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.

10. 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

11. 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

14. 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

15. 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

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

17. It’s over ! Yoohooo !!!! No questions … Pleeeeeeeeaaaaasseeee !!!!