Calculate center of SVG arc

Question

I have the following information:

• radiusX (rx)
• radiusY (ry)
• x1
• y1
• x2
• y2

The SVG spec allows you to defi

Answer 1

I'm considering the case of x-axis-rotation = 0. Equations for start and end points:

x1 = cx + rx * cos(StartAngle)

y1 = cy + ry * sin(StartAngle)

x2 = cx + rx * cos(EndAngle)

y2 = cy + ry * sin(EndAngle)

Excluding angles from equation pairs gives us:

ry^2*(x1-cx)^2+rx^2*(y1-cy)^2=rx^2*ry^2

ry^2*(x2-cx)^2+rx^2*(y2-cy)^2=rx^2*ry^2

This equation system can be analytically solved for (cx, cy) by hands or with help of math packets (Maple, Mathematica etc). There are two solutions of quadratic equation (due to large-arc-flag and sweep-flag combination).