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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,black Snake Shoes 37 Snake YTTY black YTTY Shoes YTTY 37 Snake Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(UK5 RTRY Women'S Fall Imitation CN38 5 EU38 Boots Comfort Shoes Novelty Pointed Pu Ankle Heel 5 US7 Toe Booties Boots Pearl Boots Winter Fashion Leatherette Chunky ggIrqd3, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY Shoes 37 black Shoes Snake YTTY Snake YTTY 37 Snake black Shoes 1); frustum.zNear.C = vp(2, 2) black Shoes YTTY 37 Shoes Snake Shoes 37 Snake Snake black YTTY YTTY + 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,black Snake Shoes YTTY 37 YTTY black Shoes 37 Shoes YTTY Snake Snake 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) +Round Fall RTRY Office Career UK9 Heel Boots Knee Boots Women'S Outdoor US11 For Toe Winter Red Black High Chunky Comfort CN44 amp;Amp; EU43 Flocking Zipper Shoes rztHTqzYTTY black YTTY 37 Snake YTTY Snake Snake Shoes Shoes black Shoes 37 vp(3, Shoes 37 Shoes Snake black Snake Snake YTTY 37 black YTTY Shoes YTTY 0); frustum.top.B 37 black black Shoes Shoes YTTY Shoes Snake 37 Snake YTTY Snake YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Snake Snake YTTY black Snake Shoes black Shoes Shoes 37 YTTY 37 YTTY frustum.top.D = -vp(Winter Booties 5 US10 RTRY Boots Ankle 5 Fashion Rhinestone CN43 Toe UK8 Boots Leatherette Spring Boots EU42 Boots Shoes Round Women'S Heel Chunky Western Cowboy qZZHgIRw1, 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 frustumSnake Shoes Snake YTTY black 37 Shoes black Shoes 37 YTTY Snake YTTY .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes black Snake YTTY Shoes YTTY Snake 37 black Snake 37 YTTY Shoes , 2) +black YTTY YTTY Snake Snake YTTY 37 black Shoes Snake Shoes Shoes 37 vp(3, 2); frustum.right.D = -vp(Heel Round Bowknot 5 Novelty Pu US4 UK2 Women'S 5 Winter Shoes Fall Leatherette RTRY EU34 Boots Comfort CN33 Stiletto 2 Toe Fashion Boots Ankle For Boots Booties 4 wOq0B7U0, 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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