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...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Computer graphics forum Ročník 34; číslo 5; s. 167 - 176
Hlavní autor:	Kim, Theodore
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Blackwell Publishing Ltd 01.08.2015
Témata:	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
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

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.
Bibliografie:	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 content type line 23
ISSN:	0167-7055 1467-8659
DOI:	10.1111/cgf.12705