Animation CS 148: Summer 2016 Introduction of Graphics and Imaging - - PowerPoint PPT Presentation

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Animation CS 148: Summer 2016 Introduction of Graphics and Imaging - - PowerPoint PPT Presentation

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Animation CS 148: Summer 2016 Introduction of Graphics and Imaging Zahid Hossain Animation Animation Art Driven Physics Driven 2 CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) Zahid Hossain Animation Animation

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CS 148: Summer 2016 Introduction of Graphics and Imaging Zahid Hossain

Animation

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Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 2

Art Driven Physics Driven Animation

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Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 3

Art Driven Physics Driven Computer Graphics Animation

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Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 4

Art Driven Physics Driven Computer Graphics Engineering Science Art Animation Story Telling

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Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 5

Art Driven Physics Driven Computer Graphics Engineering Science Art Animation Story Telling

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Luxo Jr. (Pixar Animation 1986)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 6

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Principles of Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 7

1981

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Squash and Stretch

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 8

Rigidity/Flexibility Lively Expressions

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Anticipation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 9

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Slow In And Slow Out

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 10

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Arcs

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 11

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Principles of Animation

https://www.youtube.com/watch?v=5l2Aem7Ll3A

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 12

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Keyframe Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 13

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Keyframes

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 14

  • Specify significant

poses

  • Automatically fill in

motion between these points in time.

http://graphics.stanford.edu/courses/cs148-10-summer/docs/10_anim_interact.pdf

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Not a New Idea

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 15

Tweening: Not a fun job!

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CAPS

Computer-Aided Production System: 1980

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 16

Tweening : Computer Does Interpolation

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Animation Curves

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 17

Curves specify paths that

  • bjects take over time

Knots are positions Tangents are velocities

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 18

?

𝑞" 𝑞# 𝑞$ 𝑞%

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 19

𝑔 𝑢 = 𝑏* + 𝑏"𝑢 + 𝑏$𝑢$ + 𝑏%𝑢%

𝑢 = 0 𝑢 =1 𝑔 0 = 𝑞$ 𝑔 1 = 𝑞% 𝑞" 𝑞#

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 20

𝑔 𝑢 = 𝑏* + 𝑏"𝑢 + 𝑏$𝑢$ + 𝑏%𝑢%

𝑢 = 0 𝑢 =1 𝑔 0 = 𝑞$ 𝑔 1 = 𝑞% 𝑔. * = 𝑞% − 𝑞" 𝑔′ 1 = 𝑞# − 𝑞$ 𝑞" 𝑞#

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 21

𝑔 0 = 𝑏* = 𝑞$

𝑢 = 0 𝑢 =1 𝑔 0 = 𝑞$ 𝑔 1 = 𝑞% 𝑔. * = 1 2 (𝑞% − 𝑞") 𝑔′ 1 = 1 2 (𝑞# − 𝑞$) 𝑞" 𝑞#

𝑔 𝑢 = 𝑏* + 𝑏"𝑢 + 𝑏$𝑢$ + 𝑏%𝑢%

𝑔 1 = 𝑏* + 𝑏" + 𝑏$ + 𝑏% = 𝑞% 𝑔′ 0 = 𝑏" = 1 2 (𝑞% − 𝑞") 𝑔.(1) = 𝑏" + 2𝑏$ + 3𝑏% = 1 2 (𝑞# − 𝑞$)

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 22

Writing the control points 𝑞5 in terms of the parameters 𝑏6

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 23

Fundamentals of Computer Graphics - Shirley Page: 365

𝑫𝟐 Continuity

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Catmull-Rom Spline: Continuity

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 24

𝑞" 𝑞# 𝑞$ 𝑞%

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 25

𝑞" 𝑞# 𝑞$ 𝑞% Incoming Tangent Outgoing Tangent

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Catmull-Rom Spline

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 26

𝑞" 𝑞# 𝑞$ 𝑞% Incoming Tangent Outgoing Tangent “Outgoing Tangent” becomes “Incoming Tagent” for the next Segment

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Framework for Animation Curves

  • Tension
  • Sharpness near keyframes
  • Continuity
  • Different in/out tangents
  • Bias
  • Overshoot or undershoot

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 27

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Framework for Animation Curves

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 28

Fundamentals of Computer Graphics - Shirley Page:420

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Bezier Curve

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 29

Fundamentals of Computer Graphics - Shirley Page:365

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Slow-In-Slow-Out

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 30

t u Bezier Curve is tunable way to implement this Replace an animation parameter 𝒖 with 𝒗(𝒖)

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Key Values vs Key Frames

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 31

  • Animation composed of several parameters
  • Parameters may not agree on which “frame” is important, i.e. there is no “key-

frame” per-se.

