c_ftkurvp(3NCARG)

✨ c_ftkurvp — interpolation for closed parametric curves ✨

ok so bestie, we're diving into the NCAR GRAPHICS zone, specifically the 3NCARG manual page for c_ftkurvp, and honestly? it's giving math but make it cute. it does interpolation for closed parametric curves. slay. 💅

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🌸 FUNCTION PROTOTYPE 🌸

int c_ftkurvp (int, float [], float [], int, float [], float [], float
[]);

no cap, that's the signature. seven args, one int return, let's go 🫶

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✨ SYNOPSIS ✨

int c_ftkurvp (n, xi, yi, m, t, xo, yo);

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💖 DESCRIPTION 💖

here's the tea on every single argument, don't skip a single one because they all matter:

• n — the number of input data values. lowkey important: it has to be (n > 1). one point is not a curve bestie, it's just a vibe. 💀
• xi — an array containing the abscissae for the input function.
• yi — an array containing the functional values, and yes, exactly like this: y[k] is the functional value at x[k] for k=0,n-1.
• m — the number of desired interpolated values. how many output points do we want, bestie? 👑
• t — contains an array of values for the parameter mapping onto the interpolated curve. any interval [tt,tt+1.] maps onto the entire curve. so like, every single unit-long window gets the whole curve. iconic behavior tbh.
• xo — an array containing the X values for the interpolated points. t[k] maps to (xo[k],yo[k]) for k=0,m-1.
• yo — an array containing the Y values for the interpolated points. t[k] maps to (xo[k],yo[k]) for k=0,m-1. yes it's the same sentence as xo and no i'm not sorry, that's the actual documented truth. 🌈

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🔥 RETURN VALUE 🔥

c_ftkurvp returns an error value, and it's exactly as per:

• = 0 — no error. we love to see it. ✨
• = 1 — if n is less than 2. (bestie you need at least two points, that's the rule 🥲)
• = 2 — if adjacent coordinate pairs coincide. not two of the same point sitting next to each other, that's a problem. 🙈

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🎀 USAGE 🎀

ok so here's what this procedure actually does: it calculates an interpolatory spline under tension through a sequence of points in the plane forming a closed curve. fancy. gorgeous. mathematically stunning. 💜

Given a sequence of distinct input points ( (x[0],y[0]), ... , (x[n-1],y[n-1]), the interpolated curve is parameterized by mapping points in the interval [0.,1.] onto the interpolated curve.

The resulting curve has a parametric representation both of whose components are splines under tension and functions of the polygonal arc length.

The value 0. is mapped onto (x[0],y[0]) and the value 1. is mapped onto (x[0],y[0]) as well, completing the closed curve. yes bestie, it comes back to where it started — that's literally the whole point of a closed curve, main character energy fr fr. 🦋

c_ftkurvp is called after all of the desired values for control parameters have been set using the procedures c_ftseti, c_ftsetr, and c_ftsetc.

heads up: the only control parameter that applies to c_ftkurvp is: sig. one singular parameter, she's the moment. 💅

The value for the parameter sig specifies the tension factor:

• values near zero result in a cubic spline
• large values (e.g. 50) result in nearly a polygonal line
• a typical value is 1. — which is the default ✨

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🌟 ACCESS 🌟

To use c_ftkurvp, load the NCAR Graphics library ngmath. simple as that, no drama. 🧚

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🦋 SEE ALSO 🦋

• fitgrid_params
• c_ftseti
• c_ftsetr
• c_ftsetc

Complete documentation for Fitgrid is available at URL http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html

go read it, i know you want to 👑

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💜 COPYRIGHT 💜

Copyright (C) 2000 University Corporation for Atmospheric Research

The use of this Software is governed by a License Agreement.

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and that's the whole page bestie 🫶 shoutout to UNIX, NCAR GRAPHICS, and the March 1998 date on the original — vintage, timeless, and still serving interpolated curves. periodt. 💖✨🎀