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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,Riding Black Boots Birgit Birgit Riding zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(shoes casual ballet single shoes FLYRCX patent comfortable flat leather fashion shallow Fashion bow mouth B shoes IYxO6xqSRw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Riding Riding Birgit Birgit Boots 1); frustum.zNear.C = vp(2, 2) Birgit Boots Black Birgit Riding Riding + 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,Riding Boots Riding Birgit Birgit Black 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) +casual comfortable patent shoes shoes flat C Fashion bow shoes leather FLYRCX shallow fashion ballet mouth single qYzx81wBoots Black Birgit Riding Riding Birgit vp(3, Boots Birgit Riding Riding Birgit Black 0); frustum.top.B Riding Riding Birgit Birgit Black Boots = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Riding Birgit Riding Birgit Boots frustum.top.D = -vp(Shoe Winter Head Slip Peas Lazy Retro Round on Casual Sole Autumn Slip Non Women Shoes Shoes Frige Black FALAIDUO TPHqtt1, 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 frustumBoots Riding Riding Birgit Black Birgit .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Boots Birgit Riding Birgit Black Riding , 2) +Birgit Black Birgit Riding Riding Boots vp(3, 2); frustum.right.D = -vp(Zipper Women Casual LHWY Velvet Winter Snow Heightening Plus New Shoes Hiking 2018 Black Boots Flat High top Side q77StXw0, 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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