public void calcViscosityForce(Sphere p)
{
Vector3 f = new Vector3(0, 0, 0);
int[] closePointInds = Game.neighborsIndicesConcatenated(p.Position);
for (int i = 0; i < closePointInds.Length; i++)
{
int index = (int)((Game.getDistance(p.Position, Game.particles[closePointInds[i]].Position) * 100) / d);
float lap = 0;
if (index <= 100 && index >= 0)
{
lap = laplacianLookup[index];
}
else
{
lap = Poly6WeightKernel(p.Position, Game.particles[closePointInds[i]].Position);
}
f += viscosity * Game.particles[closePointInds[i]].Mass * ((Game.particles[closePointInds[i]].Velocity - p.Velocity) / Game.particles[closePointInds[i]].Density) * lap;
}
// Console.WriteLine("viscosity force: " + f);
if (p.verbose)
{
Console.WriteLine("Viscocity: " + f);
}
p.NetForce += f;
}
/**
* Kernels: the following functions are the kernels used to calculate the distance weighting of particles
* as well as the effect that graident of the vector field has on the particles for each force.
*
* Sources used to find these kernels:
* https://www8.cs.umu.se/kurser/TDBD24/VT06/lectures/sphsurvivalkit.pdf
* https://nccastaff.bournemouth.ac.uk/jmacey/MastersProjects/MSc15/06Burak/BurakErtekinMScThesis.pdf
**/
//Poly6 kernel for distance weighting. used in calculating a particle's density
public float Poly6WeightKernel(Vector3 x1, Vector3 x2)
{
float r = Game.getDistance(x1, x2);
if (r > d)
{
return(0.0f);
}
return((315 / (64 * (float)Math.PI * (float)Math.Pow(d, 9))) * (float)Math.Pow(d * d - r * r, 3));
}
//Laplacian kernel for distance weighitng and vector gradient. used forcalculating viscosit force
public float laplacianKernel(Vector3 x1, Vector3 x2)
{
float r = Game.getDistance(x1, x2);
if (r > d)
{
return(0.0f);
}
return((45 / ((float)Math.PI * (float)Math.Pow(d, 6))) * (d - r));
}
//Spiky kernel for distance weighitng and vector gradient. used for calculating pressure force
public Vector3 spikyPressureKernel(Vector3 x1, Vector3 x2)
{
float r = Game.getDistance(x1, x2);
if (r > d)
{
return(new Vector3(0, 0, 0));
}
return(-1.0f * (45 / ((float)Math.PI * (float)Math.Pow(d, 6))) * (float)Math.Pow(d - r, 2) * (x1 - x2));
}
public Vector3 Poly6GradientKernel(Vector3 x1, Vector3 x2)
{
float r = Game.getDistance(x1, x2);
if (r < 1.0f)
{
r = 0.1f;
}
if (r > d)
{
return(new Vector3(0, 0, 0));
}
return((-945 / (32 * (float)Math.PI * (float)Math.Pow(d, 9))) * ((x1 - x2) * (float)Math.Pow(d * d - r * r, 2)));
}
public float CohesionKernel(Vector3 x1, Vector3 x2)
{
float r = Game.getDistance(x1, x2);
float constant = (float)(32 / (Math.PI * Math.Pow(d, 9)));
if (2 * r > d && r <= d)
{
//Console.WriteLine(1);
return(constant * (float)Math.Pow((d - r), 3) * (float)Math.Pow(r, 3));
}
else if (r > 0.0001 && 2 * r <= d)
{
//Console.WriteLine(2);
return(constant * 2 * (float)Math.Pow((d - r), 3) * (float)Math.Pow(r, 3) - (float)Math.Pow(d, 6) / 64);
}
//Console.WriteLine(3);
return(0.0f);
}
public void calcSurfaceTension(Sphere p)
{
if (p.normal.Length < gradientFieldThreshold)
{
return;
}
Vector3 f = new Vector3(0, 0, 0);
Vector3 cNormal = new Vector3(0, 0, 0);
Vector3 cCurvature = new Vector3(0, 0, 0);
float K = p.Density;
int[] closePointInds = Game.neighborsIndicesConcatenated(p.Position);
for (int i = 0; i < closePointInds.Length; i++)
{
Vector3 r = p.Position - Game.particles[closePointInds[i]].Position;
if (Game.getDistance(p.Position, Game.particles[closePointInds[i]].Position) > 0)
{
cNormal += Game.particles[closePointInds[i]].Mass * CohesionKernel(p.Position, Game.particles[closePointInds[i]].Position) * (r / r.Length);
cCurvature += p.normal - Game.particles[closePointInds[i]].normal;
K += Game.particles[closePointInds[i]].Density;
}
}
cNormal *= p.Mass * -sigma;
cCurvature *= p.Mass * -sigma;
if (K > 0.0001)
{
K = 2 * p0 / K;
}
else
{
K = 0;
}
f = K * (cNormal + cCurvature);
if (p.verbose)
{
Console.WriteLine("Surface: " + f);
}
p.NetForce += f;
}
/**
* The following functions are implementations of the langrangian fluid equations provided here:
* https://www.cs.ubc.ca/~rbridson/fluidsimulation/fluids_notes.pdf
*
* This source was linked by Amir on the game physics course page
**/
public void calcDensity(Sphere p)
{
float dense = 1f;
int[] closePointInds = Game.neighborsIndicesConcatenated(p.Position);
for (int i = 0; i < closePointInds.Length; i++)
{
int index = (int)((Game.getDistance(p.Position, Game.particles[closePointInds[i]].Position) * 100) / d);
float poly = 0;
if (false)
{
poly = poly6Lookup[index];
}
else
{
poly = Poly6WeightKernel(p.Position, Game.particles[closePointInds[i]].Position);
}
dense += Game.particles[closePointInds[i]].Mass * poly;
}
p.Density = dense;
}
