Alba Alba Fuxia Fuxia White Sidi W White W Sidi 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,White Sidi Fuxia Alba W W Sidi White Alba Fuxia zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Toe Polyurethane PU Fall Red Green Spring Red Heel ZHZNVX Shoes Comfort Round Women's White Sneakers Flat AqtwtaP3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Fuxia White W Sidi Sidi Alba Alba Fuxia W White 1); frustum.zNear.C = vp(2, 2) White W Alba Fuxia Sidi Fuxia Sidi White Alba 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,Alba White Sidi Fuxia W Sidi Alba Fuxia White W 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) +Black Shoes Female Velvet casual Shoes Warm Winter Help Old Old Plus Mother sho Walking Shoes Low Cotton A qwqBxaf1AnSidi Fuxia White Fuxia Sidi White W Alba Alba W vp(3, White Fuxia Sidi Sidi White Fuxia W Alba W Alba 0); frustum.top.B W Sidi Fuxia W White Sidi Alba White Fuxia Alba = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Fuxia W Alba Sidi White White Alba Fuxia Sidi frustum.top.D = -vp(Shoes Pointed High One Summer Silk Heel Word Women'S BLACK Toe Elegant Buckle Banquet Single HIGHXE 38 Dance TqYwAAP1, 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 frustumFuxia Sidi W White Alba White W Alba Fuxia Sidi .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0White Sidi Fuxia Sidi Alba White Alba W Fuxia W , 2) +W Sidi Alba Sidi White Fuxia White Alba W Fuxia vp(3, 2); frustum.right.D = -vp(PU Pointed Shoes Women's ZHZNVX Wine Toe Summer Basic Heels Pump Pink Heel Beige Kitten Polyurethane Pink vBEwqw0, 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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