Quaternion Julia Set Shape Optimization

We present the first 3D algorithm capable of answering the question: what would a Mandelbrot‐like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to...

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Vydané v:Computer graphics forum Ročník 34; číslo 5; s. 167 - 176
Hlavný autor: Kim, Theodore
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Blackwell Publishing Ltd 01.08.2015
Predmet:
3-D graphics
Algorithms
Analysis
and object representations
Categories and Subject Descriptors (according to ACM CCS)
Convergence
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations
Image processing systems
Optimization
Potential fields
Quaternions
Shape optimization
solid
Strategy
Studies
surface
Transformations
Translations
ISSN:0167-7055, 1467-8659
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Popis
Shrnutí:We present the first 3D algorithm capable of answering the question: what would a Mandelbrot‐like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi‐resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non‐linear transformations.
Bibliografia:istex:AACECE45E1815A76DF201CFE5F6A25E236ED199A
Supporting InformationSupporting Information
ark:/67375/WNG-SJRZZ94T-6
ArticleID:CGF12705
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12705