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Integration of Complex Shapes and Natural Patterns by Marcelo Walter B Sc Electrical Engineering Federal University of Rio Grande do Sul Brazil 1986 M Sc Computer Science Federal University of Rio Grande do Sul Brazil 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES Department of Computer

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The process of generating an image for a computer graphics object is traditionally. broken down into three steps modelling of the shape or geometric attributes such. as height width and length modelling of the visual attributes how the object is. going to look and an integration step that connects the first two a visual attribute is. defined for every point on the surface of the object The separation of modelling the. shape from modelling the visual attributes makes the whole process highly flexible. and powerful from a conceptual point of view the process is easier to handle. While generally good for many classes of objects this separation is prone. to problems when the geometry of the object is complex For example the map. ping of visual characteristics to every point of such complex surfaces is non trivial. Furthermore this separation assumes that these two steps are independent of each. other but for some objects there is an interaction between the shape modelling and. visual modelling that plays a significant role on the final image Typical examples. are patterned animals such as giraffes and leopards where the pattern visible on the. fur of an adult animal is the result of a process that took place while the animal was. an embryo in the womb In this case modelling the interplay between the embryo. growth process and the pattern formation process is as important as modelling the. individual processes themselves, In this thesis we introduce a novel solution for integrating shape and visual. modelling This solution defines the visual attributes directly on the surface of the. object as the object changes shape for example due to growth We present results. of applying this solution to a giraffe model, This thesis makes three contributions 1 a new model of mammalian pat. tern formation called Clonal Mosaic suitable for computer graphics purposes and. with strong biological plausibility The model is based on cell division and cell to. cell interactions and it can generate repeating spotted and striped patterns occurring. in several species of mammals especially the big cats and giraffes 2 a technique. to modify the shape of an object based for example on a small set of input mea. surements The technique consists of defining local coordinate systems cylinders. around the growing parts of the body each one being transformed according to the. relevant growth data while maintaining their relationship with the adjoining parts. and the continuity of the surface The local coordinates also permit ordinary anima. tion mainly as relative rotation such as in articulated objects and 3 the integration. of the modelling of Clonal Mosaic patterns with the shape modification technique. Finally this thesis advances the notion of integration of independent tools as. an important development in the field of computer graphics Individual tools have. been reaching exceptional levels of performance and therefore we need efficient ways. to integrate them smoothly,Abstract ii,Contents iv. List of Tables ix,List of Figures x,Acknowledgements xiii. 1 Introduction 1,1 1 Motivation and Overview 1,1 2 Integration of Shape and Pattern 4.
1 2 1 Texture Mapping 4,1 2 2 Previous Work on Integration 11. 1 3 Terminology 14,1 3 1 Pattern 14,1 3 2 Shape 15. 1 4 Organization of the Thesis 16,2 Models for Mammalian Coat Pattern Formation 19. 2 1 Introduction 19,2 2 Mammalian Coat Pattern Formation 20. 2 3 Pattern Formation Models in Biology 23,2 3 1 Reaction Diffusion 24.
2 3 2 Mechanochemical 29,2 3 3 Cellular Automata 30. 2 4 Pattern Formation Models in Computer,Graphics 31. 2 4 1 Turk 31,2 4 2 Witkin and Kass 33,2 4 3 Fowler Meinhardt and Prusinkiewicz 34. 2 4 4 Three Dimensional Reaction Diffusion 34,2 4 5 Cell Systems 35. 2 4 6 Discussion 35, 2 5 A Case Study Pattern Formation for the Giraffe 36.
2 6 Summary 39,3 The Clonal Mosaic Model 40,3 1 Overview and Motivation 41. 3 2 The Clonal Mosaic Model 42,3 3 The Implementation 44. 3 3 1 Cells and Groups of Cells 44,3 3 2 General Description 46. 3 3 3 Initialization 47,3 3 4 Simulation 49,3 3 5 Anisotropy 52. 3 3 6 Summary of Parameters 53,3 3 7 Efficiency Considerations 54.
