developable surface🚧

moving system

《Architectural Geometry》

instantaneous rotation: normals of each path are passing through pole at time t
instantaneous translation: normals of each path are parallel

developable surface

single curved surface
evolute: trace of curvature center 曲率中心軌跡
PQ-strip
PQ-mesh
surface development
transition pieces
空間中兩條線段的雙一次內插,可以製造曲線。
Pappus–Guldinus theorem
https://en.wikipedia.org/wiki/Pappus's_centroid_theorem
solid of revolution
面積=曲線長度x線段重心移動距離(弧長)
體積=曲線面積x面積重心移動距離(弧長)

folding

folding

Erdős–Nagy theorem

一個凹多邊形不斷翻折,最後必能變成凸多邊形。

origami

origami

https://langorigami.com/
http://jasonku.mit.edu/
https://kusudama.me/
https://www.jaist.ac.jp/~uehara/index-e.html

ICPC 3568 4640 UVa 1446

kirigami

kirigami

https://caiguijiang.github.io/publication/2020_siga_kirigami/
https://en.wikipedia.org/wiki/Kirigami