This thread prompts me to ask about something I've been pondering for a while, as to whether there's an implementation somewhere ticked away in the R resources.
So far, people have been responding to the original query in terms of increasing the numbers of points, and joining these by lines. However, if you're using PostScript output, you can draw really smooth curves by exploiting PS's "curveto" operator. This draws a cubic-curve segment in the following way: The two points you want to join with a curve will be denoted by (X0,Y0) and (X3,Y3) in the following (for reasons which will appear). The PS command is of the form x1 y1 x2 y2 X3 Y3 curevto At (X0,Y0) the tangent to the curve (as it departs from (X0,Y0) is in the direction of the directed line from (X0,Y0) to (x1,y1), and at (X3,Y3) (as it arrives) the tangent to the curve is in the direction of the directed line from (x2,y3) to (X3,Y3). The location of (X0,Y0) is not part of the command, since it is implicit in the PS "currentpoint" which is the starting point of the curve. The result is (in theory, and in practice to within the resolution of the output device) a perfectly smooth curve, provided the consecutive cubic segments have the same tangent at each of the points being joined. This can be achieved by appropriate choice of the "intermediate" points -- (x1,y2), (x2,y2) above. So far, when I've done this myself (including when using the output from R to give the points being joined), I've done the computation of the "intermediate" points "by hand". This basically involves deciding, at each of the points being joined, what the tangent to the smooth curve shouold be. Of course, there is an element of arbitrariness in this, unless there is an analytic representation of the curve on which the points lie (e.g. you're plotting sin(x)/x every pi/8, and want to join them smoothly), when all you need is the derivatives at the points. Crudely, you might evaluate the direction at a point in terms os a weighted average of the directions to its two immediate neighbours (the nearer meghbour ges the greater weight); less crudely, you might fit a quadratic through the point and its 2 neighbours and use the gradient at the middle point; and so on. Once you've decided on the tangent at each point, it's then straightforward to compute suitable "intermediate points" to serve as (x1,y2) and (x2,y2). (One application where this sort of approach is needed is in joining computed points on iso-contours, where the individual points have been determined by interpolation of spot-measurements at nearby measuring stations). Anyway. The Question: is there a general function for the above kind of smooth curve-drawing? With thanks, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 01-May-07 Time: 14:50:38 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
