c# - Formula to compute an arcuate segment length -

considering class:

public class point3d {      public double x;     public double y;     public double z;      public point3d(double x, double y, double z)     {         x = x;         y = y;         z = z;     }      public double distanceto(point3d to)     {         double dx = math.abs(to.x - x);         double dy = math.abs(to.y - y);         double dz = math.abs(to.z - z);         return math.sqrt(dx * dx + dy * dy + dz * dz);     }  } 

and class:

public class segment {      public point3d from;     public point3d to;     public double? radius;      public segment(point3d from, point3d to, double? radius)     {         = from;         = to;         radius = radius;     }      public double length     {                 {             double straightlength = from.distanceto(to);             if (radius == null)                 return straightlength;             if (radius < straightlength/ 2d)                 throw new exception();             // compute arcuate segment length         }     }  } 

i compute length of arc (with radius) passing through from , to 3d points.

some welcome!

according http://mathworld.wolfram.com/isoscelestriangle.html

straightlength / 2 = radius * sin( 1/2 * angle) 

therefore:

angle = 2 * arcsin( straightlength / 2 / radius) 

and

arclength = radius * angle;