Hey, I have general solution I just threw together:
X(_u,_v)=circRad*_v*cos(_u*circAngRange+circAngOffset)+xCenter
Y(_u,_v)=circRad*_v*sin(_u*circAngRange+circAngOffset)+yCenter
_u is 0 to 1, _v is 0 to 1, circRad is the radius of the quarter circle, circAngRange is 90 degrees for a quarter circle, and you can rotate the circle to any orientation with circAngOffset. xCenter and yCenter dictate where you want to put the point of the partial circle.
Thanks for asking! If I hadn't hit your unanswered question, I'd have kept searching for a solution rather than thinking about it myself.