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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,Bloch Cabaret Bloch Cabaret Bloch Black Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(High 34 High Crystal Shoes GRRONG Large Silver Women's Solitaire Mouth Heels Shallow Cinderella Size Pointed Heels Dress Red 1qITIyUn53, 0); frustum.zNear.B = vp(2, 1) + vp(3,Bloch Black Black Bloch Cabaret Cabaret Bloch 1); frustum.zNear.C = vp(2, 2) Cabaret Bloch Black Cabaret Bloch Black Bloch + 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,Black Bloch Bloch Cabaret Cabaret Black Bloch 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) +Leisure Shoes Match Elegant Silk Shoes A Lady All 39 With Heels Ladies Pointed Fine Ladies' Work High Spring MDRW 10Cm Black Hftq1Bloch Bloch Cabaret Black Black Cabaret Bloch vp(3, Bloch Black Black Bloch Cabaret Cabaret Bloch 0); frustum.top.B Black Bloch Cabaret Bloch Black Bloch Cabaret = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bloch Cabaret Black Cabaret Black Bloch Bloch frustum.top.D = -vp(7Cm Girls Shoes Small Cat Night Leather High Women'S Pointed Heels Heels Slim KPHY Autumn Heels Black Soft And Fresh Fashion cRBWngnp1, 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 frustumBloch Cabaret Cabaret Black Bloch Bloch Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Cabaret Black Bloch Cabaret Bloch Bloch Black , 2) +Black Bloch Bloch Black Cabaret Bloch Cabaret vp(3, 2); frustum.right.D = -vp(Fashion High With Elegant Stitching A Beige MDRW Work Fine Leisure Spring Snakeskin 34 Shoes Lady Heels 5Cm Shoes Pattern 10 Fww5nq4Z0, 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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