Welcome to Curvetopia, where we bring order and beauty to the world of 2D curves! This project aims to identify, regularize, and beautify various types of 2D curves. Starting with simple closed curves, we progressively tackle more complex shapes, including symmetry and curve completion techniques.

Our mission is to process and enhance 2D curves starting from polylines. The end goal is to output curves defined as connected sequences of cubic Bezier curves. We focus on the following key tasks:

1. Regularize Curves - Identify and regularize shapes such as straight lines, circles, ellipses, rectangles, polygons, and star shapes.
2. Explore Symmetry - Identify reflection symmetries and symmetric Bezier curves.
3. Complete Incomplete Curves - Fill gaps or complete curves that have been partially occluded.