/*
Calculate the acceleration of each particle using a grid optimized approach.
For each particle, only particles in the same grid cell and the (26) neighboring grid cells must be considered,
since any particle beyond a grid cell distance away contributes no force.
*/
void PARTICLE_SYSTEM::calculateAcceleration() {
///////////////////
// STEP 1: UPDATE DENSITY & PRESSURE OF EACH PARTICLE
for (int x = 0; x < (*grid).xRes(); x++) {
for (int y = 0; y < (*grid).yRes(); y++) {
for (int z = 0; z < (*grid).zRes(); z++) {
vector<PARTICLE>& particles = (*grid)(x,y,z);
for (int p = 0; p < particles.size(); p++) {
PARTICLE& particle = particles[p];
particle.density() = 0.0;
// now iteratate through neighbors
for (int offsetX = -1; offsetX <= 1; offsetX++) {
if (x+offsetX < 0) continue;
if (x+offsetX >= (*grid).xRes()) break;
for (int offsetY = -1; offsetY <= 1; offsetY++) {
if (y+offsetY < 0) continue;
if (y+offsetY >= (*grid).yRes()) break;
for (int offsetZ = -1; offsetZ <= 1; offsetZ++) {
if (z+offsetZ < 0) continue;
if (z+offsetZ >= (*grid).zRes()) break;
vector<PARTICLE>& neighborGridCellParticles = (*grid)(x+offsetX, y+offsetY, z+offsetZ);
for (int i = 0; i < neighborGridCellParticles.size(); i++) {
PARTICLE& neighborParticle = neighborGridCellParticles[i];
vec3 diffPosition = particle.position() - neighborParticle.position();
float radiusSquared = dot(diffPosition, diffPosition);
if (radiusSquared <= h*h)
particle.density() += Wpoly6(radiusSquared);
}
}
}
}
particle.density() *= PARTICLE_MASS;
// p = k(density - density_rest)
particle.pressure() = GAS_STIFFNESS * (particle.density() - REST_DENSITY);
}
}
}
}
///////////////////
// STEP 2: COMPUTE FORCES FOR ALL PARTICLES
for (int x = 0; x < (*grid).xRes(); x++) {
for (int y = 0; y < (*grid).yRes(); y++) {
for (int z = 0; z < (*grid).zRes(); z++) {
vector<PARTICLE>& particles = (*grid)(x,y,z);
for (int p = 0; p < particles.size(); p++) {
PARTICLE& particle = particles[p];
//cout << "particle id: " << particle.id() << endl;
vec3 f_pressure,
f_viscosity,
f_surface,
f_gravity = gravityVector * particle.density(),
colorFieldNormal;
float colorFieldLaplacian;
// now iteratate through neighbors
for (int offsetX = -1; offsetX <= 1; offsetX++) {
if (x+offsetX < 0) continue;
if (x+offsetX >= (*grid).xRes()) break;
for (int offsetY = -1; offsetY <= 1; offsetY++) {
if (y+offsetY < 0) continue;
if (y+offsetY >= (*grid).yRes()) break;
for (int offsetZ = -1; offsetZ <= 1; offsetZ++) {
if (z+offsetZ < 0) continue;
if (z+offsetZ >= (*grid).zRes()) break;
vector<PARTICLE>& neighborGridCellParticles = (*grid)(x+offsetX, y+offsetY, z+offsetZ);
for (int i = 0; i < neighborGridCellParticles.size(); i++) {
PARTICLE& neighbor = neighborGridCellParticles[i];
//if (particle.id() == neighbor.id()) continue; // SKIPPING COMPARISON OF THE SAME PARTICLE
vec3 diffPosition = particle.position() - neighbor.position();