3 3 8 Discussion 56,3 4 Results 57,3 4 1 Giraffe patterns 58. 3 4 2 Spotted patterns 60,3 4 3 Anisotropic patterns 61. 3 5 Assessing the patterns 63,3 6 Exploration of the Parameter Space 68. 3 7 Clonal Mosaic and Reaction Diffusion 69, 3 7 1 Definition of Concentrations in Clonal Mosaic 71. 3 7 2 Diffusion 72, 3 7 3 Introducing Concentrations into the CM Model 74.
3 8 Summary 76,4 Models for Shape 78,4 1 Methods to Describe Shape 78. 4 2 Methods to Represent Shape in Computer,Graphics 81. 4 2 1 Polygonal Meshes 82,4 2 2 Parametric Curves and Surfaces 84. 4 2 3 Implicit Surfaces 85,4 2 4 Conversion between representations 86. 4 3 Summary 87, 5 Applying Growth Information to Polygonal Models of Animals 88.
5 1 Introduction 89,5 2 Differential Growth and the Available Data 90. 5 3 Previous Work on Shape Transformation 96,5 4 Animal Models 98. 5 5 The Local Coordinates 99,5 6 The Growth Process 102. 5 7 Animation 106,5 8 Examples 107,5 9 Summary 111. 6 Integration 112,6 1 Overall description 112,6 2 Deriving Cell Splitting Rates from Growth.
Information 113, 6 3 Triangulation and Simplification of the Model 115. 6 4 Distributing Random Points on the Surface of a Polyhedral Model 116. 6 5 Relaxation of Points on the Surface of the Model 117. 6 6 Computing the Voronoi Diagram on a Surface 119. 6 7 Pattern generation without growth 121,6 8 Pattern generation with growth 124. 6 9 Extra control 124,6 10 Summary 126,7 Architecture of the System 128. 7 1 Pattern Synthesis Module 130,7 2 Shape Transformation Module 133. 7 3 Integration Module 135,7 3 1 Parameter file 136.
7 3 2 Cells file 137,7 3 3 Texture file 137,7 4 Summary 138. 8 Conclusions 139,8 1 Contributions 140,8 2 Future Work 141. 8 2 1 Clonal Mosaic Patterns 141,8 2 2 Growing Models of Animals 143. 8 2 3 Integration 144,Bibliography 145, Appendix A Summary of Growth Information available for the Big Cats. Giraffe and Zebra 164,List of Tables,2 1 Fetal Length for Giraffes 39.
3 1 Attributes of a cell 48, 3 2 Spot areas and spot shapes for giraffes after dagg68 67. 5 1 Measurements for a giraffe 96,5 2 Some measurements for a quarter horse 107. 5 3 Some measurements for Holstein cattle 108, 7 1 Specification for input parameter files for the onc a tool 136. List of Figures,1 1 An example of texture mapping 5. 2 1 Process of hair formation 21,2 2 Baby lion 23,2 3 Example of Reaction Diffusion patterns 26.
2 4 Fetal length for giraffes 39,3 1 Representation of cells in the system 45. 3 2 Pseudocode for computing the new position of a cell 50. 3 3 Computing the repulsive force 51,3 4 Initialization 1000 cells 51. 3 5 Division of the domain into a grid of 25 buckets 56. 3 6 G c reticulata 59,3 7 G c tippelskirchi 59,3 8 Time lapse 60. 3 9 Cheetah Acinonyx Jubatus 61,3 10 Spotted pattern 62. 3 11 Rosettes 62,3 12 Anisotropic patterns 63, 3 13 Geometric construction for a Voronoi polygon 65.
3 14 Voronoi measures for giraffes 66,3 15 Estimated and true Voronoi 66. 3 16 Voronoi measures for leopards and jaguars 67,3 17 Ocelot Felis pardalis pattern 69. 3 18 Diffusion process in Clonal Mosaic 74,5 1 Giraffe embryo 93. 5 2 Newborn giraffe 94,5 3 Adult giraffe 95,5 4 The perfect cylindrical horse 100. 5 5 Cylinder and features 102,5 6 Features defined for the horse 103.
