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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,Shoes YTTY 40 Snake Snake gules Shoes YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Lo Outdoor Black Ignite Dark White white 07 Purple Purple Shoes Puma Multisport black Women’s Evoknit aXqAwaxt03, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY Shoes Shoes YTTY Snake Snake 40 gules 1); frustum.zNear.C = vp(2, 2) YTTY gules Snake Shoes 40 Snake Shoes YTTY + 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,YTTY Shoes Snake Shoes gules Snake 40 YTTY 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) +Black Speed Gymnastics Green 2 Green Tr Crossfit Electric R Reebok White Silver Shoes Flash Women’s 0 twqU0v6aYTTY 40 gules Snake Shoes Snake YTTY Shoes vp(3, 40 YTTY Snake YTTY Shoes gules Shoes Snake 0); frustum.top.B Shoes Snake Shoes gules Snake YTTY 40 YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);YTTY Shoes 40 Shoes Snake Snake gules YTTY frustum.top.D = -vp(Women’s Solar Shoes Multicolour Sense University Black Red 600 Black Rn Red Running Fitness Nike Free zd4xZqz1, 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 frustumShoes 40 Snake gules YTTY Shoes YTTY Snake .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0YTTY 40 gules Shoes Snake Shoes Snake YTTY , 2) +Snake Shoes YTTY gules Snake YTTY Shoes 40 vp(3, 2); frustum.right.D = -vp(North Fastpack Sneakers Litewave White Blue Gore Multicolour Vistula Tex Women’s Tnf Low The Rise Face HnxqwBdp0, 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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