MESH ALGORITHMS AND THEIR RELATIONSHIP WITH SPLINES: THEORY, COMPUTATION, AND PRACTICAL APPLICATIONS
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The accurate representation of complex surfaces is central to computer graphics, CAD/CAM systems, 3D modeling, and scientific visualization. This study examines the mathematical foundations, algorithmic strategies, and computational methods underlying mesh generation and processing, emphasizing triangle, quad, and mixed meshes. It also explores the relationship between meshes and spline surfaces, including B-splines and NURBS, with practical examples illustrating how subdivision, remeshing, and spline fitting can be quantified and validated. Experiments demonstrate how discrete and parametric models can be integrated efficiently, maintaining geometric fidelity while optimizing computational resources.
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