Smooth curves passing through/near a set of points.

Hello Patrick,

I hope this mail finds you well. I'm mailing you with a copy  to the SVG public list, because we would like your help on a mathematical problem we are having.

A couple of years ago, at TPAC, we were discussing a class of curves with the property of passing through a set of points (or near, for some definition of near), and differing from the curves that SVG already has (cubic and quadratic Beziers) or might have (non-uniform rational b-spline curves) in that no off-curve control points are used to define the curve, only the on-curve knots.

I suppose these are piecewise curves with some fairing or smoothness property where the pieces join. 

Does this ring any bells? I can't even recall the name for that class of curves, sorry.

We have a couple of use cases for such curves, now; one is for graphing/charting applications where it is desired to run a smooth (for some definition of smooth) curve through a set of 2D points rather than joining them by a polyline.

The second is to run a curve through a set of 3D points (where the 3D space is a colour space) to produce colour gradients from a list of colours, without perceptual discontinuities. Current gradients effectively connect colours by polylines, so there is a perceptual discontinuity at each colour stop.

tracker, this relates to ACTION-2584

-- 
 Chris Lilley                    mailto:chris@w3.org
 Technical Director, Interaction Domain
 W3C Graphics Activity Lead
 Co-Chair, W3C Hypertext CG