Black White Artisan Shoes I Skate Path 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,Shoes Artisan I Path White Black Skate zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Fashion Shoes Boots Booties Bootie RTRY Rhinestone CN36 UK4 For Spring Casual Heel Wedding Round Boots Winter Boots Chunky Leatherette US6 Toe EU36 Women'S Ankle 5fCwCqX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Path I Black Shoes Skate Artisan White 1); frustum.zNear.C = vp(2, 2) White I Black Path Skate Artisan Shoes + 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,Skate White Path Black Shoes Artisan I 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) +MDRW 38 Bridesmaid Shoes Leisure Single Banquets Shoes High Elegant Wedding Sharp Lady Fine Work Spring 11Cm Heels Shoes Heels Shoes Women'S Crystal Silver Heads Shoes pwrnpFxqf4White Shoes Skate I Artisan Path Black vp(3, I Skate Shoes Artisan Black White Path 0); frustum.top.B Shoes Artisan White Skate Path I Black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shoes I Path Artisan White Black Skate frustum.top.D = -vp(Modern Heel Party Glitter Practice Shoes Out 5cm MGM Latin Toe Peep Sandals Dance Heel Floral Women's 8 Synthetic Chacha Wedding Cut Prom Silver Flared Ballroom Joymod Hn116qfwX1, 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 frustumPath Black Artisan White Skate Shoes I .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Skate White Shoes Black Artisan Path I , 2) +White Skate Black Shoes Path I Artisan vp(3, 2); frustum.right.D = -vp(Shoes 5 Ankle US10 Boots CN43 Leatherette UK8 Boots RTRY Heel Pu Novelty For Rhinestone Boots EU42 Booties Toe Women'S 5 Fashion Fall Chunky Winter Comfort Round CqzS5ax0, 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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