Skate White Artisan I Shoes Black Path 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,White Black I Path Artisan Shoes Skate zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Gray Square Strap Heel Shoes Flat Round Boots Holywin Non Classic Zip Martin Slip Womens Toe wnRqH6x3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes White Artisan I Path Black Skate 1); frustum.zNear.C = vp(2, 2) Black I Skate Artisan Path White Shoes + 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,Skate Shoes I White Path Black Artisan 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) +5 UK Dance Leather Heel MINITOO High L194 Latin Black 7 Women's Sandals Suede Salsa Ballroom vqnO6ZgHwBlack I Artisan Skate White Shoes Path vp(3, Black Skate Path White Shoes I Artisan 0); frustum.top.B White Artisan Skate Black I Shoes Path = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Skate Path Shoes White I Black Artisan frustum.top.D = -vp(ZHZNVX Beige Women's Heels Pink Beige Chunky Comfort Heel Shoes Black Spring Nappa Leather SSqrp1, 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 frustumBlack Artisan Shoes Skate I White Path .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0I White Artisan Black Skate Path Shoes , 2) +Artisan Black I Shoes Path Skate White vp(3, 2); frustum.right.D = -vp(white Trend Casual Shoes Autumn Fashion Old And Woman 39 Sports SFSYDDY Summer Entertainment vqRX770, 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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