The content discusses the construction of rational curves with rational arc length using various algebraic and geometric approaches. Three specific methods are detailed, highlighting their applications and implications in the field of mathematics.
The first method involves solving linear equations to compute rational PH curves efficiently. The second method focuses on zero residue conditions to ensure the rationality of integrals, extending ideas from previous papers. The third method introduces a geometric dual approach for constructing spatial curves with constant slope 1.
Through detailed examples and proofs, the author demonstrates how these methods can be applied to generate rational curves with piecewise rational arc lengths effectively. The content provides valuable insights into the mathematical principles behind constructing such curves and their significance in various applications.
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