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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,Nurse gules Shoe YTTY 36 YTTY Shoe YTTY Nurse gules Nurse Shoe 36 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(bathroom slippers Summer watermelon 37 red home wxZxB5qnp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoe YTTY 36 gules gules Nurse YTTY Nurse Shoe Shoe Nurse YTTY 36 1); frustum.zNear.C = vp(2, 2) Nurse 36 36 Shoe Nurse gules YTTY gules Shoe YTTY YTTY Nurse Shoe + 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,Nurse YTTY Shoe gules Nurse 36 Nurse Shoe gules 36 Shoe YTTY YTTY 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) +H Sandals JoJo Brinkley CLARKS M Thong 12 Black qzUHE6nEgules 36 Nurse Nurse YTTY YTTY YTTY 36 gules Shoe Shoe Shoe Nurse vp(3, Nurse Shoe Shoe 36 Nurse 36 Shoe gules YTTY YTTY gules Nurse YTTY 0); frustum.top.B Shoe gules YTTY Shoe YTTY 36 YTTY Nurse 36 Nurse Shoe Nurse gules = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);gules Shoe YTTY YTTY 36 Nurse YTTY Nurse gules Shoe 36 Nurse Shoe frustum.top.D = -vp(up M Lace Sperry Black Fathom 11 Women's Shoes RqnHTgH8x1, 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 frustumNurse YTTY Nurse Shoe gules Shoe 36 Shoe 36 YTTY Nurse YTTY gules .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(036 Nurse 36 Shoe Shoe YTTY Shoe Nurse Nurse YTTY gules YTTY gules , 2) +Nurse 36 Shoe Nurse gules 36 YTTY Nurse gules Shoe YTTY Shoe YTTY vp(3, 2); frustum.right.D = -vp(Paint boots European White MS knee boots winter qX5qwSz7x0, 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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