Interpolation uses known sample points to predict or estimate values at unknown locations. Interpolation refers to estimating data for unknown points within the same region using known data points, while extrapolation predicts data for areas beyond the known region. Both approaches are fundamental concepts in spatial interpolation. SuperMap provides three interpolation methods to simulate or create surfaces: Inverse Distance Weighted (IDW), Kriging, and Radial Basis Function (RBF). The choice of method typically depends on the distribution of sample points and the desired surface type. Generally, more densely distributed sample points yield more accurate interpolation results.
Inverse Distance Weighted (IDW) Interpolation
IDW interpolation operates on the principle of spatial proximity similarity, assuming closer points share more similarities. It calculates cell values using the weighted mean of neighboring sample points, with weights inversely proportional to distance. This efficient method provides relatively fast computation.
Key parameters influencing IDW results include power parameter and search radius:
- Power: Affects distance weighting calculation. Lower values produce smoother surfaces, while higher values preserve more details. Default power is 2.
- Search Radius: Two types available:
- Fixed Count: Uses a specified number of nearest points for each cell. Search radius varies based on point density. Points beyond maximum radius are excluded.
- Fixed Radius: Includes all points within specified radius. Expands radius if minimum point requirement isn't met.
The following figure shows IDW interpolation results with elevation as interpolation field, 100 resolution, fixed count search radius (all points), and power values of 1, 2, 3 respectively.
Spline Interpolation
Spline interpolation creates smooth surfaces passing exactly through sample points while maintaining minimum curvature. Ideal for generating visually smooth contours and surfaces, this method works best with dense, accurate data points and gradual terrain changes. Not recommended for areas with abrupt value changes or noisy data.
Three search radius types are available:
- Fixed Count: Similar to IDW's implementation
- Fixed Radius: Similar to IDW's implementation
- Block Search: Divides dataset into blocks using maximum points per block, using block-local points for interpolation
Kriging Interpolation
Kriging utilizes spatial autocorrelation and variogram models for unbiased estimation, particularly effective when data exhibits spatial dependence or directional trends. Widely used in geology and soil science, it considers spatial relationships between points within correlation ranges.
- Semivariogram Models
SuperMap supports three models:
Figure: Spherical Model Schematic 
Figure: Exponential Model Schematic 
Figure: Gaussian Model Schematic - Spherical: Shows gradual spatial correlation decrease until complete loss at specific range
- Exponential: Spatial correlation decreases exponentially with distance
- Gaussian: Approaches sill asymptotically
- Parameter Description
Key variogram parameters:
- Range: Distance where spatial correlation ceases
- Sill: Maximum semivariance value
- Nugget Effect: Y-intercept representing micro-scale variation or measurement errors
Figure: Range, Sill and Nugget Effect
SuperMap offers three Kriging variants:
- Ordinary Kriging: Assumes unknown constant mean
- Simple Kriging: Assumes known constant mean
- Universal Kriging: Incorporates deterministic trends using polynomial functions
The following table compares interpolation methods:
| Method | Extrapolation | Accuracy | Speed | Application |
| IDW | Good (uniform data) | Low | Fast | Uniform distributions |
| Spline | High | High | Fast | Dense sampling |
| Ordinary Kriging | High | High | Moderate | General purpose |
| Simple Kriging | High | High | Moderate | General purpose |
| Universal Kriging | High | High | Moderate | Trend-containing data |
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