任意多边形振荡器：将多边形合成推广至任意形状、变形及三维多面体
Arbitrary Polygon Oscillator: Generalizing Polygonal Synthesis to Arbitrary Shapes, Morphing, and Three-Dimensional Polyhedra
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中文总结 AI 辅助
本文提出任意多边形振荡器系统，通过统一弧长引擎实现任意形状多边形的音频合成、不等顶点数多边形的平滑变形及三维凸多面体的横截面波形生成，在RNBO中运行并采用抗锯齿策略提升音质。
中文摘要 AI 辅助
多边形合成通过用相位器遍历多边形的周长来生成音频；现有研究采用恒定角速度，而本文提出的系统采用恒定弧长（周长）速度。现有公式仅适用于规则的、参数化定义的多边形，在单一形状族内产生平滑的音色过渡。本文围绕统一的弧长引擎推广多边形合成：任意来源的顶点数据均可输入同一数字信号处理（DSP）流水线。首先，我们调整振荡器以接受来自外部缓冲区的任意顶点配置，使广泛类别的闭合多边形——规则、不规则或星形——均可作为波形发生器。其次，混合插值算法可实现顶点数不等的多边形之间的平滑变形，生成无参数描述的中间形状。第三，我们将该范式扩展至三维：绕三个轴旋转的凸多面体被固定水平面切割，所得横截面产生由实体方向控制的连续可变多边形。该系统在RNBO（Cycling '74）中运行，采用几何缓存策略避免逐样本重新计算。抗锯齿结合了从运行时贝塞尔切线推导的四点polyBLAMP校正与自适应过采样，可根据通用顶点配置在几何上调整校正，无需针对每种形状进行解析推导。
英文摘要
Polygonal synthesis generates audio by traversing the perimeter of a polygon with a phasor; prior work uses a constant angular velocity, whereas the proposed system adopts constant arc-length (perimeter) velocity. Existing formulations operate on regular, parametrically defined polygons, producing smooth timbral transitions within a single family of shapes. This paper generalizes polygonal synthesis around a unified arc-length engine: vertex data of any origin feed the same DSP pipeline. First, we adapt the oscillator to accept arbitrary vertex configurations from an external buffer, opening the possibility for a broad class of closed polygons -- regular, irregular, or star-shaped -- to function as a waveform generator. Second, a hybrid interpolation algorithm enables smooth morphing between polygons with unequal vertex counts, passing through intermediate shapes that have no parametric description. Third, we extend the paradigm to three dimensions: a convex polyhedron rotated about three axes is sliced by a fixed horizontal plane, and the resulting cross-section yields a continuously variable polygon controlled by the solid's orientation. The system runs in RNBO (Cycling~'74) with a geometry caching strategy that avoids per-sample recomputation. Antialiasing combines a four-point polyBLAMP correction derived from runtime Bézier tangents with adaptive oversampling, adapting the correction geometrically to general vertex configurations without per-shape analytical derivation.
发表机构
- Conservatorio Niccolò Piccinni di Bari（巴里尼科洛·皮奇尼音乐学院）
机构由 AI 辅助整理，请以论文原文为准。
