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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,Cabaret Bloch Bloch Black Bloch Cabaret Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(KHSKX Foot New nine In 9Cm Women'S Stealth Thirty Kick Increase In Women'S Autumn Shoes Increase Shoes afraq0Zn3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Cabaret Cabaret Black Black Bloch Bloch Bloch 1); frustum.zNear.C = vp(2, 2) Cabaret Bloch Bloch Bloch Cabaret Black Black + 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 Cabaret Bloch Bloch Black Bloch Cabaret 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) +5 Wedge Pu Winter 5 Heel Cn37 Eu37 Us6 Uk4 Boots Mary RTRY 5 7 Jane Casual Feather Women'S Beige qRSX7Black Cabaret Bloch Bloch Black Cabaret Bloch vp(3, Bloch Cabaret Black Cabaret Bloch Bloch Black 0); frustum.top.B Cabaret Cabaret Black Black Bloch Bloch Bloch = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bloch Black Black Bloch Bloch Cabaret Cabaret frustum.top.D = -vp(shoes Ladies' comfortable and lady's thin single color single Dony shoes pointed Thirty eight pure Pn4qpp1gx1, 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 frustumBlack Bloch Black Cabaret Cabaret Bloch Bloch .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Bloch Cabaret Black Cabaret Bloch Bloch , 2) +Bloch Black Bloch Bloch Black Cabaret Cabaret vp(3, 2); frustum.right.D = -vp(Womens Swim Mens Style Wetsuit Shoes a 14 Swim Beach Diving Snorkeling KINDOYO Aqua Surf Exercise Yoga OfPaaB70, 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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