void GenerateParticles(R3Scene *scene, double current_time, double delta_time)
{
for (int i = 0; i < scene->NParticleSources(); i++) {
R3ParticleSource *source = scene->ParticleSource(i);
// spheres
if (source->shape->type == R3_SPHERE_SHAPE) {
// remainder term for fraction of particle
double numberweshouldmake = delta_time * source->rate + source->remainder;
int nparts = (int) floor(numberweshouldmake);
source->remainder = numberweshouldmake - nparts;
for (int p = 0; p < nparts; p++) {
R3Particle *newpart = new R3Particle();
// calculate position and velocity
double u = RandomNumber();
double theta = 2*PI*u;
double v = RandomNumber();
double phi = acos(2*v-1);
double r = source->shape->sphere->Radius();
R3Point center = source->shape->sphere->Center();
double x = r*cos(theta)*sin(phi);
double y = r*sin(theta)*sin(phi);
double z = r*cos(phi);
R3Vector n = R3Vector(x,y,z);
n.Normalize();
// find tangent vector, use lecture notes to get velocity
R3Plane plane = R3Plane(R3Point(0,0,0),n);
R3Vector a;
do {
a = R3Vector(RandomNumber(),RandomNumber(),RandomNumber());
a.Project(plane);
} while (a.Length() == 0.0);
a.Normalize();
double t1 = 2*PI*RandomNumber();
double t2 = sin(source->angle_cutoff)*RandomNumber();
a.Rotate(n,t1);
R3Vector vec = R3Vector(a);
R3Vector cross = R3Vector(vec);
cross.Cross(n);
vec.Rotate(cross,acos(t2));
newpart->position = center + n*r;
newpart->velocity = vec*source->velocity;
//update
newpart->mass = source->mass;
newpart->fixed = source->fixed;
newpart->drag = source->drag;
newpart->elasticity = source->elasticity;
newpart->lifetime = source->lifetime;
newpart->lifetimeactive = source->lifetimeactive;
newpart->material = source->material;
scene->particles.push_back(newpart);
}
}
// CIRCLE
if (source->shape->type == R3_CIRCLE_SHAPE) {
double numberweshouldmake = delta_time * source->rate + source->remainder;
int nparts = (int) floor(numberweshouldmake);
source->remainder = numberweshouldmake - nparts;
for (int p = 0; p < nparts; p++) {
R3Particle *newpart = new R3Particle();
// calculate position and velocity
double r = source->shape->circle->Radius();
R3Point center = source->shape->circle->Center();
R3Plane plane = source->shape->circle->Plane();
R3Vector n = plane.Normal();
n.Normalize();
// get a random point on a circle
double xcirc, ycirc;
do {
xcirc = 2*r*(RandomNumber() - 0.5);
ycirc = 2*r*(RandomNumber() - 0.5);
} while (xcirc*xcirc + ycirc*ycirc > r*r);
// get basis vectors of circle
R3Vector tang;
do {
tang = R3Vector(RandomNumber(),RandomNumber(),RandomNumber());
tang.Project(plane);
} while (tang.Length() == 0.0);
R3Vector othertang = R3Vector(tang);
othertang.Cross(n);
othertang.Normalize();
tang.Normalize();
R3Point pos = center + tang*xcirc + othertang*ycirc;
R3Vector a = R3Vector(tang);
double t1 = 2*PI*RandomNumber();
double t2 = sin(source->angle_cutoff)*RandomNumber();
a.Rotate(n,t1);
R3Vector vec = R3Vector(a);
R3Vector cross = R3Vector(vec);
cross.Cross(n);
vec.Rotate(cross,acos(t2));
newpart->position = pos;
newpart->velocity = vec*source->velocity;
newpart->mass = source->mass;
newpart->fixed = source->fixed;
newpart->drag = source->drag;
newpart->elasticity = source->elasticity;
newpart->lifetime = source->lifetime;
newpart->lifetimeactive = source->lifetimeactive;
newpart->material = source->material;
scene->particles.push_back(newpart);
}
}
}
for (int i = 0; i < (int)scene->enemies.size(); i++) {
R3Enemy *enemy = scene->enemies[i];
// spheres
if (enemy->shape->type == R3_SPHERE_SHAPE) {
// remainder term for fraction of particle
double numberweshouldmake = delta_time * enemy->rate + enemy->remainder;
int nparts = (int) floor(numberweshouldmake);
enemy->remainder = numberweshouldmake - nparts;
for (int p = 0; p < nparts; p++) {
R3Particle *newpart = new R3Particle();
// calculate position and velocity
double u = RandomNumber();
double theta = 2*PI*u;
double v = RandomNumber();
double phi = acos(2*v-1);
double r = enemy->shape->sphere->Radius();
R3Point center = enemy->shape->sphere->Center();
double x = r*cos(theta)*sin(phi);
double y = r*sin(theta)*sin(phi);
double z = r*cos(phi);
R3Vector n = R3Vector(x,y,z);
n.Normalize();
// find tangent vector, use lecture notes to get velocity
