Happy new year everyone! I can't seem to figure out the following problem in 2-dimensions: Given two points, A and B and a radius of a circle, where is the centre of the circle so that the points A and B lie on the circumference of that circle. Now I know there are two answers, but I can choose 1 based on per-vertex normals. Example: Thanks for any help.

This sounded familiar, and sure enough: Geometric Tools for Computer Graphics, section 8.6: Circle Through Two Points with a Given Radius"

Their solution is to intersect two circles of the given radius, one centered on A and one centered on B; the two intersection points are your two potential circle positions.

To intersect two circles, see for example http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/ or google "circle intersection".

Happy new year :)

Of course! Thanks raigan.

The only two point circle is Diametric - the midpoint of the vector is the midpoint of the circle and the radius is half the length of the (diameter) input.

You might be thinking of arc length.

For a three point circle, the midpoint is the intersection of the perpendicular bisectors and the radius is the distance from the center to any point. Here is a cool Java applet demo (which loads on the bottom in a moment or so).

http://www.nvcc.edu/home/tstreilein/constructions/Circle/circle1.htm

The next algorithms in that area are Minimum Enclosing Circle (pretty easy), and then Minimum Enclosing Sphere (medium level for symmetric frustum, hard for asymmetric frustum).