## Demo of Reflected Langevin Dynamics


#### Simulation of Langevin dynamics (VP-SDE) on various domains


Stage 1/3 
<p float="left">
  <img src="figures/flower1.png" width="200"  title="Flower"/>
  <img src="figures/heart1.png" width="200"   title="Heart" /> 
  <img src="figures/polygon1.png" width="200" title="Polygon"/>
  <img src="figures/star1.png" width="200"    title="Star"/>
</p>

Stage 2/3 
<p float="left">
  <img src="figures/flower2.png" width="200"  title="Flower"/>
  <img src="figures/heart2.png" width="200"   title="Heart" /> 
  <img src="figures/polygon2.png" width="200" title="Polygon"/>
  <img src="figures/star2.png" width="200"    title="Star"/>
</p>


Stage 3/3 
<p float="left">
  <img src="figures/flower3.png" width="200"  title="Flower"/>
  <img src="figures/heart3.png" width="200"   title="Heart" /> 
  <img src="figures/polygon3.png" width="200" title="Polygon"/>
  <img src="figures/star3.png" width="200"    title="Star"/>
</p>

More iterations result in better figures. 

We choose the grid of the radius and the curves to be grid_radius=1e-2, grid_curve=1e-3, respectively. A smaller value leads to more refined trajectories but becomes more expensive.