Escher Tile Deformation via Closed-Form Solution

• Published in 2025
• Added on 2025-08-20

We present a real-time deformation method for Escher tiles—interlocking organic forms that seamlessly tessellate the plane following symmetry rules. We formulate the problem as determining a periodic displacement field and solve it analytically in closed form. Our method supports all 17 wallpaper groups and deforms both the boundary and interior of textured tiles. An adaptive fall-off parameter allows artists to control the locality and semantic intent of deformations in real-time. Applications include interactive photo editing, mesh sculpting, and pattern design for fabrication.

Links

• https://cranehechen.com/proj_escher_tile.html

Other information

BibTeX entry

@article{EscherTileDeformationviaClosedFormSolution,
	key = {EscherTileDeformationviaClosedFormSolution},
	type = {article},
	title = {Escher Tile Deformation via Closed-Form Solution},
	author = { Crane He Chen and Vladimir G. Kim},
	abstract = {We present a real-time deformation method for Escher tiles—interlocking organic forms that seamlessly tessellate the plane following symmetry rules. We formulate the problem as determining a periodic displacement field and solve it analytically in closed form. Our method supports all 17 wallpaper groups and deforms both the boundary and interior of textured tiles. An adaptive fall-off parameter allows artists to control the locality and semantic intent of deformations in real-time. Applications include interactive photo editing, mesh sculpting, and pattern design for fabrication. },
	comment = {},
	date_added = {2025-08-20},
	date_published = {2025-11-11},
	urls = {https://cranehechen.com/proj{\_}escher{\_}tile.html},
	collections = {art,the-groups-group,things-to-make-and-do},
	url = {https://cranehechen.com/proj{\_}escher{\_}tile.html},
	year = 2025,
	urldate = {2025-08-20}
}