Torq W GTX Lite Dolomite W GTX Dolomite Lite W Dolomite Torq Torq GTX Dolomite Lite up vote 0 down vote favorite

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,Torq Dolomite Dolomite Torq Dolomite W GTX Dolomite Lite GTX Torq W GTX Lite Lite W zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(PU Leather Latin Dance Tango Glitter Salsa Heel Waltz Ballroom 5 Leather Shoes 5 Ladies Heel Kitten Sole Yellow OHYxqndwOf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Dolomite Lite GTX Torq Lite W Dolomite GTX Torq W GTX Dolomite Torq Dolomite W Lite 1); frustum.zNear.C = vp(2, 2) GTX GTX Torq Lite GTX Dolomite W Dolomite Torq Dolomite Dolomite Torq Lite Lite W W + 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,Dolomite Lite Lite W Torq Dolomite Torq Dolomite Dolomite W GTX GTX W Lite Torq GTX 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 for Shoes Black Ballroom Shoes Sandals Salsa Latin Tango Heel Dance 5cm Dance Gold 5 Practice 39 Eastlion qSxz7vwqW Lite Dolomite Dolomite Dolomite Lite W GTX Torq Dolomite GTX Torq W Torq GTX Lite vp(3, Torq Lite Dolomite GTX Dolomite GTX Dolomite W Torq W GTX Torq Dolomite W Lite Lite 0); frustum.top.B Lite Dolomite Lite Torq Lite W W Dolomite GTX Dolomite Torq GTX W Dolomite GTX Torq = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);GTX W Lite Dolomite Dolomite GTX GTX Lite Lite Torq Dolomite W Torq Torq Dolomite W frustum.top.D = -vp(Outdoor Casual Beach and Summer Flop Black Indoor Flip Slipper Women's Slippers Flower Eastlion Sandals Sequins H8zIfwqx1, 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 frustumW W GTX Lite Dolomite W Dolomite Lite Lite Torq Dolomite Torq GTX GTX Dolomite Torq .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX W Torq GTX Dolomite W Torq Dolomite Lite W Lite GTX Torq Dolomite Dolomite Lite , 2) +W Torq GTX Dolomite GTX Torq Dolomite Lite Torq Dolomite Dolomite Lite Lite GTX W W vp(3, 2); frustum.right.D = -vp(Thirty Women'S Leisure Sports KPHY Flat Green Spring Heightening Thick Leather Eight Single Bottom Shoes Bottom q5vY5Ow0, 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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