CelticCraft/Plugins/VoxelFree/Shaders/Private/Erosion.usf

// Copyright 2020 Phyronnaz

// From https://hal.inria.fr/file/index/docid/402079/filename/FastErosion_PG07.pdf

#include "/Engine/Public/Platform.ush"
#include "/Engine/Generated/GeneratedUniformBuffers.ush"

RWTexture2D<float> RainMap;
RWTexture2D<float> TerrainHeight;
RWTexture2D<float> WaterHeight;
RWTexture2D<float> Sediment;
RWTexture2D<float> Outflow;
RWTexture2D<float> Velocity;

RWTexture2D<float> WaterHeight1;
RWTexture2D<float> WaterHeight2;

RWTexture2D<float> Sediment1;

// Required for tilt angle
RWTexture2D<float> TerrainHeight1;

#if __INTELLISENSE__
struct FConstants
{
    uint size;
    float dt;

    // Size of a pipe
    float l;
    // Gravity
    float g;

    // Sediment capacity
    float Kc;
    // Sediment dissolving
    float Ks;
    // Sediment deposition
    float Kd;
    
    // Rain strength
    float Kr;
    // Evaporation
    float Ke;
};
FConstants VoxelErosionParameters;
#endif

/**
 * Getter/Setters helpers as UAV must have a single component
 */
inline bool IsIn(int2 Pos) { return Pos.x >= 0 && Pos.y >= 0 && Pos.x < VoxelErosionParameters.size && Pos.y < VoxelErosionParameters.size; }
inline float GetLeft  (int2 Pos) { return IsIn(Pos) ? Outflow[uint2(Pos.x * 4 + 0, Pos.y)] : 0; }
inline float GetRight (int2 Pos) { return IsIn(Pos) ? Outflow[uint2(Pos.x * 4 + 1, Pos.y)] : 0; }
inline float GetBottom(int2 Pos) { return IsIn(Pos) ? Outflow[uint2(Pos.x * 4 + 2, Pos.y)] : 0; }
inline float GetTop   (int2 Pos) { return IsIn(Pos) ? Outflow[uint2(Pos.x * 4 + 3, Pos.y)] : 0; }
inline void  SetLeft  (int2 Pos, float Value) { Outflow[uint2(Pos.x * 4 + 0, Pos.y)] = Value; }
inline void  SetRight (int2 Pos, float Value) { Outflow[uint2(Pos.x * 4 + 1, Pos.y)] = Value; }
inline void  SetBottom(int2 Pos, float Value) { Outflow[uint2(Pos.x * 4 + 2, Pos.y)] = Value; }
inline void  SetTop   (int2 Pos, float Value) { Outflow[uint2(Pos.x * 4 + 3, Pos.y)] = Value; }

inline float2 GetVelocity(uint2 Pos)
{
    return float2(
        Velocity[uint2(Pos.x * 2 + 0, Pos.y)], 
        Velocity[uint2(Pos.x * 2 + 1, Pos.y)]);
}
inline void SetVelocity(uint2 Pos, float2 Value)
{
    Velocity[uint2(Pos.x * 2 + 0, Pos.y)] = Value.x;
    Velocity[uint2(Pos.x * 2 + 1, Pos.y)] = Value.y;
}

/**
 * WaterIncrement
 */
 
[numthreads(NUM_THREADS_CS, NUM_THREADS_CS, 1)]
void WaterIncrement(uint3 ThreadId : SV_DispatchThreadID)
{
    const uint2 Pos = ThreadId.xy;
    WaterHeight1[Pos] = WaterHeight[Pos] + VoxelErosionParameters.dt * VoxelErosionParameters.Kr * RainMap[Pos];
}

/**
 * FlowSimulation
 */

inline float HeightDifference(uint2 a, uint2 b)
{
    return TerrainHeight[a] + WaterHeight1[a] - TerrainHeight[b] - WaterHeight1[b];
}
[numthreads(NUM_THREADS_CS, NUM_THREADS_CS, 1)]
 void FlowSimulation(uint3 ThreadId : SV_DispatchThreadID)
{
    const int2 Pos    = ThreadId.xy;
    const int2 Left   = Pos + int2(-1, 0);
    const int2 Right  = Pos + int2(+1, 0);
    const int2 Bottom = Pos + int2(0, -1);
    const int2 Top    = Pos + int2(0, +1);
    
    float4 OutflowValue = float4(GetLeft(Pos), GetRight(Pos), GetBottom(Pos), GetTop(Pos));

    // Flow update
    {
        // Compute the flow from height differences
        OutflowValue += VoxelErosionParameters.dt * VoxelErosionParameters.g / VoxelErosionParameters.l *
                        float4(
                            HeightDifference(Pos, Left  ),
                            HeightDifference(Pos, Right ),
                            HeightDifference(Pos, Bottom),
                            HeightDifference(Pos, Top   ));
        OutflowValue = max(OutflowValue, 0);

        // Scale the flow down if needed
        const float OutflowSum = OutflowValue.x + OutflowValue.y + OutflowValue.z + OutflowValue.w;
        if (OutflowSum != 0)
        {
            const float K = WaterHeight1[Pos] * VoxelErosionParameters.l * VoxelErosionParameters.l / (VoxelErosionParameters.dt * OutflowSum);
            OutflowValue *= min(K, 1);
        }

        SetLeft  (Pos, OutflowValue.x);
        SetRight (Pos, OutflowValue.y);
        SetBottom(Pos, OutflowValue.z);
        SetTop   (Pos, OutflowValue.w);
    }

