應用於資訊視覺化之矩形心臟圖

Abstract

在地理資訊系統的視覺化介面中，地圖上的區域可以反映地理資訊是相當有用的。製 圖學家和地理學家提出了一種稱為矩形心臟圖的地圖，其中圖內的每一個地區被繪製 成一個矩形，且每個矩形的面積大小正比於其所對應之地理變數值(例如：人口)。由於 每一個地區的形狀被受限為矩形，所以每個矩形面積的限定可能會使得瞭解區域之間 的拓樸關連性變得很困難，因此好的矩形心臟圖是很難產生的。矩形心臟圖的外觀與 用在VLSI 電路設計之佈局規劃相當的類似，不過兩者所追求的目標函式不同：前者追 求各矩形之面積與其所反映之地理變數值的差異最小化或區域之間的拓樸關連性誤差 最小化；而後者追求面積最小化或電路繞線最短化。因此，過去在佈局規劃領域被探 索的問題也應該可以被拿來在矩形心臟圖上作探討。本計畫將參考過去在佈局規劃領 域之相關文獻，進而探討可能的矩形心臟圖在理論上與實務上的各類型議題：可切斷 的與不可切斷的矩形心臟圖、為區域標示所設計之矩形心臟圖、用不規則形狀節點之 圖形來表示矩形心臟圖、用鍛鐵法來設計矩形心臟圖、及矩形心臟圖之超節點視覺化。 最後，我們將開發一軟體平台，並在此平台上實作我們針對各議題所開發之演算法。 更進一步地，我們將移植這些演算法到有較多地理資訊系統應用之行動平台上。

In the visualization interface for geographic information system, it is much useful to represent geographical information of a region on the map by its area. Cartographers and geographers proposed a kind of map, called rectangular cartogram, in which each region is represented by a rectangle, and the size of each rectangle is proportional to its corresponding geographic variable, e.g., population. Since the shape of each region is limited to be a rectangle, the area specifications for each rectangle may make it not easy to understand correct adjacencies among regions, so that it is difficult to produce good rectangular cartograms. In fact, the appearance of rectangular cartograms is very similar to floorplans used in VLSI circuit design, but their objective functions are different: the former is to minimize the difference between each region and its corresponding geographic variable or to minimize the adjacency errors among regions; the latter is to minimize the whole layout size or the total wire length. As a result, the problems investigated in floorplanning also could be studied in design of rectangular cartograms. In this project, we will be referred to the previous results in floorplanning to investigate a variety of possible theoretical and practical issues in design of rectangular cartograms: sliceable and non-sliceable rectangular cartograms, rectangular cartograms for area labeling, rectangular cartogram represented by graphs with nonuniform nodes, rectangular cartogram using simulated annealing, as well as rectangular cartograms with super areas. Finally, we will develop a software platform, in which our algorithms designed for the above issues will be implemented and tested. Furthermore, those algorithms will be transplanted to mobile platform, which has more applications in geographic information system.