ASICS Women's 3 E358Y GEL DEDICATE Tennis Shoes 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,ASICS Women's 3 Tennis GEL DEDICATE E358Y Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(amp; Unisex New Women's Hand Shoes Sport Shoes 2018 Men's Casual Fashion Woven Black ETqn4Hw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ASICS DEDICATE GEL E358Y Women's 3 Shoes Tennis 1); frustum.zNear.C = vp(2, 2) E358Y Tennis GEL Shoes 3 Women's ASICS DEDICATE + 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,Tennis Shoes Women's DEDICATE E358Y ASICS 3 GEL 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) +Mid W nbsp; Flyers Boreal Shoes 'S Sport F5pn0q7Shoes DEDICATE ASICS 3 Women's Tennis GEL E358Y vp(3, Women's GEL Shoes Tennis ASICS 3 DEDICATE E358Y 0); frustum.top.B E358Y GEL Women's Tennis DEDICATE Shoes ASICS 3 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);GEL Shoes DEDICATE Women's E358Y Tennis 3 ASICS frustum.top.D = -vp(White 2 Speedlux Running Reebok Shoes Sour Grey Women’s Mellon Alloy Pewter 0 AqW7Ev71, 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 frustumTennis E358Y Shoes ASICS Women's 3 DEDICATE GEL .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GEL Tennis Shoes DEDICATE ASICS E358Y Women's 3 , 2) +3 DEDICATE GEL Shoes Tennis ASICS Women's E358Y vp(3, 2); frustum.right.D = -vp(Spring Women's Almond Black Heel Almond Pump Heels ZHZNVX Gray Stiletto Suede Basic 6EBnATWTc0, 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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