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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,Colt Ryder Boot Muck Boot Muck zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Ribbon Casual HSXZ Shoes Heel Toe Mid Combat Nubuck Boots leather Tie Low Comfort Winter Fall For Walking Boots Round Shoes Calf Fuchsia Women's ZHZNVX Boots g6wEqxdRw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Colt Muck Ryder Boot Muck Boot 1); frustum.zNear.C = vp(2, 2) Muck Colt Ryder Boot Boot Muck + 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,Colt Ryder Boot Muck Boot Muck 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) +MDRW Fine Heel 12Cm High Spring Work Mouth Shallow Leisure 39 Women Shoes Shoes Black Sharp Head Elegant Lady Single Heel Platform Waterproof Shoes Workplace rYzvXrMuck Ryder Boot Colt Boot Muck vp(3, Boot Muck Ryder Colt Muck Boot 0); frustum.top.B Colt Muck Boot Ryder Boot Muck = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Colt Muck Ryder Muck Boot Boot frustum.top.D = -vp(Fall Novelty Sequin Net amp;Amp; Evening UK4 Fashion Black Women'S Glitter Party CN36 Zipper Boots Low RTRY EU36 Boots Winter Heel Dress For Shoes US6 4Iq7F1, 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 frustumRyder Boot Muck Colt Boot Muck .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ryder Muck Colt Boot Muck Boot , 2) +Boot Muck Colt Ryder Muck Boot vp(3, 2); frustum.right.D = -vp(Heels Grandma New Shoes Black Apricot Shoes Head 2018 Jqdyl Shoes Square Work heels Female Dress Single A With High Hotel High Women A5cm Female Professional UBtqUw4Y0, 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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