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The complexity of 3D shapes that are represented in digital form and processed in CAD/CAM/CAE, entertainment, biomedical, and other applications has increased considerably. Much research was focused on coping with or on reducing shape complexity. But, what exactly is shape complexity? We discuss several complexity measures and the corresponding complexity reduction techniques. Algebraic complexity measures the degree of polynomials needed to represent the shape exactly in its implicit ordoi:10.1007/s00371-005-0362-7 fatcat:kyz5qzyt75f5fkdfd3nhlacqkm