Mass-Spring Systems Versatile Visualization Techniques Flexible Surfaces to Multidimensional Scaling...
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Mass-Spring Systems
Versatile Visualization Techniques Flexible Surfaces to
Multidimensional Scaling
Brian DuffyMSIM 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
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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
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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
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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
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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
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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
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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