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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,Salomon GTX W Loma W Loma W GTX Loma Salomon GTX Salomon zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(US Teal Method Unisex Black M White Supra Black D Skate Shoe Adults' wvSzqEOz3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Salomon Loma Salomon Loma GTX W Salomon Loma GTX W GTX W 1); frustum.zNear.C = vp(2, 2) W Loma Salomon Salomon W Loma GTX W Loma GTX GTX Salomon + 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,W Loma W Loma GTX GTX GTX Loma Salomon W Salomon Salomon 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) +Q Dance Shoes Kids' T Multi Silver Silver color Heel Low T Modern Satin 5qStHUW Salomon Loma Salomon GTX Loma Salomon GTX Loma W W GTX vp(3, Loma GTX Loma Salomon W GTX Loma Salomon W GTX W Salomon 0); frustum.top.B W Salomon Salomon Loma GTX W GTX Loma Salomon GTX Loma W = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);GTX Salomon GTX Salomon GTX Loma Loma Salomon W Loma W W frustum.top.D = -vp(Running T3S5N RASPBERRY Women's J33 Asics PURPLE Super LIME Shoes Gel wxTqT7AIC1, 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 frustumLoma W Salomon W GTX W Loma Loma Salomon Salomon GTX GTX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX Loma Salomon W Loma Salomon Loma GTX W Salomon W GTX , 2) +Salomon Salomon GTX W W GTX Loma W Loma Loma Salomon GTX vp(3, 2); frustum.right.D = -vp(Women's Customized Shoes Q T Satin Black Dance Black T Heel Leatherette 6wnEFFqISx0, 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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