R3Plane plane = R3Plane(R3Point(0,0,0),n);
R3Vector a;
do {
a = R3Vector(RandomNumber(),RandomNumber(),RandomNumber());
a.Project(plane);
} while (a.Length() == 0.0);
a.Normalize();
double t1 = 2*PI*RandomNumber();
double t2 = sin(enemy->angle_cutoff)*RandomNumber();
a.Rotate(n,t1);
R3Vector vec = R3Vector(a);
R3Vector cross = R3Vector(vec);
cross.Cross(n);
vec.Rotate(cross,acos(t2));
newpart->position = center + n*r;
newpart->velocity = vec*enemy->velocity;
//update
newpart->mass = enemy->mass;
newpart->fixed = enemy->fixed;
newpart->drag = enemy->drag;
newpart->elasticity = enemy->elasticity;
newpart->lifetime = enemy->lifetime;
newpart->lifetimeactive = enemy->lifetimeactive;
newpart->material = enemy->material;
scene->particles.push_back(newpart);
}
}
// CIRCLE
if (enemy->shape->type == R3_CIRCLE_SHAPE) {
double numberweshouldmake = delta_time * enemy->rate + enemy->remainder;
int nparts = (int) floor(numberweshouldmake);
enemy->remainder = numberweshouldmake - nparts;
for (int p = 0; p < nparts; p++) {
R3Particle *newpart = new R3Particle();
// calculate position and velocity
double r = enemy->shape->circle->Radius();
R3Point center = enemy->shape->circle->Center();
R3Plane plane = enemy->shape->circle->Plane();
R3Vector n = plane.Normal();
n.Normalize();
// get a random point on a circle
double xcirc, ycirc;
do {
xcirc = 2*r*(RandomNumber() - 0.5);
ycirc = 2*r*(RandomNumber() - 0.5);
} while (xcirc*xcirc + ycirc*ycirc > r*r);
// get basis vectors of circle
R3Vector tang;
do {
tang = R3Vector(RandomNumber(),RandomNumber(),RandomNumber());
tang.Project(plane);
} while (tang.Length() == 0.0);
R3Vector othertang = R3Vector(tang);
othertang.Cross(n);
othertang.Normalize();
tang.Normalize();
R3Point pos = center + tang*xcirc + othertang*ycirc;
R3Vector a = R3Vector(tang);
double t1 = 2*PI*RandomNumber();
double t2 = sin(enemy->angle_cutoff)*RandomNumber();
a.Rotate(n,t1);
R3Vector vec = R3Vector(a);
R3Vector cross = R3Vector(vec);
cross.Cross(n);
vec.Rotate(cross,acos(t2));
newpart->position = pos;
newpart->velocity = vec * 1.0;
newpart->mass = enemy->mass;
newpart->fixed = enemy->fixed;
newpart->drag = enemy->drag;
newpart->elasticity = enemy->elasticity;
newpart->lifetime = enemy->lifetime;
newpart->lifetimeactive = enemy->lifetimeactive;
newpart->material = enemy->material;
scene->particles.push_back(newpart);
}
}
}
}
void UpdateParticles(R3Scene *scene, double current_time, double delta_time, int integration_type)
{
// array of ints to be deleted
std::vector<int> tobedeleted;
// for each particle
for(int i = 0; i < scene->NParticles(); i++) {
R3Particle *particle = scene->Particle(i);
bool needstobedeleted = false;
// check lifetime deletion
if (particle->lifetimeactive) {
if (particle->lifetime < 0) needstobedeleted = true;
particle->lifetime -= delta_time;
}
R3Vector positionchange;
R3Vector velocitychange;
// Euler
if (integration_type == EULER_INTEGRATION) {
R3Vector f = ForceVector(scene, current_time, particle, particle->position, particle->velocity);
positionchange = particle->velocity*delta_time;
velocitychange = delta_time*f/particle->mass;
}
// midpoint
else if (integration_type == MIDPOINT_INTEGRATION) {
R3Vector f = ForceVector(scene, current_time, particle, particle->position, particle->velocity);
R3Point xmid = particle->position + delta_time*particle->velocity/2.0;
R3Vector vmid = particle->velocity + delta_time*f/particle->mass/2.0;
R3Vector midf = ForceVector(scene, current_time, particle, xmid, vmid);
positionchange = vmid*delta_time;
velocitychange = delta_time*midf/particle->mass;
}
// rk4
else if (integration_type == RK4_INTEGRATION) {
R3Vector fk1 = ForceVector(scene, current_time, particle, particle->position, particle->velocity);
R3Vector v1 = particle->velocity;
R3Point x2 = particle->position + delta_time*particle->velocity/2.0;
R3Vector v2 = particle->velocity + delta_time*fk1/particle->mass/2.0;
R3Vector fk2 = ForceVector(scene, current_time, particle, x2, v2);
R3Vector v3 = particle->velocity + delta_time*fk2/particle->mass/2.0;
R3Vector fk3 = ForceVector(scene, current_time, particle, x2, v3);
R3Point x4 = particle->position + delta_time*particle->velocity;
