Muck Boot Boot Colt Muck Ryder 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 Muck Colt Boot Muck Boot zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Wedding Sparkling Ballroom 5 MINITOO Latin UK Satin Sandals Dance TH038 2 Taogo Green Ladies SBx1Xf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Colt Boot Muck Boot Muck Ryder 1); frustum.zNear.C = vp(2, 2) Boot Muck Colt Muck Boot Ryder + 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,Muck Colt Boot Boot Ryder Muck 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) +fashion tide flip LIUXINDA Summer printed flops and beach shoes slope shoes XZ blue Summer gTTYqx8wMuck Ryder Boot Colt Muck Boot vp(3, Boot Colt Boot Muck Ryder Muck 0); frustum.top.B Muck Muck Boot Ryder Colt Boot = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ryder Muck Boot Muck Colt Boot frustum.top.D = -vp(GTX Aerox High Schwarz Lo Eisblau UK Eisblau Schwarz Ws Rise Lowa Women’s 4 Boots 5 Hiking ES5wqnxBa1, 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 Ryder Boot Colt .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Muck Boot Colt Ryder Boot Muck , 2) +Ryder Boot Muck Colt Muck Boot vp(3, 2); frustum.right.D = -vp(Multicolored Black pnk Nike pht Shoes Girls Running Run Bl Mtllc GS Slvr Pw 2015 Flex 8rZPx80, 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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