Calculate Center and Radius of Circle from 3 points on it

问题:

Could somebody please show code which would do this quickly? Assume we get three points p1, p2, p3 in left-->right order. Thus, the solution should also check whether or not the circle is valid, ie (p1, p2, p3) are counter-clockwise.

回答1:

To calculate the circle parameters, have a look at:

http://paulbourke.net/geometry/circlesphere/ Look for "Equation of a Circle from 3 Points (2 dimensions)"

to determine orientation, you can use the polygon area formula:

http://paulbourke.net/geometry/polygonmesh/ Look for "Calculating the area and centroid of a polygon"

Please tell me if you need this in an specific programming language.

回答2:

• Connect any two points on the circle and you have a chord.

• The perpendicular bisector of a chord must pass through the center.

• The intersection of the bisectors of two chords will be the center.

Remainder (reduction to form for most efficient calculation) is left as an exercise for the reader...

文章来源: Calculate Center and Radius of Circle from 3 points on it