Number of Points

Functional Form of Interpolation

1D Entities:


2 points

linear variation in 1D parameter space

3 points

quadratic variation in 1D parameter space

4 points

cubic variation in 1D parameter space

2D Entities:


2 points

linear variation in 2D parameter space, with no variation perpendicular to the line that connects the two points in parameter space

3 points

linear variation in 2D parameter space

4 noncolinear points

bilinear variation in 2D parameter space

4 collinear points

cubic variation in 2D parameter space, with no variation perpendicular to the line that connects the four points in parameter space

4 points, with 3 collinear

quadratic variation in 2D parameter space and linear variation perpendicular to the line that passes through the three collinear points
