Developable Surface(Under Construction!)

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線性內插,可以製造曲線。

Roulette

Brachistochrone Curve

「最速降線」。力與軌跡。

curvature = laplacian = stress

Roulette

https://www.zhihu.com/question/413178224/answer/1402560436

http://mathworld.wolfram.com/Roulette.html
https://en.wikipedia.org/wiki/Roulette_(curve)
https://en.wikipedia.org/wiki/Hypotrochoid
https://en.wikipedia.org/wiki/Brachistochrone_curve
https://en.wikipedia.org/wiki/Tautochrone_curve
https://en.wikipedia.org/wiki/Cycloid
https://en.wikipedia.org/wiki/Whewell_equation
https://en.wikipedia.org/wiki/Cesàro_equation
https://en.wikipedia.org/wiki/Catenary
https://en.wikipedia.org/wiki/Tractrix
https://en.wikipedia.org/wiki/Evolute

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。

http://www.matrix67.com/blog/archives/4780

Origami

Origami

https://langorigami.com/
http://jasonku.mit.edu/

ICPC 3568 4640 UVa 1446

Kirigami

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