Lecture 3

surface models

1. The two main methods of creating surface models are interpolation and triangulation

interpolation: we use it to help developing 3D surfaces, which is a digital representation of features, either real or hypothetical(假定的), in three-dimensional space.

Otherwise, extrapolation is to predict the value of an attribute at sites outside the area covered by existing observations

2. people need 3D surfaces to do surface analysis, which implies the analysis of continuous spatial variation. The most common application of surface analysis is digital elevation modelling (DEM).

3. A 3D surface is usually derived or calculated from continuous or  noncontinuous surfaces (point, line, polygons) and converted it into a digital 3D surface

4. ArcGIS can create and store four types of surface models: raster, triangulated irregular network (TIN), terrain datasets, and LAS datasets.

TIN

1. TINs 保存输入数据的所有精度(preserve all the precision), 对已知点的值进行建模

2. TINs是一种基于矢量(vector-based)的数字地理数据形式(digital geographic data)，将通过对一组顶点(vertices)进行三角测量(triangulating)来构建。顶点与一系列边相连，形成三角形网络

3. A TIN expects units to be in meters, not decimal degrees.

4. Method of interpolation to form these triangles:  Delaunay triangulation or distance ordering.

5. raster surface models在工作效率、使用范围以及价位上都优于TINs，TINs主要用于较小区域内的高精度建模

Raster

1. Interpolation根据有限数量的采样数据点预测cells in a raster的值，可用于预测任何地点的未知数据，如海拔、降雨量、化学浓度和噪音水平等

Interpolation

1. everything is connected, but that near things are more related than those far apart

2.Need to define or quantify that relationship to interpolate

3.Works under the principle of the continuous field data model

4. Need a high density of data for it to be reliable( 需要高密度数据以确保可靠性 )

5. Need to use an interpolator that can represent the process you are modelling

Interpolation methods

1. Global interpolators( Prediction for the whole area of interest ): Trend surface analysis+Regression( 回归 )

2. Local interpolators( Operate within a small zone around the point being interpolated ):Nearest neighbours: Tiessen polygons，Delaunay triangulation( 三角测量 )+IDW(Inverse Distance interpolation)+Splines

3. Geostatistical: Kriging

#IDW assumes that unknown value is influenced more by nearby than far away points, but we can control how rapid that decayis, however there is no method of testing for the quality of predictions