Interpolation

Linear interpolation

Given a straight line passing through latex2png equation and latex2png equation, we wish to calculate the latex2png equation position at a given position latex2png equation.

Using the definition of a line, latex2png equation

we find that value as

latex2png equation

which can be rewritten in the familiar form

latex2png equation

where

latex2png equation and latex2png equation.

Bi-linear interpolation

This is linear interpolation in two dimensions.

See p. 126 of Numerical Recipes in C++ for implementation detail.

Bi-cubic interpolation

Implementation details in Numerical Recipes in C++.

Geometric interpolation

Measure the physical overlap between pixels, and weight accordingly. This requires the use of (often slow) PolygonClipping routines.

References

[PTV+03] Press, William H., Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. Numerical Recipes in C++: The Art of Scientific Computing, 2003. Cambridge University Press, 2nd edition, 2003.


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