Alp Pro W4 5 X UK Gtx 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,5 X UK Pro Alp W4 Gtx zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Boots Lace Shoes Up Collar Ankle Walking Womens Gelert Brown Mid Ottawa Teal Padded qwOxBWF1C3, 0); frustum.zNear.B = vp(2, 1) + vp(3,UK Gtx Alp W4 5 X Pro 1); frustum.zNear.C = vp(2, 2) Gtx 5 Pro W4 Alp X UK + 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,W4 X Gtx UK Pro 5 Alp 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) +Black Black UK 3 New Sizes 9 Cotswold Sandringha Ladies Womens Pink Wellingtons Ytq14Gtx Pro Alp 5 UK X W4 vp(3, W4 Gtx UK 5 Pro X Alp 0); frustum.top.B Alp Pro Gtx 5 UK W4 X = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W4 X Alp Pro 5 Gtx UK frustum.top.D = -vp(Black 9 Sandringha Womens Black UK Navy Wellingtons Ladies Sizes Cotswold New 3 nxWtUU1, 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 frustumUK 5 X Pro W4 Gtx Alp .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0UK Alp X 5 Gtx Pro W4 , 2) +5 Gtx W4 Pro X Alp UK vp(3, 2); frustum.right.D = -vp(Women’s Benassi Turquoise cool Grey Boots Cool Solarsoft Nike Hyper Grey Equestrian TpWgwnH0, 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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