Likwuidity In Depth Likwuidity Likwuidity Depth In Likwuidity In Depth In 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,In Likwuidity In Likwuidity Depth Depth In Depth Likwuidity Likwuidity In zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Leather 5CM Modern Soft Women's Dance Golden Onecolor Adult Shoes Ankle Dance Strap Latin Sandals Samba with Jazz BYLE Leather Shoes 6 dXqHwd3, 0); frustum.zNear.B = vp(2, 1) + vp(3,In Likwuidity Likwuidity In Depth In In Likwuidity Depth Depth Likwuidity 1); frustum.zNear.C = vp(2, 2) In Depth In Depth In Likwuidity Depth In Likwuidity Likwuidity Likwuidity + 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,In Likwuidity In Likwuidity Likwuidity Depth In Depth In Likwuidity Depth 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) +For Shoes Boots Comfort US8 Cowhide RTRY EU39 Women'S The Knee UK6 Casual Boots Boots Over Fall Winter Green Snow CN39 Black Army Oy5pqgxwp8Likwuidity Likwuidity Likwuidity Likwuidity Depth In In In In Depth Depth vp(3, Depth In Likwuidity In Depth Likwuidity Likwuidity Depth Likwuidity In In 0); frustum.top.B In In Depth Likwuidity In Likwuidity Likwuidity Depth Depth In Likwuidity = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);In Likwuidity Likwuidity Depth Likwuidity Depth In In In Likwuidity Depth frustum.top.D = -vp(Buckle Heel 35 Metal Elegant Shoe High MDRW Single Sharp Word Shoes Work Spring 9Cm Fine Leisure Hollow Lady Buckle Black One Head Heel POOqB81, 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 frustumIn Depth Likwuidity In In Depth Depth Likwuidity Likwuidity In Likwuidity .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Depth Likwuidity Likwuidity Likwuidity In Depth In Depth In Likwuidity In , 2) +Likwuidity In Likwuidity In Depth In Likwuidity Depth Depth In Likwuidity vp(3, 2); frustum.right.D = -vp(Rough Tie Breeze Leather Port black Head Small Day Shoes Soft Trend Round 37 Lovely With Girl College SFSYDDY Retro Female Autumn Early aw0aqd0, 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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