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After an initial trial, where we struggled to get the program running on our systems, we discussed potential areas of research with Professor Campen and dived straight into the implementation of our ideas. The part of the algorithm that I worked on was concerned with the process of splitting given Bézier curves (for the purpose of creating a mesh), particularly how to choose the point of bisection, $$t$$. During a later stage of the algorithm, the curves are enveloped by quadrilaterals (or two triangles with a curved edge). If two quads intersect, we must split one of the curves. The key idea here was that the quads could then potentially inform how the curves were to be split. Without going into too much technical detail, I essentially tried to implement different approaches to optimize the splitting process. The graph below shows a snippet of my results.
While Strategy A is the original algorithm implementation, Strategy B and C were possible improvements to it. For both of the latter strategies I used an area function to find the point where the resulting quads would have the approximately equal area. This equal distribution could point to an optimal solution. The difference between B and C has to do with how the value of $$t$$ is iteratively changed as is shown below.