STUMTA(3NCARG)

💖 NAME 💖

okay bestie, so STUMTA is a user-modifiable routine from NCAR Graphics (yes, the 3NCARG girlies ✨). You hand it the coordinates of a point on a streamline in data, user, AND NDC space, plus the interpolated, normalized components of the vector at that point relative to data coordinate space — and it finds the directional angle of the streamline relative to NDC space at that point. it's giving geometry, it's giving mapping internals 💅

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✨ SYNOPSIS ✨

CALL STUMTA (XDA,YDA,XUS,YUS,XND,YND,DU,DV,TA,IST)

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📖 DESCRIPTION 📖

here's the full cast of characters, no skips, no skips, we love every single one 🫶

• XDA (REAL, input) — the X coordinate of a point on the streamline, in the data coordinate system. 💙
• YDA (REAL, input) — the Y coordinate of a point on the streamline, in the data coordinate system. 💙
• XUS (REAL, input) — the X coordinate of the point, in the user coordinate system. 🌱
• YUS (REAL, input) — the Y coordinate of the point, in the user coordinate system. 🌱
• XND (REAL, input) — the X coordinate of the point, in NDC space. 🔮
• YND (REAL, input) — the Y coordinate of the point, in NDC space. 🔮
• DU (REAL, input) — the interpolated value of the normalized component of the vector at the point, with direction parallel to the X axis of the data coordinate system. ⭐
• DV (REAL, input) — the interpolated value of the normalized component of the vector at the point, with direction parallel to the Y axis of the data coordinate system. ⭐
• TA (REAL, output) — THE MOMENT. 👑 the directional angle of the streamline at the point, relative to NDC space. this is the whole point of the function, she's the main character.
• IST (REAL, output) — status of the mapping operation, and listen, the values matter:
  • 0 — success 🎉
  • negative values — the mapping failed 😭
  • positive values — reserved, so do NOT use them if you're implementing a mapping routine. hands off, bestie, those aren't yours.

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🛠️ USAGE 🛠️

so here's the tea ☕ — STUMTA is a user-modifiable routine, provided to support custom mappings of the data coordinate space. You do not call it directly. ever. nope. not you. 🙈

Instead: whenever the parameter MAP specifies a mapping that Streamlines doesn't handle internally — i.e. when MAP is set to a value other than 0, 1, or 2 — Streamlines calls STUMTA once for each incremental step in the creation of a streamline. so it's like, every little baby step along the curve, it's checking in. obsessed. 🦋

The default version of STUMTA is lowkey simple: it just returns the angle implied by the incremental vector components passed to it — that is, it returns ATAN2(DV,DU). slay, queen, no notes. ✨

Now, to implement a custom mapping, you have to:

1. pick a unique mapping code — a positive integer greater than 2 🔢
2. modify each of the three routines — STUMXY, STUIXY, and STUMTA — so they recognize and respond consistently to the chosen code. all three. together. friendship bracelet energy. 🫶

In the standard distribution of NCAR Graphics, these three routines live together in a single file, stumxy.f 🏠

• STUMXY maps a point from data to user coordinate space.
• STUIXY inversely maps a point from user to data coordinate space.
• STUMTA — which is likely to be the most difficult to implement 😮‍💨 — finds the tangent angle of the streamline at a point in NDC space.

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🫧 the common block situation 🫧

STUMTA has access to a common block called STMAP, which contains a bunch of variables used to record the current transformation state. 📦

To accommodate a variety of mapping implementations, STMAP provides more information than is normally required. And bestie, listen closely:

Consider the values stored in STMAP as strictly read-only. do not touch. look with your eyes only. 👀🚫

One essential member of this common block is IMAP, which contains the value currently assigned to the MAP parameter. ⭐

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🌀 implementing a non-linear mapping 🌀

ngl, when you're implementing a non-linear mapping, an iterative differential technique will most likely be required. 😮‍💨

Go look at the routine STMPTA in stmpxy.f, which handles the pre-defined mappings, for examples of the method. 📚

Both of these use such a technique:

• the default transformation (MAP set to 0) — this one does it in order to account for possible log scaling of the user coordinate axes 📏
• the Ezmap projection (MAP set to 1) 🗺️

Basically the idea is this: the vector components must be proportionally reduced in size enough that an effectively "instantaneous" angle can be calculated. but — and this is the important but — they must not become so small that the calculation is adversely affected by the floating point precision available for the machine. tiny little numbers = chaos. 💀

Additionally, checks must be put in place to prevent the increment from stepping off the edge of the coordinate system space. 🚧

And the pre-defined mappings? they step in the opposite direction to find the angle whenever an increment in the original direction would fall off the edge. iconic problem-solving honestly 👑

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🔑 ACCESS 🔑

To use STUMTA, load the NCAR Graphics libraries ncarg, ncarg_gks, and ncarg_c — preferably in that order. order matters, bestie, we're not animals 🎀

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👀 SEE ALSO 👀

Online: stgetc, stgeti, stgetr, stinit, stream, streamlines, streamlines_params, strset, stsetc, stseti, stsetr, stuixy, stumsl, stumxy, ncarg_cbind

Hardcopy: NCAR Graphics Fundamentals, UNIX Version 📖

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⚖️ COPYRIGHT ⚖️

Copyright (C) 1987-2009
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!! 💜 this one's from the NCAR GRAPHICS manual set — the UNIX flavor — dated April 1993 (a vintage queen 👑), and the page name is STUMTA(3NCARG) if you ever need to pull it back up. go forth and compute those tangent angles, you've got this fr fr 🌈✨🦋