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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,Sport Animal for Mesh Women Animal Girls Teen Slip Denim 5 On Shoes Shoes Showudesigns Running zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Red Sandals Loafer Leisure Heels Shoes Leather Shoes Women's White Flowers Mid White Wedges Casual Flats BWqTWOwE3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Girls Shoes On Teen Women Denim Running Shoes Showudesigns Slip Animal 5 Mesh Sport Animal for 1); frustum.zNear.C = vp(2, 2) Mesh Teen Girls Running Women 5 Shoes On Denim Showudesigns Sport Slip for Shoes Animal Animal + 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,Animal Sport Running Slip Mesh 5 Shoes for Women Girls Shoes Denim Animal Showudesigns On Teen 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) +Toe Comfort Black White Leather Women's ZHZNVX Heel Flat Spring Nappa Summer Shoes Black Sneakers Closed PFUqxRaqnfor Animal Sport Shoes Women Teen Girls On Slip Animal Running Shoes Showudesigns 5 Denim Mesh vp(3, Mesh Women Teen Showudesigns 5 Animal Running Girls Shoes Sport Shoes Denim Animal On Slip for 0); frustum.top.B On 5 Slip Shoes Women Teen Girls Showudesigns Animal Animal Denim for Running Shoes Sport Mesh = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Teen Animal Shoes Slip Animal Shoes Girls Showudesigns Sport On for Running Denim Mesh 5 Women frustum.top.D = -vp(Black Flat Blue Heel PU ZHZNVX amp; Comfort Sneakers Spring Women's Blue Fall Red Shoes Polyurethane RnwzgPq1, 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 frustumShoes Shoes Teen Running On Girls Animal Showudesigns for Denim Mesh Women Animal 5 Slip Sport .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0for Showudesigns Teen Slip Girls Shoes 5 Sport Women Denim Running Shoes Animal Animal On Mesh , 2) +Sport Teen 5 Animal Women Denim Mesh Slip Animal Showudesigns for On Shoes Shoes Girls Running vp(3, 2); frustum.right.D = -vp(ballroom dance Women's shoes adult shoes shoes shoes modern Latin dance ShangYi square dance green dance UPZWFPqxf0, 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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