目錄
序
前富
第1章 概論 1
1.1 引言 1
1.2 空間數(shù)據(jù) 2
1.2.1 地理實(shí)體的特征 2
1.2.2 空間數(shù)據(jù)的類(lèi)型 2
1.2.3 空間數(shù)據(jù)的特性 3
1.2.4 空間數(shù)據(jù)的表示模型 4
1.3 空間分析的定義與內(nèi)容 5
1.3.1 空間分析的定義 5
1.3.2 空間分析的內(nèi)容 6
1.4 壁間模型與數(shù)學(xué)模型 6
1.4.1 空間模型H 6
1.4.2 空間分析模型 7
1.4.3 數(shù)學(xué)模型 7
1.5 空間分析與GIS 8
1.6 空間分析與數(shù)學(xué)基礎(chǔ) 10
1.6.1 數(shù)值計(jì)算方法 10
1.6.2 圖論 10
1.6.3 分形 10
1.6.4 小被分析 11
1.7 本書(shū)內(nèi)容安排 11
第2章 數(shù)學(xué)基礎(chǔ) 12
2.1 一元函數(shù)插值與逼近 12
2.1.1 引言 12
2.1.2 n次代數(shù)插值多項(xiàng)式 13
2.1.3 埃爾米特插值多項(xiàng)式 14
2.1.4 分段低次插值 14
2.1.5 樣條函數(shù)插值 17
2.1.6 等距B樣條函數(shù)插值 18
2.1.7 曲線(xiàn)擬合的最小二乘法 20
2.2 二元函數(shù)插值與逼近 22
2.2.1 引言 22
2.2.2 矩形區(qū)域上的代數(shù)插值逼近 23
2.2.3 矩形區(qū)域上的樣條插值逼近27
2.2.4 矩形區(qū)域上的最小二乘逼近 H 29
2.2.5 三角形區(qū)域上的插值逼近 29
2.2.6 移動(dòng)曲面擬合法 31
2.3 數(shù)值微分 32
2.3.1 一元函數(shù)的數(shù)值微分 33
2.3.2 二元函數(shù)的數(shù)值微分34
2.4 圖論基礎(chǔ) 36
2.4.1 圖 37
2.4.2 樹(shù) 38
2.4.3 最短路徑和最小生成樹(shù)39
2.4.4 有向圖及其矩陣表示 41
2.5 分形基本理論 43
2.5.1 測(cè)度與分維 43
2.5.2 分維估值方法 45
2.5.3 元標(biāo)度域 46
2.5.4 線(xiàn)狀要素分維估值 48
2.5.5 分形插值 49
2.6 小波分析基礎(chǔ) 50
2.6.1 連續(xù)小波變換 51
2.6.2 正交小波基和多尺度分析 52
2.6.3 小波正交分解 53
2.6.4 多進(jìn)制小波 55
2.6.5 其他 57
第3章 疊置分析模型 59
3.1 基本概念 59
3.1.1 基本思想 59
3.1.2 空間邏輯運(yùn)算 60
3.1.3 空間邏輯運(yùn)算規(guī)律 60
3.2 視覺(jué)信息疊置分析 61
3.3 矢量數(shù)據(jù)疊置分析 62
3.3.1 矢量數(shù)據(jù)疊置分析類(lèi)型 62
3.3.2 點(diǎn)與點(diǎn)的疊置 62
3.3.3 點(diǎn)與線(xiàn)的疊置 63
3.3.4 點(diǎn)與多邊形的疊置 63
3.3.5 線(xiàn)與線(xiàn)的疊置 64
3.3.6 線(xiàn)與多邊形的疊置
3.3.7 多邊形與多邊形的疊置 65
3.3.8 疊置分析中的誤差 66
3.4 多邊形裁剪 67
3.4.1 多邊形裁剪算法 67
3.4.2 多邊形裁剪示例 68
3.5 柵格數(shù)據(jù)疊置分析 70
3.5.1 非壓縮柵格數(shù)據(jù)的疊置分析 70
3.5.2 壓縮柵格數(shù)據(jù)的疊置分析 71
第4章 緩沖區(qū)分析模型 73
4.1 基本概念 73
4.1.1 緩沖區(qū)的定義 73
4.1.2 幾個(gè)基本概念 74
4.2 緩沖區(qū)生成算法 75
4.2.1 點(diǎn)目標(biāo)緩沖區(qū)邊界生成算法 75
4.2.2 線(xiàn)目標(biāo)緩沖區(qū)邊界生成算法 76
4.2.3 面目標(biāo)緩沖區(qū)邊界生成算法 83
4.3 動(dòng)態(tài)目標(biāo)緩沖區(qū)的生成算法 83
4.3.1 動(dòng)態(tài)緩沖區(qū)邊界生成算法 83
4.3.2 緩沖區(qū)分析特殊情況處理 85
4.4 三維空間目標(biāo)的緩沖區(qū) 86
4.4.1 三維空問(wèn)目標(biāo)緩沖區(qū)分析的一般定義86
4.4.2 三維空間點(diǎn)目標(biāo)的緩沖區(qū)分析 86
4.4.3 三維空間線(xiàn)目標(biāo)的緩沖區(qū)分析 87
4.4.4 三維空問(wèn)面目標(biāo)緩沖區(qū)邊界生成算法 89
4.4.5 三維空問(wèn)體目標(biāo)的緩沖區(qū) 89
第5章 統(tǒng)計(jì)分析模型 90
5.1 統(tǒng)計(jì)圖表分析 90
5.1.1 統(tǒng)計(jì)圖 90
5.1.2 統(tǒng)計(jì)表 91
5.1.3 基于統(tǒng)計(jì)圖表的數(shù)據(jù)擬合 92
5.2 描述統(tǒng)計(jì)分析 93
5.2.1 分布密度 93
5.2.2 均值 94
5.2.3 分布中心 95
5.2.4 距離 96
5.3 主成分分析 97
5.3.1 主成分分析問(wèn)題的轉(zhuǎn)化 97
5.3.2 主成分分析問(wèn)題的求解 98
5.3.3 主成分分析問(wèn)題的計(jì)算過(guò)程 100
5.4 聚類(lèi)分析 100
5.4.1 壁間物體的距離 101
5.4.2 系統(tǒng)聚類(lèi)法 102
5.4.3 動(dòng)態(tài)聚類(lèi)法 105
5.4.4 判別聚類(lèi) 107
5.4.5 最�。ù螅┲�撐樹(shù)聚類(lèi)方法 107
5.5 關(guān)鍵變量分析 108
5.6 典型相關(guān)分析 108
5.6.1 典型相關(guān)分析基本算法 109
5.6.2 典型相關(guān)分析計(jì)算步驟109
5.7 層次分析法 111
5.7.1 層次分析結(jié)構(gòu)模型 111
5.7.2 層次分析結(jié)構(gòu)模型的計(jì)算 112
第6章 網(wǎng)絡(luò)分析模型 115
6.1 網(wǎng)絡(luò)分析基礎(chǔ) 115
6.1.1 網(wǎng)絡(luò)中的基本元素及屬性 115
6.1.2 網(wǎng)絡(luò)的空間數(shù)據(jù)模型 117
6.2 最短路徑分析 118
6.2.1 最短路徑的數(shù)學(xué)模型 119
