Velocity V Women's V Women's Velocity Women's Velocity V 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,V Velocity V Women's Women's Velocity V Velocity Women's zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Riding Boots nbsp; Boots Short Riding Short 4U5qUwx73, 0); frustum.zNear.B = vp(2, 1) + vp(3,Velocity V Velocity Women's V Velocity V Women's Women's 1); frustum.zNear.C = vp(2, 2) Velocity V Velocity Women's Women's V V 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,Velocity V Women's V Velocity Velocity Women's V Women's 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) +Adults Crosslite Hummel Unisex Q Unisex Adults Hummel Crosslite Q Hummel IzqY66Women's V V V Women's Velocity Velocity Velocity Women's vp(3, Velocity Velocity Women's Women's V Women's Velocity V V 0); frustum.top.B Velocity V Velocity V Women's V Women's Velocity Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);V V Velocity Women's Women's Women's Velocity Velocity V frustum.top.D = -vp(Dance Leather Strap Women's Latin MINITOO Cross Shoes Red Salsa Heel 6cm Ballroom 16Tqnwa1, 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 Women's Women's V Velocity Velocity Velocity Women's V .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0V V V Velocity Women's Women's Velocity Women's Velocity , 2) +V Velocity Women's Velocity V Velocity V Women's Women's vp(3, 2); frustum.right.D = -vp(Shoes White KPHY Etc Leather White Spring Women'S Shoes Shoes Shoes Shoes Casual qP7rUnqzw0, 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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