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<p>We present a general constructive approach to blossoming for arbitrary finite dimensional univariate function spaces by altering the diagonal property of the classical blossom. We apply this approach to blossoming to develop the corresponding theory of Bernstein bases and Bézier curves including de Casteljau type algorithms for evaluation and subdivision as well as a Marsden identity for arbitrary finite dimensional univariate function spaces.</p>

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A universal approach to blossoming with applications to Bernstein bases and Bézier curves for arbitrary function spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月8日

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  • Ron Goldman,
  • Ilija Jegdic,
  • Plamen Simeonov

摘要

We present a general constructive approach to blossoming for arbitrary finite dimensional univariate function spaces by altering the diagonal property of the classical blossom. We apply this approach to blossoming to develop the corresponding theory of Bernstein bases and Bézier curves including de Casteljau type algorithms for evaluation and subdivision as well as a Marsden identity for arbitrary finite dimensional univariate function spaces.