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Interpolation with in the GIS context enables the GIS user to model earth like features using point data acquired from a gps unit or maps. Its also vital to choose a correct mapping projection and datums to construct an accurate model. More about mapping projections later.

I have illustrated various interpolation methods below but selecting the correct method depends on your knowledge of the area and how closely related the modeled features are to the known area.

Spline

This method pulls a surface over the acquired pionts resulting in a stretched effect. Spline uses curved lines (curvilinear Lines method) to calculate cell values.
Adv:
-Useful for estimating above maximum and below minimum points
-Creates a smooth surface effect
DisAdv:
-Cliffs and fault lines are not well presented because of the smoothing effect

Natural Neighbor

Each sample point is allocated to an area. 10 Sample points have their own specific area (cells in a bee hive). The size of the area is calculated based on the position and distance of it's neighboring area "neighbors". This area forms a cell and the border of the cell is know as ''Voronoi Polygon". The closer the sample points are to each other the smaller the Voronoi polygons are and visa versa.
Adv:
-Handles large numbers of sample points effeciently

Kriging

Kriging technique of estimating cell values are pretty complex. It involves measuring the distance between all possible pairs of points combined with an average weight passed on to the points. The result of the technique is then used in an auto correlation method to estimated cell values.
Adv:
-Directional influences can be accounted for: Soil Erosion, Siltation Flow, Lava Flow and Winds
- Exceeds the minimum and maximum point values
DisAdv:
-Does not pass through any of the point values and causes interpolated values to be higher or lower then real values

Inverse Distance Weighted

Distance and Sample points values are the two factors used to determine cell values in this interpolation method. Sample points values are collected and weighted according to its distance from the cell. The points closer to the cell will have a greater influence on the cells estimated value. The point values are then collected and average out which then represents the cell value
Adv:
-Can estimate extreme changes in terrain such as: Cliffs, Fault Lines
-Dense evenly space points are well interpolated (flat areas with cliffs)
-Can increase or decrease amount of sample points to influence cell values
DisAdv:
-Cannot estimate above maximum or below minimum values
-Not very good for peaks or mountainous areas




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