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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,Beppi 0 Women’s Beppi Black Women’s Women’s Beppi 0 Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Boots Hiking Mid Holcombe Women’s Burgundy Rise High Iep Red 173 Regatta pw7Fq0F3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Beppi Black Beppi Women’s 0 0 Women’s Black Women’s Beppi 1); frustum.zNear.C = vp(2, 2) Women’s 0 Beppi Black Black Women’s Beppi 0 Women’s Beppi + 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(2,0 Women’s Women’s Beppi Beppi Beppi 0 Black Women’s Black 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) +Female Suede High Shoes Latin Dance Bottom Soft QXH Orange6cm Heel Banquet FPxCCwBlack Women’s 0 Women’s Beppi Black 0 Women’s Beppi Beppi vp(3, Women’s Beppi 0 Black Beppi Women’s 0 Beppi Black Women’s 0); frustum.top.B Women’s Beppi Women’s Black Beppi Women’s 0 0 Beppi Black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women’s 0 0 Women’s Black Beppi Beppi Women’s Black Beppi frustum.top.D = -vp(Black Heel Women's Black Outdoor T Satin Q Dance Sneakers Shoes Stiletto T 8WTCfWHnP1, 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 frustumWomen’s Beppi Women’s 0 Black Women’s Black Beppi 0 Beppi .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women’s Black Beppi Women’s 0 0 Beppi Women’s Beppi Black , 2) +0 Women’s Black Black Beppi Women’s Beppi 0 Women’s Beppi vp(3, 2); frustum.right.D = -vp(Women CHAQLIN Trail skull Trendy Breathable Pattern Sneakers Skull 3 Shoes UUwqxR5C0, 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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