I'd like to configure some details of planar figure rendering by setting some properties in an application.

I suggest adding the following properties to control rendering:

"color": ColorProperty for color of the lines that represent the planar figure (e.g. a circle)
"opacity": FloatProperty for opacity of the lines that represent the planar figure (e.g. a circle)
"width": FloatProperty for widthof the lines that represent the planar figure (e.g. a circle)
"draw outline": BoolProperty. If set, the mapper will draw a second, broader line behind the main lines. This may look like an outline
"outline color": ColorProperty for the color of the outline
"outline opacity": FloatProperty for the opacity of the outline
"outline width": FloatProperty for the width of the outline
"control point color": ColorProperty for the color of control points
"control point opacity": FloatProperty for the opacity of control points
"control point width": FloatProperty for the width of the lines used for drawing control points
"control point style": PlanarFigureStyleProperty to control the shape of handles (circle or squares)