6.2.2 最短路徑分類(lèi) 119
6.2.3 最短路徑的Dijkstra 算法 121
6.2.4 Floyd 算法 123
6.2.5 A'算法 124
6.2.6 所有點(diǎn)對(duì)問(wèn)的最短路徑125
6.3 最佳路徑分析 125
6.3.1 最大可靠路徑 125
6.3.2 最大容量路徑 126
6.3.3 最佳路徑的表現(xiàn)形式 127
6.4 資源分配 128
6.4.1 基本概念 128
6.4.2 資源分配目標(biāo)方程 129
6.4.3 P-中心定位與分配問(wèn)題 129
6.5 流分析 131
6.5.1 最大流模型 131
6.5.2 最大流解法一一標(biāo)號(hào)法 132
6.5.3 最小費(fèi)用最太流問(wèn)題 133
第7章 DEM 表面建模及精度分析模型136
7.1 數(shù)字高程模型概念 136
7.1.1 基本概念 136
7.1.2 規(guī)則格網(wǎng)和不規(guī)則三角網(wǎng)DEM 137
7.2 DEM 表面建模 139
7.2.1 基于TIN 的DEM 表面建模 139
7.2.2 基于正方形格網(wǎng)的表面建模 140
7.2.3 基于混合格網(wǎng)的表面建模 142
7.2.4 表面建模的討論 142
7.3 DEM 內(nèi)插模型 142
7.3.1 整體內(nèi)插 143
7.3.2 分塊內(nèi)插 143
7.3.3 逐點(diǎn)內(nèi)插 146
7.3.4 內(nèi)插方法的討論 149
7.4 基于正方形格網(wǎng)的DEM 精度模型 149
7.4.1 DEM 精度評(píng)估指標(biāo) 150
7.4.2 DEM 精度試驗(yàn) 151
7.4.3 DEM 精度理論模型.153
7.5 基于正方形格網(wǎng)的高階插值傳遞誤差模型 155
7.5.1 基于不完全雙二次多項(xiàng)式的表面?zhèn)鬟f誤差模型 155
7.5.2 基于雙三次插值多項(xiàng)式的表面?zhèn)鬟f誤差模型 158
7.6 基于TIN 的DEM 傳遞誤差模型 160
7.6.1 TIN 格網(wǎng)上傳遞誤差表達(dá)式 160
7.6.2 TIN 上高程傳遞誤差公式 162
7.7 地形描述誤差模型 164
7.7.1 地形描述誤差概念 164
7.7.2 地形描述誤差擬合模型 165
第8章 三維地形分析模型 168
8.1 表面識(shí)和體積 168
8.1.1 表面積和體積的數(shù)學(xué)公式 168
8.1.2 表面積 169
8.1.3 體積 172
8.2 坡度和坡向 173
8.2.1 披度 173
8.2.2 坡向 176
8.3 地形起伏變化因子 178
8.3.1 曲率 178
8.3.2 地表粗糙度 179
8.3.3 格網(wǎng)面元凹凸系數(shù) 179
8.3.4 高程變異系數(shù) 180
8.4 曲面分維模型 180
8.4.1 曲面的分維數(shù)計(jì)算 181
8.4.2 分維布朗曲面（fBm) 的分維數(shù)計(jì)算 182
8.5 剖面分析 183
8.5.1 基于正方形格網(wǎng)的剖面線(xiàn) 183
8.5.2 基于TIN 的剖面線(xiàn) 185
8.6 可視化分析 186
8.6.1 兩點(diǎn)之閘的可視性 186
8.6.2 可視域 187
8.6.3 地物可視化模型 187
8.6.4 可視化分析的應(yīng)用 188
第9章 小誼分析應(yīng)用模型 189
9.1 矢量地圖數(shù)據(jù)的小波壓縮模型 189
9.1.1 基本壓縮模型 189
9.1.2 邊界處理 190
9.1.3 特征點(diǎn)迫蹤 191
9.1.4 矢量地圖數(shù)據(jù)壓縮模型 192
9.1.5 實(shí)驗(yàn)與分析 192
9.2 矢量地圖數(shù)據(jù)的多進(jìn)制小被壓縮模型 194
9.2.1 多進(jìn)制小波壓縮原理 194
9.2.2 實(shí)驗(yàn)分析和討論 195
9.2.3 地性線(xiàn)提取 196
9.2.4 多進(jìn)制小波壓縮模型 197
9.3 基于小波的DEM 數(shù)據(jù)簡(jiǎn)化模型 197
9.3.1 基于二進(jìn)制小波的簡(jiǎn)化模型 197
9.3.2 基于多進(jìn)制小潑的簡(jiǎn)化模型 198
9.3.3 實(shí)驗(yàn)及分析 198
9.4 基于小波的圖形圖像放大模型200
9.4.1 基于插值的放大模型 200
9.4.2 基于二進(jìn)制小波的放大模型 202
9.4.3 基于多進(jìn)制小波變換的放大模型 203
9.4.4 實(shí)驗(yàn)與分析 203
主要參考文獻(xiàn) 206
Contents
Foreword
Preface
Contents
Chapter 1 General Introduction 1
1.1 Introduction 1
1.2 Spatial data 2
1.2.1 The nature of geographic entity 2
1.2.2 The classification of spatial data 2
1.2.3 The characteristics of spatial data 3
1.2.4 The representation models of spatial data 4
1.3 The definition and contents of spatial analysis 5
1.3.1 The definition of spatial analysis 5
1.3.2 The scope of spatial analysis 6
1.4 Spatial models and mathematical models 6
1.4.1 Spatial models 6
1.4.2 Spatial analysis models 7
1.4.3 Mathematical models 7
1.5 Spatial analysis and GIS 8
1.6 Spatial analysis and mathematical foundation 10
1.6.1 Numerical calculation methods 10
1.6.2 Graph theory 10
1.6.3 Fractal 10
1.6.4 Wavelet analysis 11
1.7 The structure of this book 11
Chapter 2 Mathematical Foundation 12
2.1 The interpolation and approximation of one-dimension function 12
