Evolution of Supershapes for the Generation of Three-Dimensional Designs

This paper explores the evolution of three-dimensional objects with a simple generative encoding, known as the Superformula. Evolving three-dimensional objects has long been of interest in a wide array of disciplines, from engineering (e.g., robotics) to biology (e.g., studying morphological evolution). While many representations have been presented, ranging from direct encodings to complex graphs and grammars, the vast majority have possessed complex underlying encodings, which were necessary to produce varied morphologies. Here we explore the target-based evolution of Superformula, which is simply encoded as a vector of reals and show that is possible to generate very closely matching designs of a number of complex three-dimensional objects.

[1]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[2]  Marc Schoenauer,et al.  Shape Representations and Evolution Schemes , 1996, Evolutionary Programming.

[3]  Karl Sims,et al.  Evolving 3d morphology and behavior by competition , 1994 .

[4]  Peter John Bentley,et al.  Generic evolutionary design of solid objects using a genetic algorithm , 2007 .

[5]  Jordan B. Pollack,et al.  Evolutionary Body Building: Adaptive Physical Designs for Robots , 1998, Artificial Life.

[6]  Aamer Nazir,et al.  Polyhedron Evolver — Evolution of 3 D Shapes with Evolvica , 2002 .

[7]  Frank McGuire.  The Origins of Sculpture: Evolutionary 3D Design , 1993 .

[8]  Ruzena Bajcsy,et al.  Volumetric segmentation of range images of 3D objects using superquadric models , 1993 .

[9]  Ángel Fernando Kuri Morales,et al.  Clustering with an N-dimensional extension of Gielis superformula , 2008 .

[10]  Lange Van Ruusbroecstraat.  Superquadrics with Rational and Irrational Symmetry , 2003 .

[11]  John Rieffel,et al.  EvoFab: A Fully Embodied Evolutionary Fabricator , 2010, ICES.

[12]  Hod Lipson,et al.  Evolving three-dimensional objects with a generative encoding inspired by developmental biology , 2011, ECAL.

[13]  J. Gielis.  A generic geometric transformation that unifies a wide range of natural and abstract shapes. , 2003, American journal of botany.

[14]  Hirokazu Watabe,et al.  A Study on Genetic Shape Design , 1993, International Conference on Genetic Algorithms.

[15]  Peter Eggenberger-Hotz.  Evolving Morphologies of Simulated 3d Organisms Based on Differential Gene Expression , 2007 .

[16]  Gregory S. Hornby,et al.  The advantages of generative grammatical encodings for physical design , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[17]  Youssef Bokhabrine,et al.  Genetic Algorithms for Gielis Surface Recovery from 3D Data Sets , 2007, 2007 IEEE International Conference on Image Processing.

[18]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[19]  Frédéric Truchetet,et al.  Supershape Recovery from 3D Data Sets , 2006, 2006 International Conference on Image Processing.

[20]  Jason D. Lohn,et al.  Human-competitive evolved antennas , 2008, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[21]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[22]  Christian Jacob,et al.  Evolutionary and Swarm Design in Science, Art, and Music , 2008, The Art of Artificial Evolution.

[23]  Kenneth O. Stanley,et al.  Compositional Pattern Producing Networks : A Novel Abstraction of Development , 2007 .

[24]  Joshua Evan Auerbach,et al.  Dynamic Resolution in the Co-Evolution of Morphology and Control , 2010, ALIFE.

[25]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[26]  Joshua Evan Auerbach,et al.  Evolving CPPNs to grow three-dimensional physical structures , 2010, GECCO '10.

[27]  Jordan B. Pollack,et al.  Three Generations of Automatically Designed Robots , 2001, Artificial Life.

[28]  Frédéric Truchetet,et al.  Genetic algorithms for 3d reconstruction with supershapes , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).