R3Vector v4 = particle->velocity + delta_time*fk3/particle->mass;
R3Vector fk4 = ForceVector(scene, current_time,particle,x4, v4);
R3Vector finalf = (fk1+ 2*fk2 + 2*fk3 + fk4)/(6.0);
R3Vector finalv = (v1+ 2*v2 +2*v3 + v4)/(6.0);
positionchange = finalv*delta_time;
velocitychange = delta_time*finalf/particle->mass;
}
// adaptive method
else if (integration_type == ADAPTIVE_STEP_SIZE_INTEGRATION) {
int numbersteps = 1;
R3Vector poschange1;
R3Vector velchange1;
R3Vector poschange2;
R3Vector velchange2;
double error;
// do first euler
for (int step = 0; step < numbersteps; step++) {
poschange2 = R3Vector(0,0,0);
velchange2 = R3Vector(0,0,0);
R3Vector f = ForceVector(scene, current_time, particle, particle->position + poschange2, particle->velocity + velchange2);
poschange2 += particle->velocity*delta_time/numbersteps;
velchange2 += delta_time*f/particle->mass/numbersteps;
}
// half below threshold
do {
poschange1 = poschange2;
velchange1 = velchange2;
numbersteps *= 2;
// euler integrate with twice the number of steps
for (int step = 0; step < numbersteps; step++) {
poschange2 = R3Vector(0,0,0);
velchange2 = R3Vector(0,0,0);
R3Vector f = ForceVector(scene, current_time, particle, particle->position + poschange2, particle->velocity + velchange2);
poschange2 += particle->velocity*delta_time/numbersteps/2.0;
velchange2 += delta_time*f/particle->mass/numbersteps/2.0;
}
double d1 = (poschange1 - poschange2).Length();
double d2 = (velchange1 - velchange2).Length();
// error for both velocity and position
error = d1 + d2;
} while (error > ADAPTIVE_THRESHOLD);
positionchange = poschange2;
velocitychange = velchange2;
}
else {
fprintf(stderr, "invalid integration type\n");
return;
}
// new values
R3Point nextpos = particle->position + positionchange;
R3Vector nextvel = particle->velocity + velocitychange;
// check if particle needs to deleted
int i = 0;
for (; i < scene->NParticleSinks(); i++) {
R3ParticleSink *sink = scene->ParticleSink(i);
//sphere sink
if (sink->shape->type == R3_SPHERE_SHAPE) {
double r = sink->shape->sphere->Radius();
R3Point center = sink->shape->sphere->Center();
// inside the sphere?
if (R3Distance(nextpos,center) < r) needstobedeleted = true;
R3Vector toward1 = particle->position - center;
R3Vector toward2 = nextpos - center;
// goes flying through the sphere?
if (toward1.Dot(toward2) < 0) needstobedeleted = true;
}
}
if (!needstobedeleted) {
// check for bouncing in scene
R3Vector to = nextpos - particle->position;
to.Normalize();
R3Ray *r = new R3Ray(particle->position, to);
R3Intersect intersect = ComputeIntersect(scene,scene->Root(),r);
if (intersect.intersected && intersect.t < R3Distance(nextpos,particle->position)) {
R3Plane plane = R3Plane(intersect.pos,intersect.norm);
R3Point first = particle->position;
R3Point second = intersect.pos;
R3Point third = nextpos;
// calculate new position
R3Vector posreflect = third-second;
R3Vector posreflectplanar = R3Vector(posreflect);
posreflectplanar.Project(plane);
R3Vector posreflectnorm = posreflect - posreflectplanar;
R3Vector purenorm = R3Vector(posreflectnorm);
posreflectnorm *= -1*(particle->elasticity);
purenorm.Normalize();
purenorm *= -1;
nextpos = second + posreflectplanar + posreflectnorm + eps*purenorm;
// calculate new velocity
R3Vector velreflect = R3Vector(nextvel);
R3Vector velreflectplanar = R3Vector(velreflect);
velreflectplanar.Project(plane);
R3Vector velreflectnorm = velreflect - velreflectplanar;
purenorm = R3Vector(velreflectnorm);
velreflectnorm *= -1*(particle->elasticity);
purenorm *= -1;
purenorm.Normalize();
nextvel = velreflectnorm + velreflectplanar + eps*purenorm;
}
// update position
if (!particle->fixed) particle->position = nextpos;
if (!particle->fixed) particle->velocity = nextvel;
}
// push on deletion vector
else {
int del = i;
tobedeleted.push_back(del);
}
}
// deleting particles
for (unsigned int i = 0; i < tobedeleted.size(); i++) {
//swap contents of partcile vector with last element
R3Particle *temp = scene->particles.back();
scene->particles[scene->particles.size() - 1] = scene->particles[tobedeleted[i]];
scene->particles[tobedeleted[i]] = temp;
// delete last element
scene->particles.pop_back();
}
}