2.1.1 Introduction 12
2.1.2 The n-times algebraic interpolation polynomia1 13
2.1.3 The Hermite interpolation polynomial 14
2.1.4 The piecewise low-order interpolation 14
2.1.5 The spline function interpolation 17
2.1.6 The equidistant B-spline function interpolation 18
2.1.7 The least square method for curve fitting 20
2.2 The interpolation and approximation of two-dimension function 22
2.2.1 Introduction 22
2.2.2 The algebraic interpolation and approximation on a rectangle area 23
2.2.3 The spline interpolation and approximation on a rectangle area 27
2.2.4 The least square approximation method on a rectangle area 29
2.2.5 The interpolation and approximation on a triangle area 29
2.2.6 The moving surface fitting method 31
2.3 Numerical differential 32
2.3.1 The numerical differentiation of one-dimension function 33
2.3.2 The numerical differentiation of two-dimension function 34
2.4 The basic graph theory 36
2.4.1 Graph 37
2.4.2 Tree 38
2.4.3 The shortest path and minimum spanning tree 39
2.4.4 The directed graph and its representation by matrix 41
2.5 The basic fractal theory 43
2.5.1 The measure and fractal dimension 43
2.5.2 The estimation of fractal dimension 45
2.5.3 Scaleless range 46
2.5.4 The estimation of fractal dimension for linear element 48
2.5.5 The fractal interpolation 49
2.6 The basic wavelet analysis 50
2.6.1 The continuous wavelet transformation 51
2.6.2 The orthogonal wavelet base and multi-scale analysis 52
2.6.3 The orthogonal wave1et decomposition 53
2.6.4 The multi-band wavelet 55
2.6.5 The other wavelet methods 57
Chapter 3 Overlay analysis models 59
3.1 The basic conceptions 59
3.1.1 The basic principal of overlay analysis 59
3.1.2 The spatiallogic operations 60
3.1.3 The rules of spatiallogic operations 60
3.2 Overlay analysis of visual information 61
3.3 Overlay analysis of vector data 62
3.3.1 The classification of overlay analysis for vector data 62
3.3.2 Overlay between points 62
3.3.3 Overlay between point and line 63
3.3.4 Overlay between point and polygon 63
3.3.5 Overlay between lines 64
3.3.6 Overlay between line and polygon 64
3.3.7 Overlay between polygons 65
3.3.8 Error analysis in overlay spatial analysis 66
3.4 Polygon-based overlay spatial analysis 67
3.4.1 Polygon clipping algorithm 67
3.4.2 An example for polygon clipping 68
3.5 Raster-based overlay spatial analysis 70
3.5.1 The overlay spatial analysis of non-compressed raster data 70
3.5.2 The overlay spatial analysis of compressed raster data 71
Chapter 4 Buffer analysis models 73
4.1 The basic conceptions 73
4.1.1 The definition of buffer spatial analysis 73
4.1.2 Several basic concepts 74
4.2 The algorithrns of generating buffers 75
4.2.1 The algorithm of generating buffer boundary for point 75
4.2.2 The algorithm of generating buffer boundary for line 76
4.2.3 The algorithm of generating buffer boundary for surface 83
4.3 The algorithrns generating buffers dynarnically 83
4.3.1 The algorithm of generating buffer boundary dynamically 83
