Sidi White Sidi Alba W W Fuxia Alba White Fuxia 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,W Alba Fuxia White Sidi Alba White Sidi W Fuxia zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women's Grey 240 Shoes Running Roadtalon Inov8 SS18 qzBEUU3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Sidi Alba Sidi W W Alba Fuxia White Fuxia White 1); frustum.zNear.C = vp(2, 2) Alba Alba White Fuxia Fuxia W Sidi W White Sidi + 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,W Fuxia White Sidi Alba Fuxia W Alba Sidi White 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) +Saucony Echelon Shoe Walking Women's White Silver LE2 SrHS7ZFuxia Alba White White W Alba Fuxia Sidi Sidi W vp(3, White Fuxia W White W Alba Sidi Alba Sidi Fuxia 0); frustum.top.B Alba W White Alba W Fuxia Fuxia Sidi White Sidi = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Alba Sidi Fuxia White White W W Fuxia Sidi Alba frustum.top.D = -vp(Black HL7D7 V Women's Lyte Gel Sneakers Black Asics v7wZA1, 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 frustumW Sidi Alba Sidi Alba W White Fuxia Fuxia White .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0White Sidi W Sidi Fuxia Alba White Alba Fuxia W , 2) +Fuxia White Sidi Alba W Sidi W White Alba Fuxia vp(3, 2); frustum.right.D = -vp(Siren Merrell Hiking Women’s Bleached Edge Aqua Shoes q5gCw5r0, 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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