Piecewise linear transformation

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Figure 7. Delaunay Triangulation based on match pairs.




Figure 8. After piecewise linear transformation.

Figure 7 shows only triangulation of reference pairs. Transformated Census Block boundary is shown in red in both figure 7 and 8.


Figure 9. Weighted piecewise linear trnasformation(on going research).

The left figure shows piecewise linear transformation using simplical coordinates where three vertices of triangle in which point P is are used to find transformation coefficients. Whereas, the right figure shows the delaunaty triangulation and its dual, voronoi diagram after P is inserted to consider weighted piecewise linear transformation. The red lines show the edges of triange before insertion. To calculate coefficients of transformation, natural neighbor algorithm could be used but it is questionable because it considers pure mathmatical situation. For example, there is no meaning if we make traingulation based on elevatoion data without considering critical points and lines. There will need more reseach to apply weighted transformation for geograhic features like match pairs.