Introduction

Polyhedral-net splines convert a polyhedral-net into piecewise low-degree Bezier patches.

Top: input mesh, Bottom: B-spline patches generated by Polyhedral-net splines (Gray: regular Bi-2, Green: extraordinary point, Cyan: T0, Yellow: T1)

Features

• Smooth surfaces without subdividing the mesh.

• Easy, exact computation of moments, e.g. volume, center of mass, axes of inertia, …
• Preserves the polyhedral character of the input.
  Polyhedral-net splines (PnS2) generalize bi-2, bi-quadratic, splines. Bi-2 splines are by default less smooth than bi-3 splines, and curvature changes more sharply. A variant converts regular grid-like regions of bi-2 to C2 smooth bi-3 splines preserving the simple bi-2 shape. PnS3, a different package, generalizes bi-3 C2 splines.
• Well-defined and smooth across irregularities.

Implemented algorithms

1. Karčiauskas, K., & Peters, J. (2015). Smooth multi-sided blending of biquadratic splines. Computers & Graphics, 46, 172-185.
2. Karčiauskas, K., & Peters, J. (2020). Smooth polar caps for locally quad-dominant meshes. Computer Aided Geometric Design, 81, 101908.
3. Karčiauskas, K., & Peters, J. (2020). Low degree splines for locally quad-dominant meshes. Computer Aided Geometric Design, 83, 101934.

Allowable configurations

PnS2

Refinement will be applied locally for unsupported configurations

(gray: submesh / green: tensor-product splines)

Polar needs to be surrounded by quads

PnS3

Refinement will be applied locally for unsupported configurations