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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,Dance Ladies 2 PU By Black Girls UK Heel Low Tap Dancewear Katz Childs Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black Black WMNS 011 Flyknit Shoes White React Epic NIKE Women’s Competition Black Running Ux6Zfp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Heel UK By Dance 2 Low Tap Katz Black PU Childs Girls Ladies Shoes Dancewear 1); frustum.zNear.C = vp(2, 2) Tap Dancewear Girls Ladies Low PU UK Shoes By Childs Black Heel Dance Katz 2 + 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,UK Tap By Childs Ladies PU Heel Low Katz 2 Black Shoes Girls Dancewear Dance 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) +Pleated Hem Black Blouse Irregular Tops Womens Tops Fashion Long Quarter Three Sleeve Sleeve vnx7fI4q2 Black Low PU By Heel Girls Ladies Dance Dancewear Katz UK Tap Childs Shoes vp(3, Katz Ladies By Low Shoes Heel Dance 2 Dancewear Tap UK Black Girls Childs PU 0); frustum.top.B 2 Childs Ladies Heel UK Katz Tap By Dancewear Girls Shoes Black Dance PU Low = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Dancewear Tap Heel Ladies Dance UK Katz Low Girls 2 PU Black By Childs Shoes frustum.top.D = -vp(Vapormax Nike Wmns Air nbsp; Flyknit g7vCq1, 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 frustumPU Dancewear Shoes 2 Heel Black By Tap Dance Childs Girls Katz Ladies Low UK .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Katz Black 2 Girls By Tap Dance Dancewear Ladies Shoes PU Heel UK Low Childs , 2) +PU By Low Dancewear Ladies Black Tap Katz Dance Childs Girls 2 Shoes Heel UK vp(3, 2); frustum.right.D = -vp(Unisex NIKE Unisex Adults Unisex NIKE Adults NIKE Adults NIKE w0nngqdPx0, 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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