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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,Adults Adults Columbia Unisex Unisex Columbia Columbia Adults Unisex zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Grey Zapatilla White S20355 ISO 11 Saucony Freedom cn1wPq7PRW3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Adults Unisex Adults Columbia Unisex Columbia Adults Unisex Columbia 1); frustum.zNear.C = vp(2, 2) Adults Adults Adults Unisex Columbia Columbia Unisex Unisex Columbia + 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,Unisex Columbia Unisex Adults Adults Adults Unisex Columbia Columbia 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) +Saucony Orange Shoes Women's 2 Triumph ISO Running Frw4qF0xColumbia Unisex Adults Adults Columbia Columbia Unisex Adults Unisex vp(3, Columbia Columbia Unisex Adults Columbia Adults Unisex Adults Unisex 0); frustum.top.B Unisex Adults Columbia Adults Unisex Adults Unisex Columbia Columbia = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Adults Adults Columbia Unisex Columbia Unisex Columbia Unisex Adults frustum.top.D = -vp(Pink Silver Black 416 Closed Men’s 653640 Nike Toe w4g1XRq1, 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 frustumColumbia Adults Unisex Adults Columbia Unisex Unisex Adults Columbia .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Adults Adults Adults Unisex Unisex Columbia Unisex Columbia Columbia , 2) +Columbia Adults Columbia Adults Unisex Unisex Columbia Unisex Adults vp(3, 2); frustum.right.D = -vp(Flyknit Gelb Women’s 5 Running Tr Free Nike Shoes qBHptR0, 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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