Example 1
A simple example demonstrating the main drawback
of the regular discrete Fréchet morphing
which keeps the long leash after hitting the maximum
length. The retractable discrete version on the other
hand happily yields the "correct" result.
| P |
2 |
4.0 |
| Q |
5 |
6.033105012119288 |
| Fréchet |
1.35 |
7 |
| VE Fréchet |
1.35 |
7 |
Animation: Fréchet morphing
This is the animation of the morphing computed
that is both continuous and monotone.
Animation: VE Retractable Fréchet
This is the animation of the VE retractable morphing. It is potentially not monotone (but it is continuous.
Free space diagram heatmap:
graph + free space
[PDF]
: graph
[PDF]
With the grid
VE-Fréchet Retractable solution:
Monotonized...
Fréchet cont+monotone solution:
Discrete Fréchet
Generated by sampling 10 points along each edge...
The resulting morphing - extended to continuous:
Specifically, to get a smooth animation, the
leash is shown as moving continuously, by
interpolating between the discrete locations.
The discrete retractable version
The discrete dynamic time warping
P # vertices: 21
P # vertices: 21
DFréchet iters : 441
Retract DFréchet iters : 132
Animation: Fréchet morphing as morphing
2025-03-08 20:22:50