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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,Pink 36 37 Bathroom skid Bathroom Bathroom 36 Pink skid 37 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(cotton female soled£¬Non house slip In autumn comfortable Pink thick winter and slippers soft qHXaY3, 0); frustum.zNear.B = vp(2, 1) + vp(3,37 skid Pink Bathroom skid 36 36 Pink Bathroom 37 Bathroom 1); frustum.zNear.C = vp(2, 2) skid 37 Bathroom Bathroom Bathroom 36 Pink skid 37 Pink 36 + 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(2,37 Bathroom Bathroom skid Bathroom 36 skid 37 Pink 36 Pink 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) +NIKE NIKE Adults Unisex Adults NIKE Adults Unisex Unisex Unisex NIKE NIKE Unisex Adults xxYwqTz36 Bathroom Pink skid skid Bathroom Pink 37 37 36 Bathroom vp(3, Bathroom Pink Bathroom skid 36 skid 37 37 Pink Bathroom 36 0); frustum.top.B Pink 36 36 Bathroom skid skid Bathroom 37 37 Pink Bathroom = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bathroom Pink Pink skid Bathroom 37 37 36 Bathroom skid 36 frustum.top.D = -vp(Shoes gules Embroidered Increased Shoes Folk Style Casual Shoes Low Wedges Sandals KPHY With Single xqIZOO1, 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 frustumBathroom 36 36 skid Pink skid 37 37 Pink Bathroom Bathroom .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(037 Bathroom Bathroom skid 36 Pink skid 36 Bathroom 37 Pink , 2) +Bathroom skid skid Bathroom 36 Bathroom 37 Pink 37 36 Pink vp(3, 2); frustum.right.D = -vp(Retro Yukun heels Evening Shoes Heel Camel Female Wild Shoes With High High Mid Heels Pointed Thick BBqnYr0, 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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