input file   torus4.in10                50 points 50 patches

    display: Gaussian curvature of surface splines from sparse data sample
	from the torus (50 points 50 patches).
	The scale uses a linear [red, green, blue] range.
	The first two figures have a free range adapted 
	    to the curvature spectrum
	The composite figure displays curvatures in the range [-6.1:6.1]
	(higher and lower curvatures are mapped to the extremem points.)

    The approximate torus is a nice object to show because
	-- it has positive, zero and negative curvature regions and
	-- is simple enough for observers to have an 
	    intuitive notion of a good curvature distribution
	    (Steve Mann pointed this out.)
    The simplicity of the object will favour low degree splines
	    (on regular meshes like this one, surface splines are
	    box splines or tensor-product splines)

 a qualitative prediction of the curvature distribution based oly on the input mesh

 3-sided patches, cubic surface splines, all blend ratios 0.5
    
 4-sided patches, bicubic surface splines, all blend ratios 0.5


 composite figure

    upper left
    3-sided patches, cubic surface splines, all blend ratios 0.5
    3       curvature range measured  -4.519150 2.275727

    upper right
    4-sided patches, bicubic surface splines, all blend ratios 0.5
    4       curvature range  -4.491619 2.275727

    lower left
    4-sided patches, biquartic surface splines, all blend ratios 0.5
    8       curvature range  -7.176795 8.765763

    lower right
    4-sided patches, bicubic interpolating surface splines,
	all blend ratios 0.5
    45      curvature range  -7.356603 4.006425


    not shown (even though it looks more pleasing than lower right)
    4-sided patches, bicubic interpolating surface splines, 
	all blend ratios 0.55
    45	    curvature range -8.385191 2.467968