arXiv:2606.06505v1 Announce Type: cross Abstract: We introduce a user defined probabilistic polygonal representation for plane curves. Given a curve, we select vertices on the curve and connect consecutive vertices by line segments to obtain a polygonal approximation. Each segment is equipped with a user defined uncertainty parameter in the normal direction. This yields a collection of thin probabilistic geometric primitives that retain the geometrz of the underlying curve while extending it beyond the idealized deterministic one dimensional formulation. For each segment, we define a Random Va
This is a pre-print research paper, a routine publication in academic computer science and mathematics, reflecting ongoing foundational work.
While contributing to specific areas of computer graphics and AI, this technical paper does not present an immediate breakthrough or significant shift for a strategic reader outside of its niche academic field.
No immediate real-world changes or market impacts are evident from this theoretical research.
Further development of mathematical representations for geometric modeling in computer graphics and vision could occur.
Improved accuracy in 3D reconstruction and motion tracking in specialized AI applications might eventually emerge.
Potentially, more robust foundational models for agentic AI systems that interact with physical spaces could benefit from such geometric advancements many years later.
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