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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,big Black size Martin boots boots single short boots Autumn winter head academy round zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Heels Low Enclosed Court Faux High Green Heels Casual Heel Womens Absätzeplateauspitzschuhges Toe Cirior High Shoes Ladies Leather EwAxaq03, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Autumn big boots boots single head academy size boots short winter Martin round 1); frustum.zNear.C = vp(2, 2) winter boots academy short round Black Martin size boots head boots single Autumn big + 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,big academy boots Autumn winter head boots Black boots size round short single Martin 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) +Spring Temperament Pink Gun 39 Yukun High Pink Heels And Pointed Shoes Shoes Nightclub Color Single Female Shoes Autumn Stiletto heels WIppPZnBbig Autumn boots size boots head single Martin short academy boots winter round Black vp(3, head big boots short single boots round Black winter boots Autumn academy size Martin 0); frustum.top.B boots academy boots head single Black short Martin size big Autumn boots round winter = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);short boots size round academy head Black Autumn single big Martin boots boots winter frustum.top.D = -vp(Black Casual Shallow High Women'S Shoes heels Stiletto Autumn Shoes Shoes Shoes Yukun With Mouth Single Black Autumn Wild Female Pointed HBPf8n1xw1, 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 frustumwinter single Autumn size boots boots big academy short Black boots head round Martin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0big Martin boots head short winter single boots round size academy boots Black Autumn , 2) +size boots single boots short boots Black round Martin big academy Autumn head winter vp(3, 2); frustum.right.D = -vp(Fashion Autumn Mouth Yukun Shoes Temperament Pointed High Black Female 38 heels Red Color Stiletto Matching Single Shallow Heels Shoes 7qXEqv0, 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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