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WellTree: float2 alias

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Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
Meta Vens 2026-10-16 17:58:17 +02:00
commit 131895740d
2 changed files with 18 additions and 59 deletions
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1
Assets/Scripts/ServerShared/WellTree.cs
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@ -3,6 +3,7 @@ using System.Collections.Generic;
using GameCult.Caching;
using CultMath;
using static CultMath.math;
using float2 = CultMath.float2;
/// <summary>An orbit as the well tree reads it: where it hangs on the tree and the mass of the well-bearing body on it (0 for none).</summary>
public readonly struct WellNode

76
tests/Aetheria.Shared.Tests/PotentialOwnerTests.cs
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@ -73,8 +73,8 @@ public sealed class PotentialOwnerTests : IDisposable
private static void Near(float expected, float actual, float relative) =>
Assert.InRange(actual, expected - Math.Abs(expected) * relative - 1e-5f, expected + Math.Abs(expected) * relative + 1e-5f);
// The law written out: potential c r^2 / 2R^2 inside the core, c (ln(r / R) + 1/2) beyond.
private static float Phi(float c, float core, float r) => r < core ? c * r * r / (2 * core * core) : c * (log(r / core) + .5f);
// The law of a lone body written out (its global term): the Plummer potential c ln(r^2 + eps^2) / 2, eps the Roche limit.
private static float Phi(float c, float eps, float r) => c * .5f * log(r * r + eps * eps);
// A zone whose bodies have no authored gravity curves (most test zones) has no pull and no dip, and no NaN either.
[Fact]
@ -103,12 +103,13 @@ public sealed class PotentialOwnerTests : IDisposable
var zone = ZoneOf(planets, (mass, float2.zero));
var core = planets.RocheLimit.Evaluate(mass);
foreach (var r in new[] { 3f * core, 10f * core, PackRadius / 2f })
Near(planets.WellStrength.Evaluate(mass), length(zone.GetForce(new float2(r, 0))) * r, 1e-3f);
Near(planets.WellStrength.Evaluate(mass) * r * r / (r * r + core * core), length(zone.GetForce(new float2(r, 0))) * r, 1e-3f);
}
}
// The steepest pull of the Plummer well is at its softening, which is the Roche curve: it rises up to it and falls beyond.
[Fact]
public void TheCoreRadiusIsTheRocheCurve()
public void TheSteepestPullIsAtTheRocheCurve()
{
var planets = Curves();
foreach (var mass in new[] { 29.2f, 14152.4f })
@ -116,10 +117,8 @@ public sealed class PotentialOwnerTests : IDisposable
var zone = ZoneOf(planets, (mass, float2.zero));
var core = planets.RocheLimit.Evaluate(mass);
float Pull(float r) => length(zone.GetForce(new float2(0, r)));
var slope = Pull(.25f * core) / (.25f * core);
Near(slope, Pull(.5f * core) / (.5f * core), 1e-3f);
Near(slope, Pull(.9f * core) / (.9f * core), 1e-3f);
Assert.True(Pull(core) > Pull(.98f * core), "the pull still rises up to the core radius");
Near(planets.WellStrength.Evaluate(mass) / (2f * core), Pull(core), 1e-3f);
Assert.True(Pull(core) > Pull(.98f * core), "the pull still rises up to the Roche limit");
Assert.True(Pull(core) > Pull(1.02f * core), "and falls beyond it");
}
}
@ -146,10 +145,10 @@ public sealed class PotentialOwnerTests : IDisposable
ZoneOf(Constants(50f), (100f, float2.zero));
}
// core-at-roche-and-exaggeration-up: growing the core to the Roche limit (3 m^.25 to 7.32 m^.25, 2.44x) and dividing the
// global K by that factor leaves the steepest drawn slope (|grad phi| / K, at the core) where it was, and draws every
// slope outside the old core 2.44x steeper. The "before" side is the previous authoring, stated here from the ruling:
// core 3 m^.25 and K 10. The "after" side is the shipped Settings.asset read through the production zone.
// core-at-roche-and-exaggeration-up: the Plummer well's steepest pull is 0.5 c / eps at the Roche limit (eps = 7.32 m^.25),
// half the harmonic core's c / R, so K halves with the law and the steepest drawn slope stays where the previous authoring
// had it. The "before" side is stated from the ruling: core 3 m^.25 and K 10. The "after" side is the shipped
// Settings.asset read through the production zone. Outside the old core the funnel draws steeper than it did.
