[udig-devel] Re: [Geotools-devel] Re: [Geoserver-devel] WMS/lite and hig

[Martin Desruisseaux <martin.desruisseaux@xxxxxxxxxxxxx>]

Andrea Aime a écrit :
> Nice but... as far as I remember, this is not the exact solution. 
> Reprojection classes could, last time I checked, get a Shape implementation and reproject it 
> creating exact (curved) reprojected lines. So the most accurate solution should be to get the 
> box, reproject it as a Shape, and then get the bounds2d of the reprojected shape.

There is a MathTransform2D.createTransformedShape(Shape) which expect a 
Java2D shape and returns a new (transformed) Java2D shape.

In pure ISO style, there is also a Geometry.transform(...) method. This 
one is more generic (since it is not strictly 2D) and part of ISO 
specification, but not yet implemented in Geotools.

In current Geotools implementation, only the Java2D method is 
implemented. However, the default implementation has some approximations 
too:

  - We have not yet investigated the mathematic behind an exact
    analytical solution for projected curves. I suspect that it
    would not be trivial (I guess some good book must exist).

  - Current Geotools implementation computes 3 points (the first
    and the last one, and a middle point) and fits a quadratic
    curve through those 3 points. It should be exact if we assume
    that any straight line become a quadratic line (or an other
    straight line, which I consider as a particular case of a
    quadratic line with the coefficient of x² set to 0) after the
    projection. I don't know how accurate this assumption is.

  - If we want yet more accuracy, we could fit a cubic line instead
    of a quadratic line (we would then need 4 points instead of 3).
    But it would require more mathematical background, or a good book
    with formulas written for us.

  - Java2D's Shape.getBounds2D() is itself approximative in the case of
    quadratic and cubic lines. As of J2SE 1.5, it doesn't (yet) returns
    the smallest bounding box, but returns instead a box which contains
    the control points. See:

    http://bugs.sun.com/bugdatabase/view_bug.do?bug_id=4225281
    http://bugs.sun.com/bugdatabase/view_bug.do?bug_id=4851378


However, the "curved lines" approach still probably a better approach in 
the long run, since:

  - We may improve the curve fitting accuracy over time.

  - It is probably more efficient, since it transforms only 1 more point
    (in addition to the vertex transformed anyway) and performs all
    other computations (e.g. bounding box) analytically.


	Martin.