4.3.2 The special processing methods for buffer analysis 85
4.4 The buHer of three-dirnension objects 86
4.4.1 The definition of buffer analysis for three-dimension obiects 86
4.4.2 Buffer analysis for three-dimension points 86
4.4.3 Buffer analysis for three-dimension lines 87
4.4.4 The algorithms of generating buHer boundary for three-dimension surfaces 89
4.4.5 Generating buffer for three-dimension solid obiects 89
Chapter 5 Statistical analysis models 90
5.1 Analysis based on statistical charts and tables 90
5.1.1 The statistical charts 90
5.1.2 The statistic tables 91
5.1.3 The data fitting based on statistical charts and tables 92
5.2 The describing statistical analysis 93
5.2.1 The distributing density 93
5.2.2 The mean 94
5.2.3 The distribution center 95
5.2.4 The distance 96
5.3 The principal component analysis 97
5.3.1 The transformation of principle component analysis 97
5.3.2 The solving of principle component analysis 98
5.3.3 The calculation procedure of principle component analysis 100
5.4 The clustering analysis 100
5.4.1 The distance between space objects 101
5.4.2 The systematical clustering method 102
5.4.3 The dynamical clustering method 105
5.4.4 The differentiate c1ustering method 107
5.4.5 The minimum （maximum) support tree clustering method 107
5.5 The key variable analysis 108
5.6 The typical correlation analysis 108
5.6.1 The basic algorithm of typical correlation analysis 109
5.6.2 The calculation procedure of typical correlation analysis 109
5.7 The hierarchical analysis 111
5.7.1 The structure model for hierarchical analysis 111
5.7.2 The calculation of the structure model for hierarchical analysis 112
Chapter 6 Network analysis models 115
6.1 The basic conceptions 115
6.1.1 The basic elements and attributes of a network 115
6.1.2 The spatial data models of a network 117
6.2 The shortest path analysis 118
6.2.1 The mathematical models of shortest path analysis 119
6.2.2 The classification of shortest path 119
6.2.3 The Dijkstra algorithm of shortest path analysis 121
6.2.4 The Floyd algorithm 123
6.2.5 A' algorithm 124
6.2.6 The shortest path between a11 nodes 125
6.3 The optimized path analysis 125
6.3.1 The maximum reliable path 125
6.3.2 The maximum capacity path 126
6.3.3 The representation forms of optimized path 127
6.4 The resource allocation 128
6.4.1 The basic concepts 128
6.4.2 The object equation of resource allocation 129
6.4.3 The P center positioning and allocation problem 129
6.5 The flow analysis 131
6.5.1 The maximum f10w models 131
6.5.2 A solution of maximum flow-label method 132
6.5.3 The problem of both maximum flow and minimum cost 133
Chapter 7 DEM surface modeling and accuracy analysis 136
7.1 The conception of digital elevation model 136
7.1.1 The basic concepts 136
7.1.2 DEM based on regular network and irregular triangle network 137
7.2 DEM surface modeling 139
7.2.1 DEM surface modeling based on TIN 139
7.2.2 DEM surface modeling based on square grid 140