5 7 Rotation of cylinders vs joints 107,5 8 Horse transformed at 6 and 36 months 108. 5 9 Cow transformed at 6 and 24 months 109,5 10 Muybridge s and polygonal horse trotting 110. 5 11 Horse growing and trotting 110,6 1 Pipeline of the system 113. 6 2 Finding a random point on a triangle 117, 6 3 Computing distances on the surface of the model 118. 6 4 Mapping cells from face to face 119,6 5 Pattern on the surface 122.
6 6 Example of pattern generation without growth Cube 123. 6 7 Example of pattern generation without growth Giraffe 123. 6 8 Two phases in the development of a giraffe pattern 125. 6 9 Extra control 126,7 1 Architecture of the system 129. 7 2 Graphical User Interface for cm 130,8 1 Exploration of other patterns 142. Acknowledgements, After 6 years and a few months working on something big and important as a PhD. thesis it is impossible not to say the obvious I could not have done without the guid. ance support knowledge and inspiration from Alain His analogies and insights. shape the world of computer graphics I thank also the support and comments of. my supervisory committee Leah Keshet David Forsey Jack Soneyink and Mark. Reimers To James Little Richard Israel and Jane Wilhelms for their role on the. examination committee, My family in Brazil gave me the most important emotional support for stay. ing a long time away from home I missed important family gatherings the wed. ding of my sister and the birth of two nephews but I hope they believe it was. worth it The friendship from the Brazilian Gang in Vancouver Ma rio Lilian Dani. Marcelo Lane Margaret Andrea and Peixoto They made these years in Vancou. ver feel almost like in Brazil they could not prevent the bad weather though To. Dani and Marcelo a special thank you for their support in my last stay in Vancouver. as a student, So many people in Imager helped my stay in Canada become a home away.
from home Kevin Mr Acadia Coughlan Gene Lee Martin Blais Chris Healey. Bill Gates Viswha Ranjan Rob Scharein Jason Harrison Jim Boritz Makoto Anne. Lavergne Roger Tam and Chris Chiu Chris saved my thesis presentation trusting. his laptop on my hands A special thanks goes for Pierre Poulin He introduced me. to the wonderful world of graphics at UBC Rob Walker was more than a friend. he was proofreader technical advisor and a TA mate The first years in Vancouver. would be harder without the help and friendship from Antonio Scott Hazelhurst. and Tien Truong The peer support group aka Michael Sahota helped me put things. in perspective during bad times Michael McAllister provided Voronoi code for our. patterns The office mates bonding party with Margaret and Davor will always be. part of my memories, In Brazil Alex helped me become a more relaxed person and I thank him for. that Paulinho and Robson were always ready to listen to me complaining about the. rain in Vancouver At Unisinos in Brazil Fernando Oso rio helped turn the transi. tion from Canada to Brazil easier than I thought Mauro Steigleder helped turn a. laptop crisis into something manageable Thank you very much Finally nothing. of this could be done without the financial support from CNPq UNISINOS and the. Department of Computer Science at UBC,MARCELO WALTER. The University of British Columbia,December 1998,Introduction. 1 1 Motivation and Overview, One of the major goals of computer graphics is to compute an image of a virtual. scene For our purposes a scene can be any combination of objects including their. material properties Objects can be classified according to the way they interact with. light and also for many purposes whether they are manufactured objects desk car. chair or natural ones trees leopards humans This goal presents a gigantic chal. lenge considering all possible interplay of factors in even the simplest scenes As. in many other complex tasks a divide and conquer approach makes the task more. manageable and the whole process is traditionally broken into two independent parts. First we need to define the objects in a geometric sense that is we have to. build the objects in terms of their geometric properties for instance height width. and size Objects can be arbitrarily complicated, Second we need to deal with the material properties of the objects and this.