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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,blue slippers dark 44 antiskid Indoor bathroom striped 43 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(nine Cat Heads Heels 5Cm Shoes Fine Pointy High Heels Shoes LBTSQ Heel Jigs Thirty Middle And Coloring Single 7FwTx8qv3, 0); frustum.zNear.B = vp(2, 1) + vp(3,blue slippers dark 43 bathroom striped Indoor antiskid 44 1); frustum.zNear.C = vp(2, 2) dark striped slippers 44 bathroom 43 Indoor antiskid blue + 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,antiskid 43 bathroom slippers Indoor dark 44 blue striped 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) +Comfort Black Up Shoes Women's Flat Spring Fall Lace Round Heel 37 Black Toe Sneakers Canvas White Espadrilles HRx4qAIwslippers striped 44 antiskid 43 bathroom dark Indoor blue vp(3, Indoor 43 striped slippers 44 blue antiskid bathroom dark 0); frustum.top.B blue 44 bathroom dark striped antiskid Indoor slippers 43 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);dark blue striped bathroom slippers 44 43 Indoor antiskid frustum.top.D = -vp(Pool Yoga Water Shoes Surf Beach Socks Quick Cosstars for Aqua Shoes Water Aerobics Dry Swim Shoes Mens Womens ZRqw6dxPw1, 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 frustum44 43 Indoor striped antiskid bathroom slippers dark blue .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0blue Indoor dark 44 slippers striped antiskid bathroom 43 , 2) +antiskid blue 43 dark 44 striped bathroom Indoor slippers vp(3, 2); frustum.right.D = -vp(Espadrilles White Up 37 Black Fall Lace Canvas Toe White Shoes Flat Comfort Women's Sneakers Spring Heel Round OX7nq0, 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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