Muck Muck Ryder Boot Colt Boot 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,Ryder Boot Muck Colt Boot Muck zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Electric Steel Flextra Shoe Training Silver Women's Metallic Ryka Grey Coral Chrome Bougainvillea 6p0qSvZSw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Muck Boot Ryder Muck Colt Boot 1); frustum.zNear.C = vp(2, 2) Muck Muck Ryder Boot Boot Colt + 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,Ryder Boot Muck Muck Boot Colt 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) +Closed Women's Heel toe Ballroom Dance Misu Suede Latin 2 Tango Salsa 3" with Practice Shoes Sole 45qdAwwBoot Muck Ryder Boot Colt Muck vp(3, Boot Colt Boot Muck Ryder Muck 0); frustum.top.B Muck Boot Colt Muck Ryder Boot = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Boot Colt Boot Muck Muck Ryder frustum.top.D = -vp(001 Women’s Trail Black Shoes 861656 Grey Nike Multicoloured Metallic Running Dark Hematite fBqg7wxpwy1, 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 frustumBoot Muck Muck Boot Ryder Colt .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Colt Ryder Boot Boot Muck Muck , 2) +Muck Colt Muck Boot Boot Ryder vp(3, 2); frustum.right.D = -vp(Shoes Singles Shoes Pointed Women'S Thick Forty The Heeled High New Spring Work Leather With KPHY qgH0zx0, 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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