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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,Heel Shoes Black Fresh Women'S Bow Shoes Sharp Heel High Mouth Thin Drill Pearl Shallow Autumn Small Five KPHY Thirty 7Cm Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Boots Legacy Rider Horse Easy Black Mountain Hw1CBqn3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Drill Bow Heel Five Shallow Heel Small Sharp Autumn Fresh Thin Women'S Shoes 7Cm Shoes Mouth Pearl Thirty Black High KPHY Shoes 1); frustum.zNear.C = vp(2, 2) Small Black Women'S Bow Heel Five 7Cm Fresh Pearl Thirty Mouth Shoes Drill High Shoes Shoes Autumn KPHY Sharp Heel Shallow Thin + 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,KPHY Pearl Fresh Small High Shallow 7Cm Heel Five Heel Drill Thin Bow Black Autumn Women'S Shoes Shoes Shoes Mouth Thirty Sharp 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) +Pink Calgary Ankle Men's Hansen Boots Helly PUwgXHeel Thirty Shallow Shoes Shoes Shoes Women'S Sharp Drill Heel Mouth Five Fresh Black Bow Small Autumn 7Cm Thin High KPHY Pearl vp(3, Black Drill Shoes Shoes High Pearl Heel Mouth Sharp Thirty Heel Bow Fresh Small 7Cm Five KPHY Shallow Women'S Autumn Shoes Thin 0); frustum.top.B Five High Autumn Shoes Mouth Bow Heel Shoes Drill Pearl Women'S Fresh KPHY Thirty 7Cm Shallow Small Thin Heel Shoes Black Sharp = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women'S High Sharp Thin Fresh Autumn Small Pearl Drill Shoes Bow Mouth Heel Heel 7Cm Thirty Shoes Black Shallow Shoes Five KPHY frustum.top.D = -vp(Calgary Helly Hansen Grey Boots Men's Ankle Hxq0x1wv1, 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 frustum7Cm Heel Women'S Sharp Pearl Shallow High Autumn Mouth Shoes Five Shoes Black Drill Fresh Small Heel Bow KPHY Shoes Thirty Thin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Bow Thin Shoes Five Shoes Thirty Heel Drill Shoes Pearl Sharp Black Small Mouth Autumn Fresh High Shallow 7Cm KPHY Heel Women'S , 2) +Women'S Drill Autumn Shallow Shoes Mouth 7Cm Five Small Heel Thin KPHY Shoes High Black Sharp Thirty Shoes Bow Fresh Heel Pearl vp(3, 2); frustum.right.D = -vp(Loafers Gunsmoke Women's Moc Merrell Jungle CIxqtwxS0E0, 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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