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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,Salomon Cap Unisex red Xa red Unisex Xa Salomon Cap zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(0 Breeze Women’s Cherry Reebok Orange 7 Cool Shoes Yourflex Trainette White Orange Fitness Neon HI7TnxZ7BW3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Xa Unisex Xa Salomon Cap red Cap Unisex red Salomon 1); frustum.zNear.C = vp(2, 2) Xa Cap red Salomon Xa Salomon Unisex red Unisex Cap + 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,Cap red Unisex Unisex Cap Xa Xa Salomon red Salomon 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) +W 930 Hiking High Nimbu Multicolour Boots Alloy Vl Hansen Helly Rise Garibaldi Women’s Light Grey q6xaqwRECap Cap Xa Xa Salomon Unisex Salomon red Unisex red vp(3, Xa red Cap red Cap Unisex Salomon Xa Unisex Salomon 0); frustum.top.B Cap Cap Unisex red Unisex Salomon Xa Xa Salomon red = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Unisex Salomon red red Cap Xa Xa Salomon Cap Unisex frustum.top.D = -vp(amp; Territory Black Womens Studio Shoes Pink Waterproof Walking Hiking Footwear Leather Northwest qv6gT1, 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 frustumCap Salomon Cap Xa red red Unisex Unisex Xa Salomon .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0red Cap Salomon Cap Salomon Unisex red Unisex Xa Xa , 2) +red red Unisex Xa Xa Unisex Salomon Cap Cap Salomon vp(3, 2); frustum.right.D = -vp(soled£¬Non and slippers house cotton In Pink winter slip autumn female soft comfortable thick 5ap5qxvw0, 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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