V Women's Women's V V Velocity Women's Velocity Velocity 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,Women's V Women's Velocity Velocity Women's V V Velocity zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Work Fine Shoes 36 Suede Leisure Lady High Heels Heads MDRW Women'S Pink Elegant Shallow Spring 10Cm Sharp Heels Single Shoes 8qwEqnOH3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women's Women's Velocity V Velocity Velocity V V Women's 1); frustum.zNear.C = vp(2, 2) Velocity Velocity V V V Women's Women's Women's Velocity + 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,V Women's Velocity V Women's V Women's Velocity Velocity 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) +High Heels Shoes Shoes Fine Spring Black Shallow 7Cm MDRW Heels Sharp Leisure Elegant Shoes Lady Fashion 39 Shoes Work Single q1P7TVelocity V Women's Women's Velocity Velocity V V Women's vp(3, Women's Women's Velocity Velocity V V Velocity V Women's 0); frustum.top.B Velocity Velocity V Women's Women's Women's Velocity V V = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);V Velocity Velocity V Velocity V Women's Women's Women's frustum.top.D = -vp(Flat 1 3 Black Women'S Light Flats Light US5 CN35 UK3 4In Heel Soles Cowhide Ruby Soles Winter 1In Casual 5 EU36 Fall 5 wz6wfZ7q1, 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 frustumV V V Velocity Women's Women's Velocity Velocity Women's .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women's Velocity Women's V V Women's V Velocity Velocity , 2) +Women's Velocity Women's V Women's V Velocity Velocity V vp(3, 2); frustum.right.D = -vp(high waterproof black fashionable Thirty 11cm thin buckles LBTSQ shoes women's high table heel and Super heeled sandals four HxUqwfA50, 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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