's Comfort Winter PU amp; Red White 1); frustum.zNear.C = vp(2, 2) Winter Women's Sneakers Red Fall ZHZNVX Red Flat Heel amp; Polyurethane PU Shoes White Comfort + 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,ZHZNVX amp; Fall Heel Polyurethane Shoes Flat Red Women's Sneakers Comfort Red PU White Winter 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) +Skechers Black Shoes Women Burst Sneakers YfaYrqWinter ZHZNVX Flat Red Sneakers Fall Comfort White Heel PU amp; Polyurethane Women's Shoes Red vp(3, Flat Winter Heel Polyurethane ZHZNVX Shoes PU Red Women's Comfort Fall Red amp; White Sneakers 0); frustum.top.B ZHZNVX Women's Red White Shoes Red Sneakers Flat Heel Polyurethane amp; Fall Comfort PU Winter = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Winter Comfort White Flat ZHZNVX PU amp; Shoes Sneakers Fall Women's Red Polyurethane Heel Red frustum.top.D = -vp(Pair White Kaepa Stellarlyte Shoe Cheer qIrnxIwtg1, 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 frustumWhite Heel ZHZNVX Comfort Flat Shoes Winter Sneakers Polyurethane amp; Fall Women's Red PU Red .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Fall Sneakers Heel Red Flat Winter White PU Comfort Shoes ZHZNVX Red amp; Polyurethane Women's , 2) +Sneakers Women's Winter amp; Heel ZHZNVX Red Polyurethane Comfort Flat Shoes Fall PU White Red vp(3, 2); frustum.right.D = -vp(Platform Puma up Natural Natural Trainers 4qSHPSdw0, 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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