Configurable extrapolation behavior

[SouthEndMusic]

I'm interested in making interpolation types configurable in my application, where extrapolation behavior is important. Up to now we have only used LinearInterpolation, where the extrapolation is easy to understand and well behaved. This is however not the case for interpolation types that use a high order polynomial in the boundary intervals, which are continued outside the data-defined domain for extrapolation.

So, I would like to have several extrapolation options in stead of the current boolean:

1. No extrapolation allowed
2. The current extrapolation for maximum smoothness
3. Linear
4. Constant?

Would you consider this to be a good feature for DataInterpolations, or should I make a custom wrapper for my application?

[sathvikbhagavan]

I think it would be good to add those extrapolation methods here.

[SouthEndMusic]

Should the constructors keep the extrapolate keyword or can it be replaced by extrapolation_type::Symbol which has one of the above supported types (preferably also split in upper_extrapolation_type and lower_extrapolation_type)?