KURVD(3NCARG)

🎀 NAME 🎀

KURVD — interpolation and derivatives for parametric curves 💫

(okay so this is page KURVD(3NCARG) from the NCAR GRAPHICS manual, bestie, and it's a whole vibe)

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✨ SYNOPSIS ✨

CALL KURVD (T, XS, YS, XST, YST, XSTT, YSTT, N, X, Y, XP, YP, S, SIGMA)

So here's the tea 🍓: this subroutine is literally KURV2's twin, except it ALSO hands you the first and second derivatives of the component functions in the parameterization. Not just the point — the motion, the acceleration, the whole arc. Iconic behavior, honestly.

The interval [0.,1.] maps onto a curve in the plane, and the resulting curve has a parametric representation where both components are splines under tension and are functions of the polygonal arc length. Chef's kiss. 💅

🚨 REAL TALK, DO NOT SKIP: KURV1 must be called before calling KURVD. It's giving "prerequisite" and it is not optional. No KURV1, no KURVD, periodt.

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🌸 DESCRIPTION 🌸

Every argument, one by one, no gatekeeping:

• T (real, input) — the value getting mapped to a point on the curve. The interval [0.,1.] maps onto the curve in such a way that 0. lands on (X(1),Y(1)) and 1. lands on (X(N),Y(N)). And if you go outside [0.,1.]? You get extrapolation, bestie. It just keeps going. 🙈
• XS (real, output) — holds the X coordinate of the point that T maps to. 💜
• YS (real, output) — holds the Y coordinate of the point that T maps to. 💜
• XST (real, output) — holds the first derivatives of the X component with respect to T. ⚡
• YST (real, output) — holds the first derivatives of the Y component with respect to T. ⚡
• XSTT (real, output) — holds the second derivatives of the X component with respect to T. 🔥
• YSTT (real, output) — holds the second derivatives of the X component with respect to T. 🔥 (yes, that's what it says, and we are reporting it faithfully, no editing the lore)
• N (integer, input) — how many input data points you've got. Constraint: N > 1. One point is not a curve, babe. 🦋
• X (real, input) — an array holding the X values of the input points. ✨
• Y (real, input) — an array holding the Y values of the input points. Adjacent pairs of points must be distinct. Like, if two neighbors are literally the same point, that's a no. 🫶
• XP (real, input) — an array of length N, as computed by KURV1. 👑
• YP (real, input) — an array of length N, as computed by KURV1. 👑
• S (real, input) — an array of length N containing the polygonal arc lengths of the curve, as computed by KURV1. 🌈
• SIGMA (real, input) — the tension factor, aka the personality dial. Values near zero give you a cubic spline; large values (like, e.g. 50) give you nearly a polygonal line. A typical value is 1. 🎚️✨

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🔑 ACCESS 🔑

To use KURVD, load the NCAR Graphics library ngmath. That's it, that's the whole step. 💖

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👀 SEE ALSO 👀

• kurv1
• kurv2
• fitgrid_params

Complete documentation for Fitgrid is available at URL http://ngwww.ucar.edu/ngdoc/ng/ngmath/fitgrid/fithome.html — go read it, iykyk. 📚

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©️ COPYRIGHT ©️

Copyright (C) 2000 University Corporation for Atmospheric Research

The use of this Software is governed by a License Agreement. (read it, bestie, fr fr 🫡)

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okay that's the whole page!! 💜 this was KURVD(3NCARG) on UNIX, dated March 1998 — old enough to be vintage, still serving looks. slay, stay interpolated, and call KURV1 first. mwah 🎀💅✨