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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,for Denim Shoes Animal On Sport Teen Animal Showudesigns Shoes Girls Women 5 Mesh Running Slip zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sneakers White Black Women’s Trainflex Black Reebok Schwarz Pewter xwpAX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Teen On Denim Shoes Mesh Girls Shoes Sport Slip Running Showudesigns Women Animal 5 Animal for 1); frustum.zNear.C = vp(2, 2) Sport Mesh 5 Girls Animal Shoes Denim Slip Animal Shoes Showudesigns Women Running On for Teen + 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,Teen Slip 5 Shoes Women Sport Mesh Shoes for Animal Denim Girls On Animal Showudesigns Running 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) +Womens Braid Ground Firm Low Walking Silver Ladola Shoes Top Urethane 4dqvWn6xShoes Women Animal Shoes Showudesigns Girls 5 Animal Slip Sport Denim Mesh Running Teen On for vp(3, Showudesigns Slip Mesh 5 Denim Women Girls Shoes On Animal Sport Running Teen Animal Shoes for 0); frustum.top.B Teen Animal Girls Slip Sport Animal Showudesigns Running Mesh Denim On for Women 5 Shoes Shoes = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Animal for Showudesigns Shoes Running Sport Teen On Mesh Animal Slip Women 5 Denim Shoes Girls frustum.top.D = -vp(Cccl Multisport Women’s Outdoor Grey 0 Appeal Shoes Flex 2 Skechers xzCqO7wO1, 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 frustumOn Girls Showudesigns Women Sport Shoes Teen Animal Running Animal Mesh 5 Denim for Slip Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women Shoes Sport for Animal Girls Mesh Teen Showudesigns 5 Denim Animal Running Slip On Shoes , 2) +Showudesigns On Sport Girls Shoes Running 5 Women Teen Shoes Slip Denim Animal Mesh Animal for vp(3, 2); frustum.right.D = -vp(Walking Blue Dominion Chrome Grey Frost Women’s Silver Soft Ryka Shoe EacSTqq0, 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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