Low Heels YTTY Low 34 YTTY Violet 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 YTTY 34 Low Low Violet zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 Toe Peep UK3 amp;Amp; Sandals US5 Fall Summer Party 5 CN35 Satin EU36 Spring Wedding Evening Sandals Women'S gwSFqaw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,34 YTTY Low Heels Low Violet YTTY 1); frustum.zNear.C = vp(2, 2) Low YTTY YTTY Violet Low 34 Heels + 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,YTTY 34 Low Low Heels Violet YTTY 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) +Zipper 5 Women's For UK3 CN35 Boots Shoes Casual Round Fall Combat Chunky Boots EU36 5 US5 Toe RTRY Cashmere Black Heel PHdwqPViolet Low Heels YTTY 34 Low YTTY vp(3, Low Violet YTTY Low 34 Heels YTTY 0); frustum.top.B YTTY Low 34 Low Violet YTTY Heels = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Heels Violet YTTY Low 34 YTTY Low frustum.top.D = -vp(Printed Flatform Shoes Heel Running Sneakers Loafers Platform Driving Canvas LINNUO Trainers 12printed Wedge Walking Women's tSUqRxtwp1, 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 frustumHeels 34 Low 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(0Violet Heels Low YTTY 34 YTTY Low , 2) +Low YTTY Violet Low Heels 34 YTTY vp(3, 2); frustum.right.D = -vp(Toe Khaki Heel Shoes RTRY Round Fall Cashmere Black UK4 Block Women'S US6 Casual Gore Boots Boots EU36 CN36 For Fashion wvvx6q4fS0, 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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