유체역학 수상 아키텍처: 게르스트너 파도 합산, EditableMesh 정점 변형 및 선체 다점 부력 시뮬레이션

--!strict
local RunService = game:GetService("RunService")

export type WaveDef = {
    Direction: Vector2,
    Amplitude: number,
    Wavelength: number,
    Speed: number,
    Steepness: number,
}

export type WaterHull = {
    Model: Model,
    RootPart: BasePart,
    ProbeOffsets: { Vector3 },
    SubmergedVolumePerProbe: number,
    WaterDensity: number,
    LinearDamping: number,
    AngularDamping: number,
}

local GerstnerSolver = {}
GerstnerSolver.__index = GerstnerSolver

local GRAVITY = 196.2

function GerstnerSolver.new(waves: { WaveDef })
    local self = setmetatable({}, GerstnerSolver)
    self.Waves = waves
    return self
end

function GerstnerSolver:GetWaveHeightAndNormal(worldPos: Vector3, timeSec: number): (number, Vector3)
    local x = worldPos.X
    local z = worldPos.Z
    local totalY = 0
    local dDx = 0
    local dDz = 0

    for _, wave in ipairs(self.Waves) do
        local dir = wave.Direction.Unit
        local k = (2 * math.pi) / wave.Wavelength
        local omega = math.sqrt(GRAVITY * k)
        local phase = k * (dir.X * x + dir.Y * z) - omega * timeSec

        local cosP = math.cos(phase)
        local sinP = math.sin(phase)

        totalY += wave.Amplitude * cosP
        dDx += -dir.X * (k * wave.Amplitude) * sinP
        dDz += -dir.Y * (k * wave.Amplitude) * sinP
    end

    local normal = Vector3.new(-dDx, 1, -dDz).Unit
    return totalY, normal
end

function GerstnerSolver:ApplyBuoyancy(hull: WaterHull, dt: number, timeSec: number)
    local root = hull.RootPart
    local rootCF = root.CFrame
    local rootVel = root.AssemblyLinearVelocity
    local rootAngVel = root.AssemblyAngularVelocity
    local com = root.AssemblyCenterOfMass

    local totalForce = Vector3.zero
    local totalTorque = Vector3.zero

    for _, offset in ipairs(hull.ProbeOffsets) do
        local probeWorld = rootCF:PointToWorldSpace(offset)
        local waveHeight, waveNormal = self:GetWaveHeightAndNormal(probeWorld, timeSec)
        local depth = waveHeight - probeWorld.Y

        if depth > 0 then
            local displacedVolume = math.min(depth * 1.5, 1.0) * hull.SubmergedVolumePerProbe
            local buoyantMagnitude = displacedVolume * hull.WaterDensity * GRAVITY
            local buoyantForce = Vector3.new(0, buoyantMagnitude, 0)

            local probeVel = rootVel + rootAngVel:Cross(probeWorld - com)
            local dragForce = -probeVel * (hull.LinearDamping * displacedVolume)

            local netProbeForce = buoyantForce + dragForce
            totalForce += netProbeForce

            local leverArm = probeWorld - com
            totalTorque += leverArm:Cross(netProbeForce)
        end
    end

    local angDampingTorque = -rootAngVel * hull.AngularDamping
    totalTorque += angDampingTorque

    root:ApplyAssemblyForce(totalForce)
    root:ApplyAssemblyTorque(totalTorque)
end

return GerstnerSolver