V2EX b-spline

B-spline

定义 Definition

B-spline(B样条)是一种用于表示与生成平滑曲线或曲面的数学工具,常见于计算机图形学、CAD(计算机辅助设计)、数值分析与数据拟合中。它通过一组控制点结向量(knot vector)来定义形状,具有局部可控、稳定且易于计算的特点。(B-spline 还有更深入的数学定义与不同阶数/次数的形式。)

发音 Pronunciation (IPA)

/bi splan/

例句 Examples

A B-spline curve looks smooth even with only a few control points.
B样条曲线即使只有少量控制点,看起来也能很平滑。

By adjusting the knot vector, the designer changed the B-spline’s local curvature without affecting the entire shape.
通过调整结向量,设计师在不影响整体形状的情况下改变了B样条的局部曲率。

词源 Etymology

B-spline中的 B 通常解释为 basis(基函数/基),表示它由一组基样条基函数组合而成;spline 原本指制图与造船等行业中用于画平滑曲线的“弹性压条/样条”,后来被借用到数学与计算机领域,用来指代“通过分段多项式拼接得到的平滑曲线”。

相关词 Related Words

文学与典籍 Literary Works

  • The NURBS Book(Les Piegl & Wayne Tiller)
  • Curves and Surfaces for CAGD: A Practical Guide(Gerald Farin)
  • An Introduction to Splines for Use in Computer Graphics and Geometric Modeling(Richard H. Bartels, John C. Beatty, Brian A. Barsky)
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