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Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Page 1: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

Mass-Spring Systems

Versatile Visualization Techniques Flexible Surfaces to

Multidimensional Scaling

Brian DuffyMSIM 742: Visualization II

Page 2: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Mass-Spring Construction

Masses Bound by Springs Surface Vertices Individual Objects Relative Resistance Values

Springs Push & Pull Masses Use Hooke’s Law for Tension Spring Coefficients Drive

Alignment Impose Chain Reactions

Iterative Adjustments Drive Proper Placement of Masses

Page 3: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Diverse Uses

Fabric Simulation Human Tissue Simulation Simulating Hair Multidimensional Scaling

Large Datasets with Many VariablesNatural Clustering of Similar Entities

Page 4: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Fabric Simulation Springs Between Vertices

Rectangular for Basic Shape Diagonals Prevent Shearing Bend Springs Control Folding

Collisions Cause Draping Vertex-level Collisions Springs Control Fabric Shape

Forces Applied to Vertices Gravity, Wind, Mechanical

Page 5: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Human Tissue Simulation

Critical Vertices Move Based on Muscles

Skin Surface Follows Critical Vertices

Skeletal Structure Imposes Limitations on Movements

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Simulating Hair Wisp Skeletons Use Both

Linear and Angular Springs Between Rigid Bodies

Implicit Backward Euler Method Improves Speed and Supports Torsional Motion

Page 7: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Multidimensional Scaling Project N-Dimensions in 2D or

3D Views

Calculate Proximity Between Points

Springs Between Points

Proximity is Relaxed Spring Length

N2 – N Springs Required

Large Data Sets Present Challenges

Page 8: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Multidimensional Scaling Improved Processing Time

Sample √N Points as Parents Position Parents Assign Each Point to a Parent

via Nearest Neighbor Process Place Springs Within Clusters

and Between Parent Nodes

Reduced from N√N to N5/4 Calculations 100,000+ Items with 14+

Dimensions are Now Possible

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Future Work

Cross-Culture Historical Time ClusterReplaces Traditional TimelinesFocuses on Similarities of Events and Conditions

Interactive Humans Convey Details of the EventsPersonalize Event Causes and ConsequencesRealistic Expressions and Gestures

Page 10: Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling Brian Duffy MSIM 742: Visualization II

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Brian DuffyMSIM 742: Visualization II

May 7, 2008

Conclusions

Mass-Spring Systems are Versatile Visualization Tools

Relatively Simple Iterative Implementations

Best Effects on Small to Medium Sized Datasets

Powerful Tool for All Graphics Software Developers