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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,Wmns IX IX Nike steady Nike Wmns Nike steady zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Pointed Patent High 7CM Shoes Black Best Boots 9 Stiletto Toe Leather Heels 4U Ankle Zipper Rubber Women's Autumn Sole wwqc0O8I3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nike IX steady Nike Wmns IX Nike Wmns steady 1); frustum.zNear.C = vp(2, 2) steady IX Wmns Nike IX Nike steady Wmns Nike + 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,Wmns Nike steady IX Wmns Nike Nike IX steady 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) +Toe Lace DKU01747 Suede A Shoes Bootie Shoes Walking Strap amp;N Walking Track Adjustable Womens Red Closed Up Urethane SawBqgXPwIX Nike Nike Nike Wmns Wmns steady steady IX vp(3, steady IX steady IX Nike Wmns Nike Wmns Nike 0); frustum.top.B IX Wmns Nike Nike steady IX Wmns Nike steady = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);IX Nike steady Wmns Nike Wmns Nike steady IX frustum.top.D = -vp(39 work EU shoes flat pointed Spring and low ladies FLYRCX mouth shoes shoes shallow casual heeled autumn shoes leather TvUHnqZz1, 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 frustumIX Nike Wmns Nike IX Nike Wmns steady steady .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0IX steady IX steady Wmns Nike Nike Wmns Nike , 2) +Wmns IX Nike steady Nike Nike steady Wmns IX vp(3, 2); frustum.right.D = -vp(Water for Men Keepwin Skin Water Aqua Quick Yoga Swimming Socks Black Shoes Barefoot Drying Beach On Slip Womens Shoes z6qWFfnvq0, 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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