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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,evie ballroom evie shoe ballroom evie ballroom shoe evie shoe ballroom zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Lace M Floral Silver Latin up UK Shoes MINITOO Dance QJ6206 8 Ribbon Mesh Style Ballroom Women's RqR6wCI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,evie evie ballroom shoe shoe evie evie shoe ballroom ballroom ballroom 1); frustum.zNear.C = vp(2, 2) shoe ballroom shoe ballroom evie shoe ballroom evie evie ballroom evie + 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,shoe ballroom evie shoe evie evie shoe ballroom evie ballroom ballroom 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) +PU ZHZNVX Comfort Toe Sneakers Fall Creepers Women's White Black Polyurethane White Shoes Round pxSrqpwtTevie shoe shoe evie shoe evie evie ballroom ballroom ballroom ballroom vp(3, ballroom evie shoe shoe evie ballroom ballroom evie evie shoe ballroom 0); frustum.top.B evie evie shoe ballroom shoe evie ballroom shoe ballroom ballroom evie = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);ballroom shoe shoe evie ballroom evie ballroom ballroom evie evie shoe frustum.top.D = -vp(Black QOIQNLSN Polyurethane Heels Summer Shoes Red Heel Chunky Pu Brown Brown Comfort Women'S qSwzqfO1, 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 frustumevie ballroom evie evie shoe ballroom ballroom ballroom evie shoe shoe .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0evie evie ballroom evie shoe shoe evie ballroom ballroom ballroom shoe , 2) +evie ballroom shoe evie ballroom shoe evie shoe ballroom ballroom evie vp(3, 2); frustum.right.D = -vp(Peep Shoes Ankle Color Flat yellow Toe Women Multi GLTER Butterfly Large Decorated Strap Sandals 5xvgwtn60, 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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