  • Create path for each parameter, which has key-values specified in appropriate

frames.

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Specialized Curves for Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 32

“Wiggly Splines”

Kass and Anderson, SIGGRAPH 2008

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Interpolating Orientations

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 33

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Interpolating Matrices ?

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 34

90° CW 90° CCW Not a rotation !

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Euler Angles

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 35 http://www.chrobotics.com/wp-content/uploads/2012/11/Inertial-Frame.png

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Gimbal Lock

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 36

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Spherical Linear Interpolation (SLERP)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 37

LERP: Linear Interpolation

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Spherical Linear Interpolation (SLERP)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 38

Quaternions [Hamilton 1843]

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Quaternions

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 39

Quaternions Euler Matrix

https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles

For conversion formulae

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Character Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 40

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Recall: Hierarchical Modeling

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 41

Body Torso Head Shoulder LeftArm UpperArm LowerArm Hand RightArm UpperArm LowerArm Hand Hips LeftLeg UpperLeg LowerLeg Foot RightLeg UpperLeg LowerLeg Foot

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Forward Kinematics (FK)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 42

Manipulate degrees

  • f freedom directly,

construct geometry hierarchically.

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Inverse Kinematics (IK)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 43

Determine change in parameters from position

  • f end effector.
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Inverse Kinematics (IK)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 44

Determine change in parameters from position

  • f end effector.
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Skinning and Bone Animation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 45

  • Skeleton
  • Nodes represents joints
  • Joints are local Coordinate Systems (frames)
  • Edges represents bones
  • Skin
  • 3D model/surface driver by skeleton

Both are designed in a reference pose (rest pose)

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Skeleton in Reference Pose

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 46

  • Root Frame expressed with respect to the world: 𝑆*
  • Relative Joint Coordinate Frames - 𝑆", 𝑆$, 𝑆% … 𝑆6

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Skeleton in Reference Pose

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 47

  • Root Frame expressed with respect to the world: 𝑆*
  • Relative Joint Coordinate Frames - 𝑆", 𝑆$, 𝑆% … 𝑆6
  • Mapping from local frame to world
  • 𝐵6 = 𝑆* … 𝑆? 6 𝑆6, 𝑞 𝑘 : Parent of joint j

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Animating Skeleton

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 48

Rotation at a joint j

Mapping from Local Frame to World in Reference Pose Mapping from Local Frame to World in Animated Pose

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Character Rigging

  • Embed Skeleton into a Mesh (Skin)
  • Assign Mesh Vertex to one or more

bones to allow

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 49 http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Character Rigging

  • Embed Skeleton into a Mesh (Skin)
  • Assign Mesh Vertex to one or more

bones to allow

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 50

Vertex Assignments Often Done Manually (Choose the closest “bones”)

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Rigid Skin Limitations

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 51

Reference Pose Animated Pose

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Rigid Skin Limitations

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 52

Reference Pose Animated Pose

Leads to abrupt motion near the joint

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Linear Blend Skinning

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 53

Weight needs to be convex

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Linear Blend Skinning

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 54

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Linear Blend Skinning

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 55

Artists paint these weights

Maya

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Linear Blend Skinning: Limitations

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 56

Candy Wrapper Effect

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Why Candy-Wrapper in LBS ?

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 57 http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Why Candy-Wrapper in LBS ?

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 58

Linear SLERP

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Solution to Candy-Wrapper

  • Dual Quternion Skinning [Clifford 1873]
  • Kavan et al.,ACMTOG 2008
  • Model rigid transformation (Rotation+Translation)
  • Map 6 dimensional manifold into 8 dimensional

space

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 59 http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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LBS vs Dual-Quaternion Skinning

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 60

Linear Blend Skinning Dual-Quaternion Skinning

http://www.cs.cmu.edu/~yaser/Lecture-9-Skinning%20and%20Body%20Representations.pdf

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Physically Based Animation

Teaser (David will teach next week)

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 61

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Two-way Solid-Fluid Coupling

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 62

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Detailed Cloth Simulation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 63

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Fracture and Rigid Body

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 64

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Hybrid Daisy Chain

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 65

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Fluid Simulation

CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 66

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SLIDE 67

CS 148: Summer 2016 Introduction of Graphics and Imaging Zahid Hossain

Animation