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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,slippers dark blue Indoor antiskid 43 striped bathroom 44 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 US7 5 Fashion Boots Leatherette Boots UK5 RTRY Round Pu Shoes Women'S amp;Amp; Comfort For Boots CN38 High Stiletto EU38 Bowknot Party Heel Fall Winter Knee Toe Novelty FFqBg8xw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,dark striped slippers antiskid 44 bathroom blue 43 Indoor 1); frustum.zNear.C = vp(2, 2) 44 bathroom dark Indoor blue slippers antiskid striped 43 + 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(2,44 slippers striped Indoor 43 antiskid blue dark bathroom 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) +Office Spring Boots Leatherette For Boots Winter RTRY Shoes CN43 Round Chunky Boots 5 amp;Amp; Ankle Heel 5 Career Toe US10 Casual Zipper EU42 Booties Women'S Fashion UK8 q6EawUxwt43 dark blue slippers Indoor striped 44 antiskid bathroom vp(3, slippers 44 antiskid striped dark Indoor bathroom blue 43 0); frustum.top.B bathroom Indoor 44 antiskid 43 slippers blue striped dark = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);slippers Indoor 43 antiskid striped 44 blue dark bathroom frustum.top.D = -vp(Shoes Pad Foot Design Adhesive Waterproof Pairs Shoes Nakefit Anti Activities Lover Stick db on for Barefoot with Barefoot Soles Water Summer 5 slip Hot and for Invisible Pink 50ndUx1, 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 frustumbathroom antiskid dark 44 blue Indoor 43 slippers striped .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0blue 43 Indoor antiskid 44 bathroom striped dark slippers , 2) +44 blue slippers dark 43 antiskid Indoor bathroom striped vp(3, 2); frustum.right.D = -vp(Fashion 5 CN43 Toe Boots For Leatherette Evening Party Up Boots Shoes Comfort Lace Round UK8 US10 RTRY Over Knee 5 EU42 Women'S Pu Dress Boots The Winter Novelty amp;Amp; wSfx0Pq80, 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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