Hyperbolic Trees A Focus + Context Technique John lamping Ramana Rao Peter Pirolli Joy Mukherjee

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

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

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

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

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

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

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

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.

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

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

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

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

Animated Transitions Maintains object constancy Helps user assimilate changes across views Generated using ‘n th -root’ concept Bottleneck – display performance Compromises for quick redisplay -draw less of the fringes -draw lines rather than arcs -drop text during animation

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

Evaluation Learnability -* * * * * Retention -* * * * * Ease of use -* * * * * Error recovery -* * * * User satisfaction -* * * *

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