    // Update water height
    {
        const float DeltaVolume = VoxelErosionParameters.dt * (
                                   GetRight(Left) +
                                   GetLeft(Right) +
                                   GetTop(Bottom) +
                                   GetBottom(Top) +
                                   -OutflowValue.x +
                                   -OutflowValue.y +
                                   -OutflowValue.z +
                                   -OutflowValue.w);
        WaterHeight2[Pos] = WaterHeight1[Pos] + DeltaVolume / (VoxelErosionParameters.l * VoxelErosionParameters.l);
    }

    // Boundaries
    if(Pos.x == 0)
    {
        SetLeft(Pos, 0);
    }
    else if (Pos.x == VoxelErosionParameters.size - 1)
    {
        SetRight(Pos, 0);
    }
    if (Pos.y == 0)
    {
        SetBottom(Pos, 0);
    }
    else if (Pos.y == VoxelErosionParameters.size - 1)
    {
        SetTop(Pos, 0);
    }

    // Update velocity
    {
        float2 DeltaWaterA;
        float2 DeltaWaterB;
        DeltaWaterA.x = GetRight(Left) - GetLeft(Pos);
        DeltaWaterB.x = GetRight(Pos)  - GetLeft(Right);
        DeltaWaterA.y = GetTop(Bottom) - GetBottom(Pos);
        DeltaWaterB.y = GetTop(Pos) - GetBottom(Top);

        float2 DeltaWater;
        // Avoid spikes
        if (abs(DeltaWaterA.x + DeltaWaterB.x) < 0.001)
        {
            DeltaWater.x = DeltaWaterA.x;
        }
        else
        {
            DeltaWater.x = (DeltaWaterA.x + DeltaWaterB.x) / 2;
        }
        if (abs(DeltaWaterA.y + DeltaWaterB.y) < 0.001)
        {
            DeltaWater.y = DeltaWaterA.y;
        }
        else
        {
            DeltaWater.y = (DeltaWaterA.y + DeltaWaterB.y) / 2;
        }

        const float MeanWater = (WaterHeight1[Pos] + WaterHeight2[Pos]) / 2;
        const float Divisor = VoxelErosionParameters.l * MeanWater;
        if (Divisor == 0)
        {
            SetVelocity(Pos, DeltaWater);
        }
        else
        {
            SetVelocity(Pos, DeltaWater / Divisor);
        }
    }
}

/**
 * ErosionDeposition
 */

// Return sin(tilt angle)
inline float TiltAngle(int2 Pos)
{
    // https://math.stackexchange.com/questions/1044044/local-tilt-angle-based-on-height-field

    const int2 Left   = Pos + int2(-1, 0);
    const int2 Right  = Pos + int2(+1, 0);
    const int2 Bottom = Pos + int2(0, -1);
    const int2 Top    = Pos + int2(0, +1);

    if (!IsIn(Left)   ||
        !IsIn(Right)  ||
        !IsIn(Bottom) ||
        !IsIn(Top))
    {
        // We don't want the sediments to be stuck there
        return 0.5;
    }

    const float DeltaXL = (TerrainHeight[Left  ] - TerrainHeight[Pos]) / 2;
    const float DeltaXR = (TerrainHeight[Right ] - TerrainHeight[Pos]) / 2;
    const float DeltaYB = (TerrainHeight[Bottom] - TerrainHeight[Pos]) / 2;
    const float DeltaYT = (TerrainHeight[Top   ] - TerrainHeight[Pos]) / 2;

    const float Sum = max(DeltaXL * DeltaXL, DeltaXR * DeltaXR) + max(DeltaYB * DeltaYB, DeltaYT * DeltaYT);
    
    return sqrt(Sum / (1 + Sum));
}

[numthreads(NUM_THREADS_CS, NUM_THREADS_CS, 1)]
 void ErosionDeposition(uint3 ThreadId : SV_DispatchThreadID)
{
    const uint2 Pos = ThreadId.xy;

    float C = VoxelErosionParameters.Kc * TiltAngle(Pos) * length(GetVelocity(Pos));
    const float S = Sediment[Pos];

    const float K = C > S ? VoxelErosionParameters.Ks : VoxelErosionParameters.Kd;
    float Diff = K * (C - S);
    if (Diff > 0)
    {
        Diff = min(Diff, TerrainHeight[Pos]);
    }
    else
    {
        Diff = -min(-Diff, Sediment[Pos]);
    }

    TerrainHeight1[Pos] = TerrainHeight[Pos] - Diff;
    Sediment1[Pos] = Sediment[Pos] + Diff;
}

/**
 * SedimentTransportation
 */

[numthreads(NUM_THREADS_CS, NUM_THREADS_CS, 1)]
 void SedimentTransportation(uint3 ThreadId : SV_DispatchThreadID)
{
    const uint2 Pos = ThreadId.xy;
    const float2 SamplePos = Pos - GetVelocity(Pos) * VoxelErosionParameters.dt;
    const uint2 Floor = floor(SamplePos);
    const uint2 Ceil = ceil(SamplePos);
    const float2 Frac = SamplePos - Floor;
    Sediment[Pos] = lerp(
                        lerp(Sediment1[uint2(Floor.x, Floor.y)], Sediment1[uint2(Ceil.x, Floor.y)], Frac.x),
                        lerp(Sediment1[uint2(Floor.x, Ceil .y)], Sediment1[uint2(Ceil.x, Ceil .y)], Frac.x),
                        Frac.y);
}

/**
 * Evaporation
 */

[numthreads(NUM_THREADS_CS, NUM_THREADS_CS, 1)]
 void Evaporation(uint3 ThreadId : SV_DispatchThreadID)
{
    const uint2 Pos = ThreadId.xy;
    WaterHeight[Pos] = WaterHeight2[Pos] * (1 - VoxelErosionParameters.Ke * VoxelErosionParameters.dt);

    // Also copy the height data
    TerrainHeight[Pos] = TerrainHeight1[Pos];
}