Fundamentals of Warping and Morphing

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1 Fundamentals of Warping and Morphing Luiz Velho IMPA - Institututo de Matemática Pura e Aplicada

2 Outline Metamorphosis in Nature Conceptual Framework Overview of Warping and Morphing Applications in Computer Graphics Paradigm of the Universes Structure of the Course

3 Metamorphosis "transformation of a shape and its visual attributes" Intrinsic in our Environment Deformations in Nature Man-made Deformations Powerful Concept Comparison of Shapes

4 Shape Change In Nature Living Beings internal forces Growth Processes Locomotion

5 Plant Growth

6 Shape Change In Nature Inanimate Things external forces Environmental Phenomena Mechanical Processes

7 Erosion

8 Man-Made Deformations Reshape Matter Arts & Crafts Modeling Industry Manufacturing

9 Industrial Object

10 Comparison of Shapes Classes of Shapes Transformation Group of n Parameters Correlation Related Shapes

11 Classification of Plants

12 Comparison of Shapes Classes of Shapes Transformation Group of n Parameters Evolution Transitional Shapes

13 Crocodile Skull

14 Characteristics of Deformations Action Continuous Discontinuous Effect Non-Permanent (elastic) Permanent (inelastic) Volume Preserving Non-Preserving

15 Rules for a Good Morph Most Natural Physically Plausible Perceptually Correct

16 Images and Perception Image: Representation of Objects Sequence of Images: Animation Image Blending -> Transitions Related Shapes x Unrelated Shapes

17 Cross Dissolve of Unrelated Images Unrelated Shapes Time / Space Changes ( passage of time/space )

18 Metamorphosis of Similar Shapes Related Shapes Metamorphosis (interpolation of attributes)

19 Metamorphosis and Graphics Computer Graphics Model Deformation Image

20 Model Deformation Deform the Model Render

21 Image Deformation Render Deform Image

22 Conceptual Framework Goals Integrated View Common Theory Unifying Concepts Graphical Objects Shape Transformations

23 Graphical Objects Components Shape (geometric support) Attributes (visual properties) Examples Particle Systems, 2D Drawings, Images, Surfaces, Volumes

24 Example: 2D Drawing Shape Graphical Object color texture Attributes

25 Shape Transformations Operations Warping: Unary Op Morphing: Binary Op Two Related Problems, Same Framework 1 - Given Object A and Xform, find Object B 2 - Given Object A and Object B, find Xform

26 1 - Warping A F (t)? 2 - Morphing A? B

27 Warping and Morphing of Graphical Objects Processing Pipeline Geometry Deformation Attribute Generation Object Combination

28 Geometry Deformation Change of Coordinate Systems Intrinisc Extrinsic

29 Attribute Generation Domain Uniformization Resampling (adjust to new geometry) Range Compatibilization (morphing) Homogenization (attribute equivalence) ex: Color Spaces CIE-xyz / RGB

30 Object Combination Correspondence between Objects Domain (shape) Range (attributes) Steps Geometry Alignment Attribute Blending (morphing)

31 Warping Pipeline

32 Morphing Pipeline (note: warping as morphing)

33 Implementation Issues Specification Type of Transformation Rate of Change Computation User Interface

34 Specification of Transformations Global Transformations Affine Maps Projective Maps Non-Linear Maps

35 Examples of Global Transformations Rotation Perspective Pinch

36 Specification of Transformations Piecewise: (parts + continuity) Domain Decomposition Vector Fields

37 Examples of Piecewise Transformations Triangulation Displacement Fields

38 Computation of Transformations Direct Moving Points of the Object p U p f (p) Suitable for: Parametric Representations

39 Computation of Transformations Indirect Transform the Ambient Space F: R n U R n Suitable for: Implicit Representation Can be used also for Parametric Representation

40 User Interface Features Object Properties Functional Perceptual Uses Handle for Transformations Object Correspondence

41 User Interface: Features

42 Features and Perception

43 Features and Perception obs: sound / motion

44 Transformation of Graphical Objects Particle Systems Curves and Surfaces Images and Volumes

45 Transformation of Points Discrete Enumeration Specification Force Fields Computation Direct

46 Particle Systems

47 Transformation of Curves and Surfaces Parametric Description Specification Control Points Computation Direct

48

49 Transformation of Images and Volumes Volumetric/Implicit Description Specifiaction Change of Coordinate System Computation Indirect

50

51 Applications in Graphics Modeling Animation Special Effects Shape Analysis

52 Modeling I Shape Operators Deformations ex: taper, twist, bend Usage Simulation of Manufacturing Processes

53 Examples of Deformation Operators

54 Modeling II Shape Families Interpolation n-parameters Usage Style Evolution Features

55 Bottle (1-parameter) t

56 rayban Sun Glasses (2-parameters) square s round t cat

57 Animation Emphasis Stretch Squash * Distortion Motion

58 Stretch and Squash

59 Animation Control Keyframing Inbetweening * Distortion Motion

60 Animation Keyframes Inbetweens

61 Special Effects Transitions Dissolve Wipe

62 Example: Wipe Patterns

63 Special Effects Transformations Image Surface

64 ADO Mirage

65 Image Analysis Fitting Registration

66 Texture Registration

67 Image Analysis Matching Recognition

68 Modal Analysis 5.1 template 24.4 object match strain energy

69 Paradigm of the Universes Understanding an Area Levels of Abstraction Conceptual Issues

70 Levels of Abstraction Physical Universe Mathematical Universe Representation Universe Implementation Universe

71 Conceptual Issues 1 - Define the Elements of Math Universe graphical objects 2 - Specify Operators on Math Universe shape transformations 3 - Construct Representation Schemes specification

72 Structure of the Course Luiz Velho - Overview Jonas Gomes - Graphical Objects - Transformations Bruno Costa - Computation Lucia Darsa Thad Beier - Specification - Applications