Ruppert's algorithm

Alright kiddo, let me explain Ruppert's algorithm in a way that's easy for a five-year-old like you to understand. It's a way of creating triangles on a surface so that they all fit together really nicely, a bit like a jigsaw puzzle.

Imagine that you have a big sheet of paper that you want to cut up into triangles. You start by drawing a few points on the paper, and then you draw lines between them to create triangles. But you don't just draw any old triangles – you want to make sure that they're all roughly the same size and shape.

So, you start with the points you have and draw the triangles between them. But sometimes there are areas where the triangles are too big or too small. That's where Ruppert's algorithm comes in.

Ruppert's algorithm looks for areas where the triangles are too big or too small and adds more points in those areas. When you add more points, you can create more triangles that fit together better. It's like cutting a jigsaw piece in half – you can fit more pieces together in the same area.

But Ruppert's algorithm doesn't just add points randomly – it looks for areas where the triangles are stretched out, and it adds points there to make the triangles more even. This creates a smoother surface with fewer jarring differences between the triangles.

And that's basically what Ruppert's algorithm does – it adds points to areas where the triangles are too big or small, so that they all fit together better and create a smoother surface. It's a neat trick that makes sure that every piece of the jigsaw puzzle fits together perfectly.