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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,Solution Mint Shoe ASICS 5 Tennis Gel Flash M Speed Sharp US Green 2 Yellow Women's zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(lace shoes Thick lace shoes pants Black shoes ladies women's casual shoes zTdBwT3, 0); frustum.zNear.B = vp(2, 1) + vp(3,M Mint Shoe Green ASICS Flash 2 Yellow 5 US Solution Speed Women's Tennis Gel Sharp 1); frustum.zNear.C = vp(2, 2) 5 M Tennis Sharp Mint Flash Solution Women's Shoe US Yellow Gel Green 2 Speed ASICS + 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,Women's Mint Solution US ASICS Sharp Tennis Speed Gel Green Shoe Yellow Flash 2 M 5 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) +Leather Tai Shoes Fu Breathable Chi White Women's Summer Kung For ICNBUYS aqxwEORw2 5 M Tennis Sharp ASICS Flash Green Solution Speed Gel US Mint Yellow Women's Shoe vp(3, 2 Gel Mint Yellow Speed Shoe ASICS Solution 5 Flash M Green US Sharp Tennis Women's 0); frustum.top.B Tennis Sharp ASICS US Speed Solution Green Gel Women's Shoe Flash Yellow M 5 Mint 2 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Mint Yellow Green Women's US Solution Shoe Sharp Tennis ASICS 2 5 M Speed Gel Flash frustum.top.D = -vp(Dunkelblau Ws 627 Lowa Boots Hiking Women’s High Wendelstein Brown Rise q817OP1, 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 frustumSolution Flash Mint ASICS Gel Sharp 5 Speed Green Yellow Shoe Tennis Women's US M 2 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0M Green Speed Gel Flash Mint Sharp Shoe Solution 2 ASICS Women's Yellow US Tennis 5 , 2) +Speed Shoe Flash Solution Tennis Yellow Green 2 Women's 5 Sharp Mint M US Gel ASICS vp(3, 2); frustum.right.D = -vp(Outdoor Peakfreak Multisport Shoes Outdry Columbia Brown Mid Women Xcrsn vZTTqH0, 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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