[Fact]
public void ThePeakDrawnSlopeStaysAndTheFunnelDrawsSteeper()
{
@ -165,10 +164,8 @@ public sealed class PotentialOwnerTests : IDisposable
var peakBefore = c / oldCore / oldExaggeration;
Assert.InRange(Drawn(planets.RocheLimit.Evaluate(mass)), peakBefore * .98f, peakBefore * 1.02f);
var rocheOverOldCore = planets.RocheLimit.Evaluate(mass) / oldCore;
var farBefore = c / (3f * oldCore) / oldExaggeration;
Near(rocheOverOldCore, Drawn(3f * oldCore) / farBefore, 1e-2f);
Assert.InRange(Drawn(3f * oldCore) / farBefore, 2.44f * .99f, 2.44f * 1.01f);
Assert.InRange(Drawn(3f * oldCore) / farBefore, 2.9f, 2.98f);
}
}
@ -247,8 +244,9 @@ public sealed class PotentialOwnerTests : IDisposable
}
}
// A lone body is a global term: it pulls as the Plummer well at every range, with no rim and no gate.
[Fact]
public void TheTailIsAPointMassWithNoRimAndNoGate()
public void TheGlobalTermIsPlummerAtEveryRange()
{
var planets = Curves();
var zone = ZoneOf(planets, (273.9f, float2.zero));
@ -259,7 +257,7 @@ public sealed class PotentialOwnerTests : IDisposable
{
var at = new float2(r * cos(angle), r * sin(angle));
var force = zone.GetForce(at);
Near(c, length(force) * r, 1e-3f);
Near(c * r * r / (r * r + core * core), length(force) * r, 1e-3f);
Assert.True(dot(normalize(force), normalize(-at)) > .9999f, "the pull points at the body");
}
}
@ -297,7 +295,7 @@ public sealed class PotentialOwnerTests : IDisposable
var c = planets.WellStrength.Evaluate(273.9f);
var core = planets.RocheLimit.Evaluate(273.9f);
Assert.Equal(0f, lone.GetHeight(new float2(PackRadius, 0)), 4);
Near(-c * (log(PackRadius / core) + .5f) / k, lone.GetHeight(float2.zero), 1e-4f);
Near(-c * .5f * log((PackRadius * PackRadius + core * core) / (core * core)) / k, lone.GetHeight(float2.zero), 1e-4f);
var two = ZoneOf(planets, (29.2f, new float2(-300f, 0f)), (14152.4f, new float2(300f, 0f)));
var c0 = planets.WellStrength.Evaluate(29.2f);
@ -305,7 +303,7 @@ public sealed class PotentialOwnerTests : IDisposable
var c1 = planets.WellStrength.Evaluate(14152.4f);
var core1 = planets.RocheLimit.Evaluate(14152.4f);
const float step = .5f;
// Inside the two cores as well, out to their outer bands (0.5 R to R), where the potential is the quadratic bowl.
// Inside the two softenings as well, where the Plummer potential is smooth through the centre.
var inCore = new[]
{
float2(-300f + .5f * core0, 0f), float2(-300f, .65f * core0), float2(-300f - .86f * core0, 0f), float2(-300f + .6f * core0, .6f * core0),
@ -326,44 +324,4 @@ public sealed class PotentialOwnerTests : IDisposable
}
}
}
// Inside the core the potential is the bowl c r^2 / 2R^2 all the way out to R: the drop from a lone body's centre to a point
// at r is exactly that, from the middle of the core to a hair inside its edge (the log form agrees with the bowl to second
// order at R, so only a tight tolerance sees a join that sits just inside it).
[Fact]
public void TheCoreIsTheBowlUpToItsEdge()
{
foreach (var k in new[] { 1f, 10f })
{
var planets = Curves(k);
foreach (var mass in new[] { 29.2f, 14152.4f })
{
var zone = ZoneOf(planets, (mass, float2.zero));
var c = planets.WellStrength.Evaluate(mass);
var core = planets.RocheLimit.Evaluate(mass);
foreach (var fraction in new[] { .5f, .75f, .9f, .95f, .98f, .99f, .996f })
foreach (var angle in new[] { 0f, 2.3f })
{
var r = fraction * core;
var drop = (zone.GetHeight(new float2(r * cos(angle), r * sin(angle))) - zone.GetHeight(float2.zero)) * k;
Near(c * fraction * fraction / 2f, drop, 2e-5f);
}
}
}
}
[Fact]
public void TheCoreMeetsTheTailAtItsRadius()
{
var planets = Curves();
foreach (var mass in new[] { 29.2f, 14152.4f })
{
var zone = ZoneOf(planets, (mass, float2.zero));
var core = planets.RocheLimit.Evaluate(mass);
var inside = new float2(core * (1f - 1e-3f), 0);
var outside = new float2(core * (1f + 1e-3f), 0);
Assert.InRange(abs(zone.GetHeight(inside) - zone.GetHeight(outside)), 0f, abs(zone.GetHeight(outside)) * 1e-3f);
Assert.InRange(abs(length(zone.GetForce(inside)) - length(zone.GetForce(outside))), 0f, length(zone.GetForce(outside)) * 1e-3f);
}
}
}