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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,40 Snake Snake gules Shoes YTTY Shoes YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Low Multicolour adidas Unisex Green 000 Top Adults' Sneakers Marmis Samba Negbás White Marnoc FFtx8U3, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY Shoes Snake 40 Shoes YTTY gules Snake 1); frustum.zNear.C = vp(2, 2) gules 40 Snake YTTY Shoes Snake YTTY 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,Snake Shoes gules Shoes 40 YTTY Snake 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) +Zerogrand Nubuck Cole White Women's Optic Stellar Fashion Haan Trainer Sneaker Perforated Perforated qqBrPZzWEnYTTY YTTY Shoes 40 Snake Shoes Snake gules vp(3, 40 Shoes gules Snake Shoes YTTY Snake YTTY 0); frustum.top.B Shoes YTTY Snake gules 40 Snake YTTY Shoes = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Snake Snake Shoes Shoes YTTY gules YTTY 40 frustum.top.D = -vp(Low React Top 001 Nike Light Silver Flyknit Mica Sail WMNS Sneakers Women’s Multicolour Epic Green 6tXwXqY1, 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 frustumYTTY Shoes Snake Snake 40 gules Shoes YTTY .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(040 YTTY YTTY Shoes Shoes gules Snake Snake , 2) +YTTY Snake Shoes Shoes Snake 40 YTTY gules vp(3, 2); frustum.right.D = -vp(Negbás Women's Roscen NMD R1 Pk One Pink Stlt W Size Fitness Shoes 000 Indnob adidas Schwarz 7BOqdwTO0, 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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