Nicely Drawing Tree-Structured Diagrams on the Euclidian Plane

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A tree-structure is T=(V,E,r,width,depth,Int_x,Int_y),where (V,E) is an ordered tree (a tree denotes an ordered tree),V is a set of cells ,and B is a set of edges.The root cell is r E V .The map width V→R is the width function of the cells.The vertical length is represented by width(p),which is called the width of the cell p.The map depth V R is the depth function of the cells.The horizontal length is represented by depth(p),which is called the depth of the cell p.A real value Int_x (Int_y) is the minimum interval of cells with respect to the x-coordinate (y-coordinate).Int and Int_y are spaces where to draw connection lines among cells.A placement of a tree-structure T=(V,B,r,width,depth,Int_x,Int_y) is defined by the function π:V→R^2 π_x(p) and π_y(p) denote the x-coordinate and the y-coordinate of p respectively,where π(p)=(x,y).We suppose that the c-coordinate directs from left to right and thep-coordinate directs downward because of the application to program diagrams,and we suppose that the topleft point of a cell is assigned by its coordinate.Let T be a trestructure and r be a placement ofT.Then,D=(T,π)is called a tree-structured diagram.We define the location of a cell as follow.The width of a tree-structured diagram D=(T,π)is defined bywidth(T,π)≡max{π_y(q)+width(q)-π_y(p)|p and q are cells in T and π_y(p) &le π_y(q)}.The level of a cell p is defined by the number of edges between the cell p and the root cell.For a cell p,the function Index is defined by Index(p)≡0:if p is the root cell {i:if p is the i-th child of the parent of p.We have implemented a system for generating Hichart [3] tree-structured diagrams which is output on the character displays such as used with PC and Host machines.There fore,the eumorphous conditions are also applied on the integral lattice.Because of the recent widespread use of Unix workstations and bit-map displays,however,we are forced to develop the Hichart system on bit-map displays,on which the location is indicated by using values on the Euclidianplane.In this paper,we modify the eumorphous conditions[1,4]and introduce new conditions on the Euclldian plane.Next,we provide 0(n)-time algorithm that corresponds to the new conditions.Results of this paper will be applied to drawings of structured program diagrams including Hichart,PAD SPD,TSF,tree-styled browser among others.
一般社団法人情報処理学会の論文
1993-03-01

Nicely Drawing Tree-Structured Diagrams on the Euclidian Plane

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