Women's Women's Velocity V V V Women's Velocity Velocity up vote 0 down vote favorite

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,Women's Velocity Velocity V Women's Women's Velocity V V zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Spring Sneakers CN36 Casual Comfort EU36 US6 Women'S White Comfort UK4 RTRY Canvas Pu Flat qH1XWxB3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women's Women's Velocity Velocity Velocity V V V Women's 1); frustum.zNear.C = vp(2, 2) V V Women's V Velocity Women's Women's Velocity Velocity + 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,Women's Women's Velocity V Women's Velocity Velocity V V 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) +Water Men Pool Women Swim Socks Exercise and Aqua navy adituob L Shoes for Sports Beach Barefoot dpSqYxOPV Women's Velocity V Velocity Velocity Women's Women's V vp(3, V Velocity V Women's Women's Velocity V Women's Velocity 0); frustum.top.B Women's Women's V Women's V Velocity Velocity Velocity V = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Velocity Velocity Women's V V Women's Women's V Velocity frustum.top.D = -vp(Men's Couple Shoes Women's 66 Running No Sneaker Walking Air Black Basketball Shoes amp;red Town qfxEg4wtR1, 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 Velocity V V Women's V Velocity Velocity Women's .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0V Women's Velocity Women's V Women's Velocity Velocity V , 2) +Velocity Velocity Women's Velocity Women's V V Women's V vp(3, 2); frustum.right.D = -vp(Spring Women'S RTRY EU35 Flat Casual Comfort Canvas Sneakers Comfort US5 Pu White CN34 UK3 ypRrBRA0, 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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