exspline(3alleg4)

📦 version 4.4.3.1, in debian bookworm, debian trixie, ubuntu jammy, ubuntu noble, ubuntu questing, ubuntu resolute, ubuntu stonking

💖 exspline — Allegro manual, section 3alleg4 💖

okay bestie, welcome to the Allegro manual page for exspline — yes it's a game programming library, yes this is the example program, and yes we are going to make smooth curvy motion paths and it's going to be gorgeous 🦋

✨ NAME ✨

exspline — constructing smooth movement paths from spline curves. Part of the Allegro game programming library. periodt 💅

🌸 SYNOPSIS 🌸

#include <allegro.h>

Example: exspline

🎀 DESCRIPTION 🎀

so like. this program is a whole demo of using spline curves to build smooth paths that connect a bunch of node points, and ngl that is so useful for making realistic motion and animations. main character energy for your sprites, fr fr 💃

the technique — okay listen — is you connect the series of guide points p1..p(n) with spline curves going p1-p2, p2-p3, etc. every single spline has to pass through both of its guide points, so those points have to be used as the first and fourth of the spline control points. and the fun bit (the ✨fun✨ bit) is coming up with sensible values for the second and third spline control points, so that the spline segments have equal gradients where they meet. not me solving this: here's the solution that came out of it:

for each guide point p(n), calculate the desired tangent to the curve at that point. the take was: that's the vector p(n-1) -> p(n+1), which is super easy to compute with the inverse tangent function, and it gives decent looking results. one implication of this (important!! don't skip) is that you need two dummy guide points, one at each end of the curve — they get used in the tangent calculations but they are not connected to the set of splines. sneaky little helpers 🫶

once you have those tangents, calculating the spline control points is lowkey easy. for a spline between guide points p(a) and p(b):

  • the second control point should lie along the positive tangent from p(a)
  • the third control point should lie along the negative tangent from p(b)

how far they're placed along those tangents controls the shape of the curve. and the finding was: applying a 'curviness' scaling factor to the distance between p(a) and p(b) works well. chef's kiss 😌

one thing to note about splines (vibe check ⚠️): the generated points are not all equidistant. instead they tend to bunch up nearer to the ends of the spline, which means you'll need to apply some fudges to get an object moving at a constant speed. but on the other hand — and this is the cute part — in situations where the curve has a noticeable change of direction at each guide point, the effect can actually be quite nice, because it makes the object slow down for the curve. it's giving intentional ✨

👑 SEE ALSO 👑

and that's the whole page bestie, no cap 💜 this one's straight outta the Allegro docs, version 4.4.3, exspline(3alleg4) — go make something curvy and iconic 🌈⭐🎀

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