D-Form
D-Form is a surface, of zero Gaussian curvature, given by a parametrisation, immersed.
Open D-Form in the interactive viewer →
aperiodic def-parametric flat immersed implemented misc
Properties
- Family
- misc
- Given by
- a parametrisation
- Curvature
- zero Gaussian curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: the developable is determined by numerically rolling and joining the two ellipse boundaries; no closed-form parametrisation is known. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- T. Wills, "D-Forms: 3D Forms from Two 2D Sheets," Bridges 2006, pp. 503-510.
- J. Sharp, "D-Forms and Developable Surfaces," Bridges 2005, pp. 121-128; "D-Forms" (Tarquin, 2009) -- also the source of the anti-D-form.
- R. R. Orduno, N. Winard, S. Bierwagen, D. Shell, N. Kalantar,
- A. Borhani, E. Akleman, "A Mathematical Approach to Obtain Isoperimetric Shapes for D-Form Construction," Bridges 2016, pp. 277-284.
- E. Demaine, J. O'Rourke, "Geometric Folding Algorithms" (Cambridge, 2007), ch. 25 -- Alexandrov gluings.
- H. Pottmann, J. Wallner, "Computational Line Geometry" (Springer, 2001) -- poses the D-form shape question.