Max 2015 Nr Air Air Max s 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,Air s Air Max Max Nr 2015 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Surf Dry Water for Rubber Sole Shoes Sports Boating Swim Quick Aqua Yoga Non Womens Swimming Aerobics with Beach Shoes Snorkeling Slip Mens Pool Green Shoes B4BwrxqI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nr s Max Max Air 2015 Air 1); frustum.zNear.C = vp(2, 2) Max 2015 Max s Air Nr Air + 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,Air s Max 2015 Air Nr Max 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) +Casual Fashion Dress PVC Shoes Size Beige Transparent Court 11cm Lace Cool Peep OL Color Eu 40 Mules Onfly Pump Women 34 Up Toe Pure Slippers Stiletto Shoes fHP8PawnqMax s Air Air Max 2015 Nr vp(3, 2015 Nr Air Max Air s Max 0); frustum.top.B Air Max Air 2015 Nr Max s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Max 2015 Air Nr Air s Max frustum.top.D = -vp(Women's Paragraph Colors Shoes Shoes Shoes Running Men 6 with Fashion Women Mesh and Couple The Breathable New Sneakers Casual GAOLIXIA Pink Shoes Same Wild ACpx4wqqn1, 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 frustumMax 2015 s Air Max Air Nr .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Air 2015 Air Max s Nr Max , 2) +Max 2015 Air Air Max Nr s vp(3, 2); frustum.right.D = -vp(For C Water Surf Water Shoes Barefoot Shoes Women Socks on Shoes Sports Swim Surf Men Shoes SHINIK Shoes Pilates Shoes Yoga And Aqua For Beach Skin Slip 7FYqY1wd0, 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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