The lifespan model of GIS data representation over scale space

Multi-scale representations of spatial data is one of the key technologies in GIS applications. It plays an important role in such applications as seamless data navigation, progressive Web transfer and self-adaptable visualization. This paper aims at the objective by small size of data volume to realize high granularity multi-representation, presenting a data model, namely the lifespan model over scale space, to divide the spatial data into different representation scene over scale space. To construct the object-oriented model of representation lifespan, we consider that during the whole life time [S₀, S_n], an object has some base representations g₀, g₁hellipgm, which related to some key happening point s₀, s₁hellipsm over scale space. An essential evolution of the representation arises at each key happening point, such as from polygon to polyline. But between two adjacent key scale points S_i and S_j, the evolutions of the representation are smooth. So the middle representations between [S_i, S_j] can be derived by a transformation function f. Based on this consideration, the scale based transformation is defined as a tri-tuple: T_ij: <f_i, [S_i1, S_i2], {g_ij}>, where f_i is the transformation function, [S_i1, S_i2] the scale range controlled by two key scale points S_i1 and S_i2 and {g_ij} the base representation status associated with the key scale point of S_i1 or S_i2. Then the representation of the object at any scale S_x can be formulized as: R_x=f_i({g_ij},x). Considering the transformation properties of gradual change vs. abrupt change, we summarize four types of transformation functions. They are (1) traditional map generalization, (2) interpolation (morphing) transformation, - (3) LOD accumulation and (4) equal transformation.