It seems you can get the points from the Path2D via a PathIterator. It's a bit counter-intuitive (though probably necessary), but it returns coordinates and the type of the segment. You can use the latter in a switch and the former to draw lines or curves depending on the type of segment it is. I think this would be better anyway, because otherwise it will remain a question if there are discrepencies between the visible and the invisible shape.

Thanks very much for this response.  I have not used a PathIterator (Path2D was already a step up on the learning curve, since I come to Java from Processing, rather than the other way around!), but I will do some self-education and see if I can get this to work.  Thanks again for the guidance.  Will post some code if I figure out how to do this.

Create the sketch using the JAVA2D renderer. Then access the Graphics2D context see sketch code below

import java.awt.Graphics2D;

Graphics2D g2d;

void setup(){
  size(400,400,JAVA2D);
 
  g2d = (Graphics2D)((PGraphicsJava2D)this.g).g2;
 
}

Once you have g2d then it makes available all the Java features not exposed by Processing.  Below is example code to draw a filled rounded rectangle.

1. // Create a 1 pixel wide stroke
2. BasicStroke stroke = new BasicStroke(1, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND);
3. // Create a rounded rectangle
4. RoundRectangle2D shape = new RoundRectangle2D.Float(x,y,w,h,mitre,mitre);
5. // Set the color to use
6. g2d.setColor(fcol);
7. // Draw the shape fill (solid colour inside)
8. g2d.fill(shape);
9. // Set the stroke to use (strokeWeight)
10. g2d.setStroke(stroke);
11. // Set the color to use
12. g2d.setColor(scol);
13. // Draw the shape border
14. g2d.draw(shape);

The g2d context also gives you access to powerful features such as clipping to shapes etc.