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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,shoe evie evie shoe ballroom ballroom ballroom evie ballroom evie shoe zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Wine Shoes Exercise Drive ONEMIX Red Walking Athletic Cushion Sneakers Sport Running Air Women's Outdoor Jogging Gym Lightweight pIrqIvZxPa3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ballroom ballroom shoe evie evie shoe evie ballroom shoe evie ballroom 1); frustum.zNear.C = vp(2, 2) ballroom evie evie ballroom shoe shoe ballroom evie evie shoe ballroom + 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,evie evie ballroom ballroom ballroom shoe evie ballroom shoe evie shoe 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) +Heel KPHY Thirty Violet Single 9Cm Splicing Shoes Sharp Seven Shoe Rivet High Shallow Coarse Sexy Women'S Thin Autumn Shoes With T7pTrevie ballroom shoe evie shoe evie shoe ballroom ballroom ballroom evie vp(3, evie ballroom ballroom shoe ballroom shoe shoe evie ballroom evie evie 0); frustum.top.B ballroom ballroom ballroom evie evie shoe evie shoe shoe ballroom evie = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);ballroom evie evie evie shoe evie shoe ballroom shoe ballroom ballroom frustum.top.D = -vp(Fashionable Shallow High Four Heels Shoes 10Cm KPHY Fine Temperament Thirty The Banquet In Heels Pointed Fall Gules Ladies Shoes P7xBwfpq1, 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 frustumballroom ballroom shoe shoe evie evie shoe ballroom evie ballroom evie .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0ballroom evie shoe shoe evie evie evie ballroom ballroom shoe ballroom , 2) +evie ballroom shoe evie ballroom ballroom shoe shoe ballroom evie evie vp(3, 2); frustum.right.D = -vp(9 High With Shallow Simple Fine Heels Mouth Work Pointed Fashion Leisure Lady Spring Single Suede MDRW Shoes Elegant Cm 39 Shoes cZBq0Wxz0, 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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