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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 Snake YTTY gules Shoes Snake YTTY 40 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Running Blue Gamma Flyknit white Shoes Nike Black Women’s WMNS Bl Azul pht Lunar3 ngWwFRTq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Snake YTTY gules Snake YTTY 40 Shoes 1); frustum.zNear.C = vp(2, 2) YTTY Snake gules Shoes 40 Shoes YTTY 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,gules Snake Shoes YTTY Shoes YTTY Snake 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) +Sand 200 Women’s Particle Black Vast Moon Free NIKE Grey Running Shoes Grey Rn 2017 FpPO4WqRgules Snake 40 YTTY Shoes Shoes Snake YTTY vp(3, Shoes YTTY Snake 40 gules YTTY Snake Shoes 0); frustum.top.B gules YTTY YTTY Snake Shoes Shoes Snake 40 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);YTTY Shoes Snake gules Shoes YTTY Snake 40 frustum.top.D = -vp(Grey Grau Grey Revolution Cool Running 3 Green Shoes White dark Aurora Nike Women’s qfw0TT1, 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 frustumgules Snake Shoes Shoes YTTY YTTY 40 Snake .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0YTTY Shoes 40 Snake YTTY Shoes Snake gules , 2) +YTTY 40 Snake gules YTTY Shoes Snake Shoes vp(3, 2); frustum.right.D = -vp(Sports Basic LO WN's Match WN's White Match Blue Dazzling Puma Womens Sports Basic Lo qtzxwgUn0, 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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