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

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Presentation transcript:

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

Brian Duffy MSIM 742: Visualization II 2 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

Brian Duffy MSIM 742: Visualization II 3 May 7, 2008 Diverse Uses Fabric Simulation Human Tissue Simulation Simulating Hair Multidimensional Scaling  Large Datasets with Many Variables  Natural Clustering of Similar Entities

Brian Duffy MSIM 742: Visualization II 4 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

Brian Duffy MSIM 742: Visualization II 5 May 7, 2008 Human Tissue Simulation Critical Vertices Move Based on Muscles Skin Surface Follows Critical Vertices Skeletal Structure Imposes Limitations on Movements

Brian Duffy MSIM 742: Visualization II 6 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

Brian Duffy MSIM 742: Visualization II 7 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 N 2 – N Springs Required Large Data Sets Present Challenges

Brian Duffy MSIM 742: Visualization II 8 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 N 5/4 Calculations  100,000+ Items with 14+ Dimensions are Now Possible

Brian Duffy MSIM 742: Visualization II 9 May 7, 2008 Future Work Cross-Culture Historical Time Cluster  Replaces Traditional Timelines  Focuses on Similarities of Events and Conditions Interactive Humans  Convey Details of the Events  Personalize Event Causes and Consequences  Realistic Expressions and Gestures

Brian Duffy MSIM 742: Visualization II 10 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

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