float radiusSquared = dot(diffPosition, diffPosition);
if (radiusSquared <= h*h) {
vec3 poly6Gradient, spikyGradient;
Wpoly6Gradient(diffPosition, radiusSquared, poly6Gradient);
WspikyGradient(diffPosition, radiusSquared, spikyGradient);
if (particle.id() != neighbor.id()) {
f_pressure += (float)(particle.pressure()/pow(particle.density(),2)+neighbor.pressure()/pow(neighbor.density(),2))*spikyGradient;
f_viscosity += (neighbor.velocity() - particle.velocity()) * WviscosityLaplacian(radiusSquared) / neighbor.density();
}
colorFieldNormal += poly6Gradient / neighbor.density();
colorFieldLaplacian += Wpoly6Laplacian(radiusSquared) / neighbor.density();
}
}
}
}
} // end of neighbor grid cell iteration
f_pressure *= -PARTICLE_MASS * particle.density();
f_viscosity *= VISCOSITY * PARTICLE_MASS;
colorFieldNormal *= PARTICLE_MASS;
particle.normal = -1.0f * colorFieldNormal;
colorFieldLaplacian *= PARTICLE_MASS;
// surface tension force
float colorFieldNormalMagnitude = colorFieldNormal.length();
if (colorFieldNormalMagnitude > SURFACE_THRESHOLD) {
particle.flag() = true;
f_surface = -SURFACE_TENSION * colorFieldNormal / colorFieldNormalMagnitude * colorFieldLaplacian;
}
else {
particle.flag() = false;
}
// ADD IN SPH FORCES
particle.acceleration() = (f_pressure + f_viscosity + f_surface + f_gravity) / particle.density();
// EXTERNAL FORCES HERE (USER INTERACTION, SWIRL)
vec3 f_collision;
collisionForce(particle, f_collision);
}
}
}
}
}
/*
Calculate the acceleration of every particle in a brute force manner (n^2).
Used for debugging.
*/
void PARTICLE_SYSTEM::calculateAccelerationBrute() {
///////////////////
// STEP 1: UPDATE DENSITY & PRESSURE OF EACH PARTICLE
for (int i = 0; i < PARTICLE::count; i++) {
// grab ith particle reference
PARTICLE& particle = _particles[i];
// now iteratate through neighbors
particle.density() = 0.0;
for (int j = 0; j < PARTICLE::count; j++) {
PARTICLE& neighborParticle = _particles[j];
vec3 diffPosition = particle.position() - neighborParticle.position();
float radiusSquared = dot(diffPosition, diffPosition);
if (radiusSquared <= h*h)
particle.density() += Wpoly6(radiusSquared);
}
particle.density() *= PARTICLE_MASS;
// p = k(density - density_rest)
particle.pressure() = GAS_STIFFNESS * (particle.density() - REST_DENSITY);
//totalDensity += particle.density();
}
///////////////////
// STEP 2: COMPUTE FORCES FOR ALL PARTICLES
for (int i = 0; i < PARTICLE::count; i++) {
PARTICLE& particle = _particles[i];
//cout << "particle id: " << particle.id() << endl;
vec3 f_pressure,
f_viscosity,
f_surface,
f_gravity(0.0, particle.density() * -9.80665, 0.0),
n,
colorFieldNormal,
colorFieldLaplacian; // n is gradient of colorfield
//float n_mag;
for (int j = 0; j < PARTICLE::count; j++) {
PARTICLE& neighbor = _particles[j];
vec3 diffPosition = particle.position() - neighbor.position();
vec3 diffPositionNormalized = normalize(diffPosition); // need?
