Lobke and Companions

Explore the shapes you can construct from congruent conical segments.

Instructions

• The sliders control various parameters of the conical segment.
• When pointing at a label in front of a slider or toggle bar, you get a tooltip with a brief explanation.
• You cannot edit the segment sequence directly. Instead, use the buttons at the bottom.
• Selecting render preview will include a preview of the four possible continuations at the end of the strip. Clicking a previewed segment will add it to the strip.
• Selecting show info will display the length (number of segments), and the gap between the first and the last segment (to help ensure closure).
• The predefined settings popup menu offers some predefined settings.
• Reduce n and m to improve rendering performance. For instance n=16 and m=1 will do fine while exploring. When finished, you can increase the values to obtain a smoother picture: n=36 and m=6 are good.

Literature

Tom Verhoeff and Koos Verhoeff.
``Lobke, and Other Constructions from Conical Segments'',
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture,
pp. 309-316.