To Draw a Tree Pat Hanrahan Computer Science Department Stanford University Motivation Hierarchies File systems and web sites Organization charts Categorical classifications Similiarity and clustering Branching processes Genealogy and lineages Phylogenetic trees Decision processes Indices or search trees Decision trees Tournaments Page 1 Tree Drawing Simple Tree Drawing Preorder or inorder traversal Page 2 Rheingold-Tilford Algorithm Information Visualization Page 3 Tree Representations Most Common … Page 4 Tournaments! Page 5 Second Most Common … Lineages Page 6 http://www.royal.gov.uk/history/trees.htm Page 7 Demonstration Saito-Sederberg Genealogy Viewer C. Elegans Cell Lineage [Sulston] Page 8 Page 9 Page 10 Page 11 Evolutionary Trees [Haeckel] Page 12 Page 13 [Agassiz, 1883] 1989 Page 14 Chapple and Garofolo, In Tufte [Furbringer] Page 15 [Simpson]] [Gould] Page 16 Tree of Life [Haeckel] [Tufte] Page 17 Janvier, 1812 “Graphical Excellence is nearly always multivariate” Edward Tufte Page 18 Phenograms to Cladograms GeneBase Page 19 http://www.gwu.edu/~clade/spiders/peet.htm Page 20 Page 21 The Shape of Trees Page 22 Patterns of Evolution Page 23 Hierachical Databases Stolte and Hanrahan, Polaris, InfoVis 2000 Page 24 Generalization • Aggregation • Simplification • Filtering Abstraction Hierarchies Datacubes Star and Snowflake Schemes Page 25 Memory & Code Cache misses for a procedure for 10 million cycles White = not run Grey = no misses Red = # misses y-dimension is source code x-dimension is cycles (time) Memory & Code zooming on y zooms from fileprocedurelineassembly code zooming on x increases time resolution down to one cycle per bar Page 26 Themes Cognitive Principles for Design Congruence Principle: The structure and content of the external representation should correspond to the desired structure and content of the internal representation. Apprehension Principle: The structure and content of the external representation should be readily and accurately perceived and comprehended. [B. Tversky in press] Page 27 Metaphors Survey the space of designs Best metaphors have been refined over time (and have stood the test of time) Need to understand and appreciate what makes metaphors effective It takes both creativity and experience, algorithms and aesthetics, to create new metaphors. Often one element is lacking “Graphical excellence is multivariate,” therefore mix your metaphors Depiction How to map information to graphics Central problem in visualization Formal systems needed Automation and composition Need high-level tools to make this easy Key theorists: Bertin, Cleveland, Mackinlay, MacEachren, Wilkinson Page 28 Challenge Best visualizations designed by humans Computer mediated communication is becoming ubiquitous Therefore: Visualizations are regressing Challenge: Develop algorithms that produce high-quality, effective designs Acknowledgements Tamara Munzner Chris Stolte Diane Tang Maneesh Agrawala Barbara Tversky Page 29.