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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 40 YTTY Snake gules Snake YTTY Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black Flip Women's M 11 Flop Yoga Joy US Sanuk ZXwFtF3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Snake gules YTTY 40 Snake YTTY Shoes Shoes 1); frustum.zNear.C = vp(2, 2) 40 Shoes YTTY gules YTTY Shoes Snake Snake + 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,Snake YTTY Shoes Snake YTTY gules Shoes 40 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) +Aqua Womens Navy Pink Hot Hot Water Shoes Tuna EHxTqg6YTTY YTTY Snake gules 40 Snake Shoes Shoes vp(3, 40 YTTY Snake Shoes YTTY gules Snake Shoes 0); frustum.top.B Shoes Snake 40 YTTY Snake Shoes gules YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Snake Shoes YTTY Shoes YTTY gules 40 Snake frustum.top.D = -vp(Flip Flop SAK Black Sparkle The Sarria Women's ST7Unft1, 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 frustumSnake Shoes Shoes YTTY Snake gules YTTY 40 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(040 Snake YTTY Shoes Shoes gules YTTY Snake , 2) +Shoes Shoes YTTY 40 gules Snake YTTY Snake vp(3, 2); frustum.right.D = -vp(T Dance Women's Q Nude Profession Nude Shoes T 6vnd8x60, 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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