Statecharts aka Harel Charts visual formalism (cid:0) higraph based (rigour) (cid:0) diverse applications; (cid:0) in particular: concurrent systems behaviour McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 1/39 Visualising Information complex (cid:0) non-quantitative, structural (cid:0) topological, not geometrical (cid:0) Euler (cid:0) (cid:150) graphs (nodes, edges: binary relation); hypergraphs (cid:150) Venn diagrams (Jordan curve: inside/outside): enclosure, intersection McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 2/39 Venn diagrams, Euler circles P&Q P Q B P&Q&R P&R Q&R A R topological notions: (cid:0) enclosure, exclusion, intersection Used to represent mathematical set operations: (cid:0) union, intersection, difference McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 3/39 Hypergraph a c b d e f g h i a hypergraph a graph topological notion: connectedness (cid:0) Used to represent relations between sets. (cid:0) X X Hyperedges: 2 2 (cid:0) (cid:1) (cid:2) McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 4/39 Higraphs: combining graphs and Venn diagrams sets + cartesian product (cid:0) hypergraphs (cid:0) McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 5/39 Blobs: set inclusion, not membership A D E McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 6/39 Unique Blobs (atomic sets, no intersection) A C D W B X P K Q R N U L O V F S M T P E empty space has no meaning, intersection must be identi(cid:2)ed (cid:0) atomic blobs are identi(cid:2)able sets (cid:0) other blobs are union of enclosed sets (cid:0) McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 7/39 Unordered Cartesian Product: Orthogonal Components A C D W B X Y P K Q R N U L O V F M S P T G H E K G H L M N O P (cid:3) (cid:2) (cid:3) (cid:5) (cid:2) (cid:5) (cid:5) (cid:4) (cid:6) (cid:4) (cid:6) McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 8/39 Meaningless constructs C A D B McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 9/39 Simple Higraph blobs orthogonal components A B J D C E K L F M G H I McGill,October,2001 [email protected] Higraphs/StateCharts/ObjectModelling 10/39