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Visualizing Multivalued Data from 2D IVisualizing Multivalued Data from 2D Incompressible Flows Using Concepts ncompressible Flows Using Concepts
from Paintingfrom Painting
R. M. Kirby H. Marmanis D. H. Laidlaw R. M. Kirby H. Marmanis D. H. Laidlaw Brown UniversityBrown University
Presented by Hsin-Ji Wang & Chaoli Wang
Oil Painting of the Impressionist Basic Fluid Mechanics Concepts Related Work Visualization Methodology Example 1: Rate of Strain Tensor Example 2: Turbulent Charge and Turbulent
Current Summary and Conclusions
Oil Painting of the ImpressionistOil Painting of the Impressionist
The multiple layers of brush stokes in these paintings provide a natural metaphor of constructing visualization from layers of synthetic “brush stokes”.
The works of three painters they studied– Gogh, Vincent van (1853-1890)– Monet, Claude-Oscar (1840-1926)– Cezanne, Paul (1839-1906)
Oil Painting of the ImpressionistOil Painting of the Impressionist
Two Cypresse (1889)
Van Gogh, whose large, expressive, discrete strokes carry meaning both individually and collectively.
Oil Painting of the ImpressionistOil Painting of the Impressionist
Woman Seated under the Willows
Monet, whose smaller stokes are often meaningless in isolation – the relationships among the stokes give them meaning, far more than in van Gogh.
Oil Painting of the ImpressionistOil Painting of the Impressionist
The Card Players (1890-1892)
Cezanne, who combined strokes into cubist facets, playing with 3D perspective and time within his paintings more than either van Gogh or Monet. His layering also incorporates more atmospheric effects. In a sense, his work shifts from surface rendering toward volume rendering.
Oil Painting of the ImpressionistOil Painting of the Impressionist
Van Gogh's The Mulberry Tree (1889) illustrates the visual shorthand that van Gogh used with his expressive stokes. Multiple layers of stokes combine to define regions of different ground cover, aspects of the hillside, and features of the tree. An underpainting shows the "anatomy" of composition of the scene in broad stokes.
Oil Painting of the ImpressionistOil Painting of the Impressionist
Capture the marriage between direct representation of independent data and the overall intuitive feeling of the data as a whole
Space: encode different information at different scales
Time: design visualizations so that important data features are mapped to quickly seen visual features
Choose the artists in whom you have a passionate interest, any artist has lessons to offer to visualization
Basic Fluid Mechanics ConceptsBasic Fluid Mechanics Concepts
Vorticity Reynolds Number Rate of Strain Tensor Turbulent Charge Turbulent Current
Basic Fluid Mechanics ConceptsBasic Fluid Mechanics Concepts
Vorticity – ξ = × u▽ – Vorticity is primarily used to describe the rotation of fl
uid.– If × u▽ = 0 then the fluid is irrotational– else the fluid is rotational
Basic Fluid Mechanics ConceptsBasic Fluid Mechanics Concepts
Reynolds Number– Reynolds number = ρVD / μ – Reynolds number is proportional to { (inertial force) /
(viscous force) } and is used in momentum, heat, and mass transfer to account for dynamic similarity.
Basic Fluid Mechanics ConceptsBasic Fluid Mechanics Concepts
Rate of Strain Tensor
– The symmetric part is known as the rate of strain tensor
– The anti-symmetric part is known as vorticity
Basic Fluid Mechanics ConceptsBasic Fluid Mechanics Concepts
Turbulent charge and turbulent current
– The turbulent charge and turbulent current, collectively referred to as turbulent sources, could substitute the role of vorticity in more complicated flows.
Related WorkRelated Work
Multivalued data visualization– “Feature-based” methods– Statistical methods– Icons– Layering
Flow visualization– Spot noise– Line integral convolution
Computer graphics painting
Visualization MethodologyVisualization Methodology
Developing a visualization method involves– Breaking the data into components– Exploring the relationships among components– Visually expressing both the components and
their relationships
Example 1: Rate of Strain TensorExample 1: Rate of Strain Tensor
Data breakdown Visualization design
– Priority Velocity Vorticity
– Layering Primer Underpainting Ellipse layer Arrow layer Mask layer
Example 1: Rate of Strain TensorExample 1: Rate of Strain Tensor
Simulated 2D flow past a cylinder at Simulated 2D flow past a cylinder at Reynolds number = 100Reynolds number = 100
Example 1: Rate of Strain TensorExample 1: Rate of Strain Tensor
Simulated 2D flow past a cylinder at Simulated 2D flow past a cylinder at Reynolds number = 500Reynolds number = 500
Example 1: Rate of Strain TensorExample 1: Rate of Strain Tensor
Experimental 2D flow past an airfoilExperimental 2D flow past an airfoil
Example 2: Turbulent Charge and Turbulent currentExample 2: Turbulent Charge and Turbulent current
Drag reduction (riblets) Data breakdown Visualization design
– Priority Overall location of the turbulent charge Vorticity Structure of the flow – velocity field Fine details
– Layering Primer and underpainting Arrow layer
Turbulent source layer Mask layer
Turbulent charge and turbulent current of Turbulent charge and turbulent current of simulated 2D flow past a cylinder at Reynolds simulated 2D flow past a cylinder at Reynolds
number = 500number = 500
Example 2: Turbulent Charge and Turbulent currentExample 2: Turbulent Charge and Turbulent current
Reynolds Reynolds number = 100number = 100
Example 2: Turbulent Charge and Turbulent currentExample 2: Turbulent Charge and Turbulent current
Reynolds Reynolds number = 500number = 500
Example 2: Turbulent Charge and Turbulent currentExample 2: Turbulent Charge and Turbulent current
Combination of Combination of velocity, vorticity,velocity, vorticity, rate of strain, tu rate of strain, turbulent charge arbulent charge and turbulent currnd turbulent current for Reynolds ent for Reynolds number = 100number = 100
Example 2: Turbulent Charge and Turbulent currentExample 2: Turbulent Charge and Turbulent current
Summary and ConclusionsSummary and Conclusions
Borrow concepts from oil painting– Underpainting– Brush strokes– Layering
Represent many values at each spatial location in different perspectives
Get a complete idea of both the dynamics and kinematics of the flow
Provide catalyst for future understanding of more complex fluid phenomena
Thank you!Thank you!