float radiusSquared = dot(diffPosition, diffPosition);
if (radiusSquared <= h*h) {
if (radiusSquared > 0.0) {
//neighborsVisited++;
//cout << neighborsVisited << endl;
//cout << neighbor.id() << endl;
vec3 gradient;
Wpoly6Gradient(diffPosition, radiusSquared, gradient);
f_pressure += (particle.pressure() + neighbor.pressure()) / (2.0f * neighbor.density()) * gradient;
colorFieldNormal += gradient / neighbor.density();
}
f_viscosity += (neighbor.velocity() - particle.velocity()) * WviscosityLaplacian(radiusSquared) / neighbor.density();
colorFieldLaplacian += Wpoly6Laplacian(radiusSquared) / neighbor.density();
}
}
f_pressure *= -PARTICLE_MASS;
//totalPressure += f_pressure;
f_viscosity *= VISCOSITY * PARTICLE_MASS;
colorFieldNormal *= PARTICLE_MASS;
particle.normal = -1.0f * colorFieldNormal;
colorFieldLaplacian *= PARTICLE_MASS;
// surface tension force
float colorFieldNormalMagnitude = colorFieldNormal.length();
if (colorFieldNormalMagnitude > surfaceThreshold) {
particle.flag() = true;
f_surface = -SURFACE_TENSION * colorFieldLaplacian * colorFieldNormal / colorFieldNormalMagnitude;
}
else {
particle.flag() = false;
}
// ADD IN SPH FORCES
particle.acceleration() = (f_pressure + f_viscosity + f_surface + f_gravity) / particle.density();
// EXTERNAL FORCES HERE (USER INTERACTION, SWIRL)
vec3 f_collision;
collisionForce(particle, f_collision);
}
}
void CppParticleSimulator::updateSimulation(const Parameters ¶ms, float dt_seconds) {
// Set forces to 0 and calculate densities
for (int i = 0; i < positions.size(); ++i) {
forces[i] = {0, 0, 0};
float density = 0;
for (int j = 0; j < positions.size(); ++j) {
glm::vec3 relativePos = positions[i] - positions[j];
density += params.get_particle_mass() * Wpoly6(relativePos, params.kernel_size);
}
densities[i] = density;
}
// Calculate forces
for (int i = 0; i < positions.size(); ++i) {
float iPressure = (densities[i] - params.rest_density) * params.k_gas;
float cs = 0;
glm::vec3 n = {0, 0, 0};
float laplacianCs = 0;
glm::vec3 pressureForce = {0, 0, 0};
glm::vec3 viscosityForce = {0, 0, 0};
for (int j = 0; j < positions.size(); ++j) {
glm::vec3 relativePos = positions[i] - positions[j];
// Particle j's pressure force on i
float jPressure = (densities[j] - params.rest_density) * params.k_gas;
pressureForce = pressureForce - params.get_particle_mass() *
((iPressure + jPressure) / (2 * densities[j])) *
gradWspiky(relativePos, params.kernel_size);
// Particle j's viscosity force in i
viscosityForce += params.k_viscosity *
params.get_particle_mass() * ((velocities[j] - velocities[i]) / densities[j]) *
laplacianWviscosity(relativePos, params.kernel_size);
// cs for particle j
cs += params.get_particle_mass() * (1 / densities[j]) * Wpoly6(relativePos, params.kernel_size);
// Gradient of cs for particle j
n += params.get_particle_mass() * (1 / densities[j]) * gradWpoly6(relativePos, params.kernel_size);
// Laplacian of cs for particle j
laplacianCs += params.get_particle_mass() * (1 /densities[j]) * laplacianWpoly6(relativePos, params.kernel_size);
}
glm::vec3 tensionForce;
if (glm::length(n) < params.k_threshold) {
tensionForce = {0, 0, 0};
} else {
tensionForce = params.sigma * (- laplacianCs / glm::length(n)) * n;
}
//glm::vec3 n = {0, 0, 0};
glm::vec3 boundaryForce = {0, 0, 0};
boundaryForce = calculateBoundaryForceGlass(params, i);
// Add external forces on i
forces[i] = pressureForce + viscosityForce + tensionForce + params.gravity + boundaryForce;
// Euler time step
velocities[i] += (forces[i] / densities[i]) * dt_seconds;
positions[i] += velocities[i] * dt_seconds;
}
checkBoundariesGlass(params);
glBindBuffer (GL_ARRAY_BUFFER, vbo_pos);
glBufferData (GL_ARRAY_BUFFER, positions.size() * 3 * sizeof (float), positions.data(), GL_STATIC_DRAW);
}
