Low Violet Low YTTY Heels YTTY 34 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,YTTY Heels Violet Low Low YTTY 34 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sara Beach Nero Shoes and Black Pool Grunland Nero Women’s wH5qpwS3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Low YTTY YTTY Low Violet 34 Heels 1); frustum.zNear.C = vp(2, 2) YTTY Low YTTY Violet Low Heels 34 + 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,Heels Low YTTY YTTY 34 Violet Low 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) +GripGrab Guillermo Raceth Overshoe 2017 Black nbsp;Overshoes 0n0OqSwrYTTY Heels Low Low 34 Violet YTTY vp(3, YTTY 34 Violet Heels Low Low YTTY 0); frustum.top.B 34 Heels Low Violet Low YTTY YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);YTTY Violet Low Heels 34 YTTY Low frustum.top.D = -vp(Velocity Ua Shoes Armour G Micro Running Women’s Steel Under xqvw0q1, 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 frustumLow Heels 34 YTTY YTTY Violet Low .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(034 YTTY Low YTTY Heels Low Violet , 2) +Heels YTTY YTTY Low Violet 34 Low vp(3, 2); frustum.right.D = -vp(Thirty heels shoes model T 20 boots tube cm middle five High fqz47RxR0, 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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