Computational Geometry and Geometric Optimization aims to arrange multiple objects in a confined space to achieve some objective. In this thesis, I explore two such problems: Surgical Suture Placement and Seed Placement for Polyculture Gardens.

Suture placement is crucial for patient outcomes, and surgeons typically rely on rules of thumb and experience to choose needle entry and exit points for suture placement. I present SP2DEEF: Suture Planning 2D Equalizing Elliptical Forces, an algorithm that computes entry and exit points to optimize suture forces, improving wound closure and minimizing scarring. SP2DEEF takes as input the wound curve along with scaling information as input, and generates a full, optimized suture plan that can be fine-tuned by the surgeon. Experiments suggest that our suturing algorithm outperforms a naive baseline, and physical phantom experiments suggest that it performs comparably or superior to an expert surgeon. My team and I are currently in the process of developing a publicly-available website which will make the SP2DEEF pipeline fully accessible, the link will be provided shortly at https://github.com/BerkeleyAutomation/SP2DEEF.

The spatial arrangement of plants in a garden or small farm is especially important for poly- culture agriculture to reduce water and pesticide use. We present PolyPoD, a new algorithm for seed placement. Given a polygonal planting area boundary (convex or non-convex) and number and types of seeds, PolyPoD generates the variable radius poisson disk distribution, yielding viable seed placements. Results suggest that PolyPoD outperforms our previous seed placement algorithm with the goal of avoiding over-competition for resources, under- utilization of space, and plant segmentation difficulties. The PolyPoD platform will also offer free access on a website for polyculture farmers worldwide. Source code, documentation, and the website link are available at https://github.com/BerkeleyAutomation/PolyPoD.




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