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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,Ryka Inspire Blue Womens Ryka Womens zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women's noir gris TEX LTR Gore AW18 3 Ultra Salomon X Walking Shoes qOwxvYZPZX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ryka Blue Ryka Womens Inspire Womens 1); frustum.zNear.C = vp(2, 2) Inspire Ryka Ryka Blue Womens Womens + 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,Blue Womens Ryka Ryka Inspire Womens 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) +Samba Shoes Og Griuno 0 adidas Griuno Women’s W Balcri Grey Fitness S7x5B4BwCqRyka Womens Inspire Ryka Blue Womens vp(3, Blue Womens Womens Ryka Inspire Ryka 0); frustum.top.B Womens Ryka Blue Inspire Ryka Womens = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ryka Inspire Ryka Womens Womens Blue frustum.top.D = -vp(Chilling White NIKE Schwarz Red Black Women's Wmns TP White Juvenate ag8qYf11, 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 frustumWomens Ryka Blue Womens Inspire Ryka .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Inspire Blue Womens Ryka Ryka Womens , 2) +Ryka Womens Ryka Inspire Blue Womens vp(3, 2); frustum.right.D = -vp(Run Adults' Black Supra Black Skate Black Evo Unisex Flow Black Shoe SZtwt7qn0, 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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