Converting between Arc Definitions

I'm struggling to figure out the math to convert between two different definitions of an arc.

The source definition includes a start point, end point and control point on the arc as well as the eccentricity of the ellipse and the angle of rotation of the major axis.

I need to convert this into an Arc definition I can use to initialize an ArcSegment which need a start and endpoint, semimajor and semiminor axes (given as a Size structure), and angle of rotation of the major axis.

I believe the start/end points and angle of major axis rotation transfer nicely but I'm not sure how to get the semimajor and semiminor axes given the eccentricity and control point in the s开发者_如何学JAVAource definition of the arc.

Any geometry experts able to help?