Hyperbolic Trees

1
Hyperbolic Trees

• A Focus Context Technique
• http//www.acm.org/sigchi/chi95/proceedings/papers
  /jl_bdy.htm
• John lamping
• Ramana Rao
• Peter Pirolli
• Joy Mukherjee

2
Essentials

• Visualizing Hierarchies
• Features
• - More space to a part
• - Still maintain context
• Scheme
• - Lay out on hyperbolic plane
• - Map this to a circular display

3
Inspiration

• Escher woodcut
• - Size diminishes outward
• - devilish growth in no. of components
• - Uniformly embedding an exponentially growing
  structure
• Space available to a node with all its children
  falls of continuously with distance from the
  center

4
Related Work

• Peer work
• - Document Lens
• - Perspective Wall
• - The Cone Tree
• - Tree Maps
• - Prune and Filter
• Problems
• - None provide a smooth blend of focus
  context

5
Issues

• Layout
• Mapping and Representation
• Change of focus
• Node Information
• Preserving Orientation
• Animated Transitions

6
Layout

• Features
• - Circumference and area of circles grow
  exponentially with radius
• - Recursive algorithm laying out each node
  based on local information
• - Divergence of parallel lines on a hyperbolic
  plane
• - Easy implementation
• - Required only once

7
Layout

• Mechanism
• - Allocate a wedge of the hyperbolic plane to
  each node
• - Place children along an arc in the wedge
• - maintain distance from itself and between the
  children
• - Recurse on each child
• - Each wedge retains the same angle

8
Layout

• Variations
• - non-uniform trees
• allocate larger wedge to sibling with
  more children
• decreases variation in node separation
• - using less than 360
• put all children in one direction

9
Mapping and Representation

• Poincar\e model ( conformal mapping )
• - preserves angles
• - distorts lines into arcs
• Klein model
• - preserves lines, distorts angles
• Cannot have it both ways
• Poincar\e preferred
• - points near the edge get more screen area than
  in Klein's model.

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Change of Focus

• Rigid transformation of hyperbolic plane
• Mapping the new plane back to the display
• Multiple transformations
• - compose into single transformation
• - avoids loss of floating point precision
• Compute transformation for nodes with display
  size at least one pixel
• - Bound on redisplay computation

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Node Information

• Features
• - circles on the hyperbolic plane are circles
  on the Euclidean disk
• - decrease in size with distance from center
• Mechanism
• - display node information based on the
  circular area available for the node

12
Preserving Orientation

• Rotation
• - translation on the hyperbolic plane causes
  the display to rotate
• - may lead to different view of a node when
  revisited
• - nodes further from the line of translation
  rotate more
• Solution
• - most direct translation between points
  specified a rotation about the point moved

13
Preserving Orientation

• Approaches for adding rotation
• - always keep original orientation of the root
• hence all nodes maintain their original
  orientations
• - explicit lack of orientation
• node in focus fans out in one and only
  direction
• hence each node is viewed in one and one
  way only

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Animated Transitions

• Maintains object constancy
• Helps user assimilate changes across views
• Generated using nth-root concept
• Bottleneck display performance
• Compromises for quick redisplay
• - draw less of the fringes
• - draw lines rather than arcs
• - drop text during animation

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Pros and Cons

• Pros
• - Easy blending between focus and context
• - Avoids distortion and hiding of information
• - Scaling up to 10 times space for text
• Cons
• - May lead to cramping if each node has several
  children
• - Not much accompanying information

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Evaluation

• Learnability
• -
• Retention
• -
• Ease of use
• -
• Error recovery
• -
• User satisfaction
• -

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Its over ! Yoohooo !!!!

• No questions Pleeeeeeeeaaaaasseeee !!!!