29 lines
1.4 KiB
C#
29 lines
1.4 KiB
C#
using CultMath;
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using static CultMath.math;
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using float2 = CultMath.float2;
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/// <summary>
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/// The law of one gravity well: a 2D point mass with a softened core. Outside the core radius the potential is
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/// logarithmic and the pull is c / r; inside it the pull falls linearly to zero at the centre and meets the tail in
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/// value and slope at the core radius. c is the well's strength (u^2/s^2), R its core radius (u). No threshold
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/// anywhere: a well pulls at every distance. Zone.GetForce and Zone.GetHeight sum this over a zone's bodies.
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/// </summary>
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public static class GravityField
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{
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// The potential at distance r from the body, defined up to a constant (callers subtract their reference).
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// A well of no strength (a body whose curves are unauthored, so c = 0 and R = 0) digs nothing.
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public static float Potential(float c, float coreRadius, float r) =>
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c == 0f ? 0f :
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r < coreRadius
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? c * r * r / (2 * coreRadius * coreRadius)
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: c * (log(r / coreRadius) + .5f);
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// The acceleration at `offsetFromBody`, toward the body: zero at the body itself.
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public static float2 Acceleration(float c, float coreRadius, float2 offsetFromBody)
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{
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var r = length(offsetFromBody);
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if (r == 0f) return float2.zero;
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var pull = r < coreRadius ? c * r / (coreRadius * coreRadius) : c / r;
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return -offsetFromBody / r * pull;
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}
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}
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