From: Steve Schafer <steve@fenestra.com>

Date: Wed, 09 May 2007 21:30:50 -0400

To: <www-svg@w3.org>

Message-ID: <etr443pb273fcf13focsn6ddm0j135uo6i@4ax.com>

Date: Wed, 09 May 2007 21:30:50 -0400

To: <www-svg@w3.org>

Message-ID: <etr443pb273fcf13focsn6ddm0j135uo6i@4ax.com>

On Wed, 9 May 2007 16:28:07 -0400, you wrote: >I'm trying to create a smooth production decline curve with a dataset of >20 points. I explored the Bezier quadratic and cubic curves available >under SVG but it looks like they need control points outside my dataset >to function. Looks like I would need control points between each of the >20 points to get this to work. I would appreciate any ideas to generate >control points or even better, ideas on generating a smooth curve >without generating control points. Fitting a curve to data does _not_ involve generating a curve that goes through every point. An equation for the curve should be based on a model that purports to explain the observed data (exponential, polynomial, etc.). Any of a number of curve-fitting algorithms may be used to generate that equation (you can do it in Excel, for example). But generating a smooth curve that just happens to look good is meaningless; unless there is a model behind the curve, the curve itself adds no information to the graph. Production decline curves (oil?) are outside of my area of expertise, but I'm guessing that a first-order approximation would be exponential, and a second-order approximation would be a sum of exponentials (sometimes called a "long-tailed" exponential). Once you have the equation for the curve, you can either plot it directly (lots of points connected by straight-line segments) or apply a standard transformation that will take the equation and endpoints as input and give you a "best fit" approximation consisting of one or more Bézier curve segments. It's that transformation process that will give you the control points needed to specify the Bézier curve(s). The bottom line is that all of this process is pretty much outside the scope of SVG; you need to do this _before_ you can generate the SVG that will produce the actual image. Bézier curves are an excellent _representation_ of the result of curve-fitting, but they're generally not too useful during the _process_ of fitting a curve to empirical data, as they have too many degrees of freedom (and, of course, they rarely correspond to any theoretical model of the data). Steve Schafer Fenestra Technologies Corp. http://www.fenestra.com/Received on Thursday, 10 May 2007 01:31:00 UTC

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