7.2.3 DEM surface modeling based on mixed grid 142
7.2.4 The discussions on surface modeling 142
7.3 DEM interpolation models 142
7.3.1 The overall interpolation 143
7.3.2 The partitioning interpolation 143
7.3.3 The moving interpolation 146
7.3.4 The discussions on interpolation methods 149
7.4 The accuracy model for grid DEM 149
7.4.1 The index on DEM accuracy evaluating 150
7.4.2 The experiments of DEM accuracy 151
7.4.3 The theoretical models on DEM accuracy 153
7.5 The error propagation model for grid DEM based on high order interpolation 155
7.5.1 The surface error propagation model based on a biquadratic interpolation 155
7.5.2 The surface error propagation model based on a bicubic interpolation 158
7.6 The error propagation model for TIN-based DEM 160
7.6.1 The error propagation formula for TIN 160
7.6.2 The elevation error propagation formula for TIN 162
7.7 The error description model of terrain 164
7.7.1 The concepts on descriptive error model for terrain 164
7.7.2 The fitting models on descriptive error model for terrain 165
Chapter 8 The three-dimension terrain analysis models 168
8.1 Surface area and volume 168
8.1.1 The mathematical formulae on surface area and volume 168
8.1.2 Surface area 169
8.1.3 Volume 172
8.2 Slope and aspects 173
8.2.1 Slope 173
8.2.2 Aspect 176
8.3 The factor of terrain change 178
8.3.1 Curvature 178
8.3.2 Roughness of terrain surface 179
8.3.3 The gurgitation coefficient of grid surface 179
8.3.4 The coefficient on elevation variation 180
8.4 The surface description based on fractal model 180
8.4.1 The fractal calculation for surface 181
8.4.2 The fractal calculation for fBm 182
8.5 The profile analysis 183
8.5.1 The profile line for grid DEM 183
8.5.2 The profile line based on TIN 185
8.6 The analysis based on visualization 186
8.6.1 The visibility between two points 186
8.6.2 The visible field 187
8.6.3 The visualization models for ground objects 187
8.6.4 The applications of visibility analysis 188
Chapter 9 Wavelet analysis models 189
9.1 The wavelet compress model for vector map data 189
9.l.1 The basic models 189
9.l.2 The boundary processing 190
9.l.3 The tracing feature points 191
9.l.4 The compress model for vector map data 192
9.l.5 The experiments and analysis 192
9.2 The multi-band wavelet compress model for vector map data 194
9.2.1 The multi band wavelet compress principle 194
9.2.2 The experiments and discussions 195
9.2.3 The extraction of terrain feature lines 196
9.2.4 The multi-band wavelet compress model 197
9.3 The DEM simplification model based on wavelet 197
9.3.1 The two-band wavelet simplification mode1 197
9.3.2 The multi-band wavelet simplification model 198
9.3.3 The experiments and analysis 198
9.4 The magnifying model of image based on wavelet 200
9.4.1 The magnifying model based on interpolation 200
9.4.2 The magnifying model based on two-band wavelet 202
9.4.3 The magnifying mode1 based on multi-band wave1et 203
9.4.4 The experiments and analysis 203
References 206