4 ms·

All 3 methods fail on this example https://i.imgur.com/rKcdjpv.jpg https://i.imgur.com/rKcdjpv.jpg

• nullc 4y ago
  That cusp isn't a failure, so much as the definition of parallel not matching your expectations. You can't have the radius of the curve smaller than your offset without forcing a cusp. If you imagine dragging an eraser across the 'roadway' produced by the parallel lines, you'll see that the solution with the cusp still obeys the constraint that the lines are a constant distance apart for every point along the road, it's just that it turns so tight your eraser needs to turn in place at the corner.
• jansan 4y ago
  Actually, that's what the offset of the curve looks like. Take a pencil and paper and draw a parabola. Then try to draw an offset curve to the inside with an offset greater than the smallest curvature radius of the parabel. You will get this strange path with two cusps and an inverted curve between them. Try it out, it is an eye opener.