[postgis-devel] Cubic splines in GML

[Mark Cave-Ayland]

Andrei Ionita wrote:

> Hi everyone,
> 
> I am seeking help on understanding the concept that GML is defining for
> cubic splines. I am involved in writing an interpolation algorithm in
> the deegree software that returns points on a cubic spline.
> 
> Firstly, I have been looking at the GML definition of cubic splines and
> wondering how to interpret it. There, a cubic spline consist of control
> points and starting and ending tangent vectors. It appears as the
> piecewise cubic polynomials (that are defined mathematically for a cubic
> spline) can be deduced from the two tangents, but how does one do that?
> 
> Or is the target of the GML type not one of defining a rigorous math object?

See http://en.wikipedia.org/wiki/Bezier_splines for more information. 
There are several variations on parametric cubic curves, but Bezier is 
one of the most common formulations.

> Apart from that however, I would also like to ask if someone from
> PostGIS has stumbled upon a discrete algorithm for interpolating cubic
> splines, or at least can give me some literature references.

I'm fairly sure you should be able to either implement a simple 
algorithm yourself, or locate a suitable library routine from the 
reference above.


HTH,

Mark.

-- 
Mark Cave-Ayland - Senior Technical Architect
PostgreSQL - PostGIS
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