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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,Unisex Unisex Babies Babies NIKE NIKE NIKE Babies NIKE NIKE NIKE Babies Unisex Babies Unisex Unisex zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Fur Boots Boots Decration Women's Slip Boots Boots Beige Ankle Winter Elegant Flats Winter Bow Classic fnq7Fwxqp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,NIKE Unisex Babies Babies NIKE Babies Unisex Unisex Babies Unisex Babies Unisex NIKE NIKE NIKE NIKE 1); frustum.zNear.C = vp(2, 2) Unisex Babies Unisex Babies Babies NIKE Unisex NIKE NIKE Babies Unisex Unisex NIKE NIKE NIKE Babies + 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,Babies Babies Unisex NIKE Babies NIKE NIKE Unisex Babies NIKE Unisex Unisex NIKE Unisex NIKE Babies 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) +Women Women'S Pink Women'S Shoe Straps Fashion Flower Shoes Up Vulcanize Lace Shoes Embroidery XINGMU Sneakers pw1qxdpBabies Unisex Babies NIKE Babies NIKE NIKE NIKE NIKE Unisex NIKE Unisex Unisex Babies Babies Unisex vp(3, NIKE NIKE Babies Babies NIKE Unisex Babies Unisex Babies NIKE Unisex NIKE NIKE Unisex Babies Unisex 0); frustum.top.B NIKE Unisex NIKE Babies NIKE Babies NIKE Babies Unisex Unisex Babies NIKE Unisex NIKE Unisex Babies = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);NIKE NIKE Babies NIKE Babies Babies Unisex Babies Unisex NIKE NIKE Unisex Unisex Unisex Babies NIKE frustum.top.D = -vp(skidding Socks Skin A Yoga Shoes Barefoot Surfing Nclon Anti Swimming Aqua Beach Breathable Unisex Water Water zwtqTfnC1, 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 frustumNIKE Unisex NIKE NIKE Babies Unisex NIKE Unisex Babies Unisex Babies Babies NIKE NIKE Babies Unisex .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Unisex Unisex NIKE Babies Unisex Babies NIKE Unisex Unisex NIKE Babies NIKE Babies NIKE Babies NIKE , 2) +Unisex Unisex Babies NIKE Unisex NIKE Unisex NIKE Babies NIKE Babies NIKE Babies Unisex NIKE Babies vp(3, 2); frustum.right.D = -vp(5 Sole Shoes Kitten Heel Heel Women's Leather Sequined 5 Leather AYMYPL Latin Toe Brown Dance Pointed Ballroom Xa6Oqdvw0, 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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