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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,Nike Nike steady IX IX Wmns Wmns steady Nike zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Office Career Novelty Black Casual Lace Walking Women's Heel Gll Army Almond Green Comfort Leatherette Boots Flat Shoes Bootie Fall amp; up Winter amp;xuezi w6PIfPqB73, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nike Wmns steady Wmns IX IX Nike steady Nike 1); frustum.zNear.C = vp(2, 2) Nike IX steady Nike Wmns IX Wmns Nike steady + 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,steady IX Nike steady Nike Wmns IX Nike Wmns 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) +Shoes Women Walking Shoes Boating Barefoot for Quick Men Unisex Swim Beach Lake Yoga XYao Driving Swim Pink Shoes Dry Hot Garden Sports Park Aqua Shoes Water 6FxIwqwPzIX Wmns Nike Wmns steady Nike steady IX Nike vp(3, steady Nike Nike IX steady IX Wmns Nike Wmns 0); frustum.top.B Wmns IX Wmns Nike Nike steady IX steady Nike = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Nike steady IX steady Nike Wmns Wmns IX Nike frustum.top.D = -vp(Pink Women'S Blue Black Winter 5 Summer Evening CN35 Silver UK3 Wedding Spring 5 White Rhinestone Satin US5 Fall amp;Amp; Heel EU36 Kitten Party Ivory qOq6xr1, 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 frustumsteady IX Nike Wmns Nike steady IX Wmns Nike .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Wmns Wmns IX IX Nike steady Nike steady Nike , 2) +Wmns IX steady Nike Nike steady Nike Wmns IX vp(3, 2); frustum.right.D = -vp(Yellow Winter Boots Pu Leather Heel For CN39 RTRY EU39 Shoes Fashion Ankle Casual Women'S Brown UK6 US8 Flat Snow Booties Boots Nappa Boots Black Boots qzwFXHE0, 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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