Interpolation Methods in Computer Graphics

Interpolation is a method of constructing new data points within range of discrete set of known data points. The number of data points obtained by sampling or experimentation represents values of function for limited number of values of independent variable.

The main task of Interpolation is to find suitable mathematical expression for known curve. This technique is used when we have to draw curve by determining intermediate points between known sample points.

Types of Interpolation methods :

• Inverse Distance Weighted (IDW) –
  In this method, estimation of cell values is done by averaging values of sample data points in neighborhood of each processing cell. A specified number of points or all points within specified radius can be used to determine output value of each location. The point closer to center of cell have more influence or weight in averaging process.
  
  
• Kriging –
  Kriging is geostatistical procedure that considers both distance and degree of variations between known data points when estimating values in unknown areas. In this procedure, there is generation of an estimated surface from scattered set of points with z-values.
• Natural Neighbor –
  Natural Neighbour interpolation method finds closest subset of input samples to query point. It applies weights to input samples based on proportionate areas to interpolate value. It is also known as Sibson or “area-stealing” interpolation.
• Spline –
  In this interpolation method, estimation of values is done using mathematical function that minimizes overall surface curvature and results in smooth surface that passes exactly through input points.
• Spline with barriers –
  Spline with barriers method is similar to spline method, only difference is that this tool honors discontinuities encoded in both input barriers and input point data.
• Topo to raster –
  This method uses technique specifically designed to create surface that more closely represents natural drainage surface and better preserves stream networks from input contour data.
• Trend –
  It is a global polynomial interpolation that fits smooth surface defined by mathematical function (a polynomial) to input sample points. The trend surface changes gradually and captures coarse-scale patterns in data.