tailieunhanh - Art of Surface Interpolation-Chapter 5:Solving special tasks In the next sections there are examples of interpolation problems,

Tham khảo tài liệu 'art of surface interpolation-chapter 5:solving special tasks in the next sections there are examples of interpolation problems,', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 5 Solving special tasks In the next sections there are examples of interpolation problems which need special procedures to be solved. Most of the procedures are directly coded in the graphical user interface SurGe but some procedures are solved using stand-alone utilities. Zero-based maps Certain types of maps for example maps of pollutant concentration in some area maps of precipitation maps of rock porosity or permeability and so on have a common feature -their z-values cannot be negative. Let us name these maps as zero-based maps. If a smooth interpolation is used for such types of maps there is a real danger that the resulting function will be negative in some regions. As discussed in paragraph Smoothness of interpolation and oscillations undesired oscillations and improper extremes cannot be avoided in such cases. For this reason the graphical user interface SurGe offers a possibility using the menu item Substitute below to substitute all z-values of the surface which are less than a specified constant for example zero by this constant. Similarly the menu item Substitute above enables to cut off values of the surface exceeding the specified constant. As an example of a zero-based map we will use the data set containing sulphate concentration measured in a soil layer. An interesting comparison of results obtained using different interpolation methods provides an evaluation of how maximal and minimal z-val-ues of points XYZ were exceeded by the generated surface. As in all preceding examples the Kriging method was used with the linear model and zero nugget effect the Radial basis function method with the multiquadric basis functions and zero smoothing parameter and the Minimum curvature method were used with a tension of 0 1. These are summarized in the following table. interpolation method exceeding the minimal value exceeding the maximal value Kriging -18 8455 -4 4299 Radial basis functions -18 8455 -4 4299 Minimum curvature -46 4989