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GENERATION OF ADVANCED ESCHER-LIKE SPIRAL TESSELLATIONS�生成先進的埃舍爾式螺旋鑲嵌圖案

王語麟 2023.11.15

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Outline

  • Introduction
  • Related work
  • method
  • Result

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Introduction

  • Introduction
  • Related work
  • method
  • Result

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Escher-like spiral tessellations

  • Escher‘s spiral art gained popularity in the 1950s but was challenging to achieve such exact repetition due to hand-drawing limitations.
  • This paper introduces a direct method for constructi-ng precise symmetrical Escher-like spiral tilings using shaders.

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Related work�

  • Introduction
  • Related work
  • method
  • Result

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Kaplan's thoughts

  • In the first step, an image with a periodic tiling is generated
  • In the second step, the image is transformed by the antiMercator mapping

Escher-like spiral tessellations by

the antiMercator mapping

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Method�

  • Introduction
  • Related work
  • method
  • Result

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Cyclic spiral tilings

  • Logarithmic Spirals
  • Transformations and Rotations under an Abelian Symmetry Group
  • Changing Escher-like Spiral Tessellations in Structure

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Derived spiral tilings

  • Conformal Mapping

three specific conformal mappings and their application to construct derived spiral tilings.

  • Stereographic Projection

from a unit sphere to the complex plane, transforming origins and infinities

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Method

  • Pre-designed Wallpaper Templates
  • Created Within a Specified Area

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Generation of Escher-like spiral tessellations

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Method

  • Generate stereo images under different templates through stereo projection method

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Result��

  • Introduction
  • Related work
  • method
  • Result

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Compare with hand-designed templates�

  • Do not strictly satisfy the translational symmetry

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Compare with Kaplan

  • Kaplan's method is only a line pattern, while the author's method creates more diverse spiral tessellations with deco-rative elements like lines and colors.

Kaplan’s Method→

This Paper's Method→

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Compare with Kaplan(cont.)

  • Kaplan's method permits the use of different plane patterns for di-verse outcomes, whereas the author's method employs the same type of pattern.

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Application

Have good aesthetic value and commercial potential.

  • porcelain paintings, vases, and woodcuts rendered by spiral tessellations

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