Arbitrary Polygon Oscillator: Generalizing Polygonal Synthesis to Arbitrary Shapes, Morphing, and Three-Dimensional Polyhedra

arXiv:2608.24726v1 Announce Type: new Abstract: 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 B\'ezier tangents with adaptive oversampling, adapting the correction geometrically to general vertex configurations without per-shape analytical derivation.

Abstract: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.

Computation and Language (cs.CL)

arXiv:2608.24726 [cs.CL]

(or arXiv:2608.24726v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2608.24726 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Arbitrary Polygon Oscillator: Generalizing Polygonal Synthesis to Arbitrary Shapes, Morphing, and Three-Dimensional Polyhedra

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