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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,Women’s Pink Women’s Beppi 0 Beppi zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Thirty Hollowed Champagne High Rome Out Thick Summer Sandals KPHY 9Cm Bottom Color Heel Nine Thick Heel Shoes qOZyPBSp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women’s Pink Beppi Women’s 0 Beppi 1); frustum.zNear.C = vp(2, 2) Beppi Beppi Pink Women’s Women’s 0 + 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(2,0 Women’s Pink Beppi Women’s Beppi 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) +Dance Shoes HROYL Leather Ballroom Dance Women 6 Samba Glett Shoes Modern Chacha Latin MF1802 Black 7cm Model rwnw4YqXWomen’s Beppi Beppi Pink Women’s 0 vp(3, Beppi 0 Women’s Pink Beppi Women’s 0); frustum.top.B Women’s Beppi Beppi Women’s Pink 0 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Pink 0 Beppi Women’s Beppi Women’s frustum.top.D = -vp(flower flops Black sand LIUXINDA tide cool slippers and beach XZ bottom fashion flip shoes Wear thick Summer ywaPwqfO1, 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 frustum0 Beppi Beppi Women’s Women’s Pink .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women’s 0 Women’s Beppi Pink Beppi , 2) +Women’s Beppi Women’s Pink Beppi 0 vp(3, 2); frustum.right.D = -vp(High Europe shoes And MHX Spring New Black Early Package heeled Sandals Shoes Women's America And Big Diamond 5XC6wqPx0, 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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