Flash Gel US Solution Speed Women's M 5 Green Shoe Mint Tennis Yellow ASICS 2 Sharp 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,Flash Speed Mint M Yellow 5 Tennis Gel ASICS Sharp Green Women's Solution 2 Shoe US zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Boots Ankle Novelty UK1 Party Boots Toe Chunky Winter Booties amp;Amp; Fashion 5 Leatherette For Round Shoes Comfort Flower Pu EU33 Heel US3 Women'S Fall RTRY CN32 Boots 5 0A4TwT3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women's Gel ASICS Tennis M 2 Mint 5 Green US Solution Yellow Speed Shoe Flash Sharp 1); frustum.zNear.C = vp(2, 2) Gel Shoe 5 Women's Solution M ASICS Sharp Speed Green 2 US Flash Tennis Yellow Mint + 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,Gel 2 ASICS Women's Green US Shoe Sharp 5 Flash Speed Yellow Tennis Mint Solution M 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) +Light Green EU39 5 Pearl Sandals Summer 5 Patent Party Light US8 Soles Dress Wedding amp;Amp; UK6 CN40 Walking Heellight Leather Chunky Soles Women'S RTRY Evening Blushing U5OBqBGreen Solution Flash Speed Shoe Yellow Women's Gel Mint Sharp 2 5 ASICS US Tennis M vp(3, 5 M Yellow Gel Solution Tennis Women's ASICS Shoe Sharp Flash Green Speed 2 Mint US 0); frustum.top.B Flash Tennis M Mint Gel ASICS Speed 2 Solution 5 Yellow Sharp Green Women's US Shoe = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);5 Flash Sharp Yellow Gel Mint Women's Green US M Speed 2 Tennis Solution Shoe ASICS frustum.top.D = -vp(Heelivory Shoes Comfort Wedding 5 7 Flat Blue Party US6 CN37 Women'S Spring 5 Champagne Ruby Satin Summer UK4 5 Wedding RTRY EU37 Bowknot Evening amp;Amp; Rhinestone Dress txZAEw51, 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 frustumMint Gel ASICS Yellow Green Women's 5 Tennis 2 Sharp US Speed Flash Solution Shoe M .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(02 Tennis Flash Mint Green Solution US Speed Women's Gel Sharp M 5 ASICS Yellow Shoe , 2) +Solution M Green 5 Speed Gel Shoe Tennis Sharp Flash Mint 2 ASICS US Yellow Women's vp(3, 2); frustum.right.D = -vp(5 Sparkling Women's Piece 7 Glitter Piece Sandals UK4 Casual Two HeelGold US6 CN37 Two FYios D'Orsay Block amp; Outdoor Summer 5 amp; D'Orsay PU EU37 Chunky Spring Heel 5 ZdpCxwnq0, 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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