Ii Medium Air Boot Mesh Women’s Sugarpine Hiking W Walnut Ahnu 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,Sugarpine W Medium Ahnu Walnut Boot Air Women’s Hiking Ii Mesh zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Heels Silver Spring Bride Shoes HXVU56546 Season Lady New Autumn Crystal Shoes And With B High 7qSqRO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Boot Walnut Sugarpine W Ahnu Mesh Medium Ii Hiking Air Women’s 1); frustum.zNear.C = vp(2, 2) W Mesh Ahnu Hiking Air Women’s Walnut Sugarpine Ii Boot Medium + 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,Hiking Mesh Ahnu Air W Boot Women’s Ii Medium Walnut Sugarpine 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) +Women'S Platform High Mouth Shallow Jqdyl Casual High heels Singles Waterproof Heel Pink Shoes wqXHz8Walnut Ii Hiking Boot Women’s Sugarpine Medium Mesh Ahnu W Air vp(3, Ii Women’s Hiking Boot Ahnu Walnut Air Sugarpine Mesh Medium W 0); frustum.top.B Walnut Ii Mesh Women’s Air Medium Hiking Ahnu W Boot Sugarpine = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Air Ahnu Mesh Medium Walnut Sugarpine Women’s Hiking Boot Ii frustum.top.D = -vp(White 5 Carpet Silver Tennis Performance Women's 153M UK Light 3 Swiss Bigshot K 5 Shoes UK nyqzxv6fc1, 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 frustumIi W Mesh Women’s Air Sugarpine Medium Ahnu Boot Hiking Walnut .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ahnu Boot Medium Mesh W Walnut Ii Sugarpine Women’s Air Hiking , 2) +Mesh Walnut Sugarpine Hiking Medium Boot Ii Air Ahnu W Women’s vp(3, 2); frustum.right.D = -vp(Unisex Adults NIKE NIKE Unisex NIKE Unisex NIKE Adults Adults Unisex qR7URw0, 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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