Gas Particle simulation Collision calculation C++ - c++

Question

This I feel is a rather complicated problem, I hope I can fit it in to small enough of a space to make it understandable. I'm presently writing code to
simulate Ideal gas particles inside a box. I'm calculating if two particles will collide having calculated the time taken for them to reach their closest point. (using an example where they have head on collision).
In this section of code I need to find if they will collide at all for two particles, before then calculating at what time and how they collide etc.
Thus for my two paricles:
Main.cpp
Vector vp1(0,0,0);
Vector vv1(1,0,0);
Vector vp2(12,0,0);
Vector vv2(-1,0,0);
Particle Particle1(1, vp1, vv1);
Particle Particle2(1, vp2, vv2);
Particle1.timeToCollision(Particle2);
Within my program I define a particle to be:
Header File
class Particle {
private:
Vector p; //position
Vector v; //velocity
double radius; //radius
public:
Particle();
Particle(double r, const Vector Vecp, const Vector Vecv);
void setPosition(Vector);
void setVelocity(Vector);
Vector getPosition() const;
Vector getVelocity() const;
double getRadius() const;
void move(double t);
double timeToCollision(const Particle particle);
void collideParticles(Particle);
~Particle();
};
Vector is another class that in short gives x, y, z values. It also contains multiple functions for manipulating these.
And the part that I need help with, within the .cpp (Ignore the cout start and letters etc, they are simple checks where my code exits for tests.)
Given the equations:
I have already written code to do the dot product and modulus for me and:
where
s is distance travelled in time tac.
double Particle::timeToCollision(const Particle particle){
Vector r2 = particle.getPosition();
Vector r1 = p;
Vector v2 = particle.getVelocity();
Vector v1 = v;
Vector r0 = r2 - r1;
Vector v = v2 - v1;
double modv;
double tca;
double result = 0;
double bsqr;
modv = getVelocity().modulus();
cout << "start" << endl;
if(modv < 0.0000001){
cout << "a" << endl;
result = FLT_MAX;
}else{
cout << "b" << endl;
tca = ((--r0).dot(v)) / v.modulusSqr();
// -- is an overridden operator that gives the negation ( eg (2, 3, 4) to (-2, -3, -4) )
if (tca < 0) {
cout << "c" << endl;
result = FLT_MAX;
}else{
cout << "d" << endl;
Vector s(v.GetX(), v.GetY(), v.GetZ());
s.Scale(tca);
cout << getVelocity().GetX() << endl;
cout << getVelocity().GetY() << endl;
cout << getVelocity().GetZ() << endl;
double radsqr = radius * radius;
double bx = (r0.GetX() * r0.GetX() - (((r0).dot(v)) *((r0).dot(v)) / v.modulusSqr()));
double by = (r0.GetY() * r0.GetY() - (((r0).dot(v)) *((r0).dot(v)) / v.modulusSqr()));
double bz=(r0.GetZ() * r0.GetZ() - (((r0).dot(v)) * ((r0).dot(v)) / v.modulusSqr()));
if (bsqr < 4 * radsqr) {
cout << "e" << endl;
result = FLT_MAX;
} else {
}
cout << "tca: " << tca << endl;
}
}
cout << "fin" << endl;
return result;
}
I have equations for calculating several aspects, tca refers to Time of closest approach.
As written in the code I need to check if b > 4 r^2, I Have made some attempts and written the X, Y and Z components of b out. But I'm getting rubbish answers.
I just need help to establish if I've already made mistakes or the sort of direction I should be heading.
All my code prior to this works as expected and I've written multiple tests for each to check.
Please inform me in a comment for any information you feel I've left out etc.
Any help greatly appreciated.

Answer 1

You had several mistakes in your code. You never set result to a value different from 0 or FLT_MAX. You also never calculate bsqr. And I guess the collision happens if bsqr < 4r^2 and not the other way round. (well i do not understand why 4r^2 instead of r^2 but okay). Since you hide your vector implementation I used a common vector library. I also recommend to not use handcrafted stuff anyway. Take a look into armadillo or Eigen.
Here you go with a try in Eigen.
#include <iostream>
#include <limits>
#include <type_traits>
#include "Eigen/Dense"
struct Particle {
double radius;
Eigen::Vector3d p;
Eigen::Vector3d v;
};
template <class FloatingPoint>
std::enable_if_t<std::is_floating_point<FloatingPoint>::value, bool>
almost_equal(FloatingPoint x, FloatingPoint y, unsigned ulp=1)
{
FloatingPoint max = std::max(std::abs(x), std::abs(y));
return std::abs(x-y) <= std::numeric_limits<FloatingPoint>::epsilon()*max*ulp;
}
double timeToCollision(const Particle& left, const Particle& right){
Eigen::Vector3d r0 = right.p - left.p;
Eigen::Vector3d v = right.v - left.v;
double result = std::numeric_limits<double>::infinity();
double vv = v.dot(v);
if (!almost_equal(vv, 0.)) {
double tca = (-r0).dot(v) / vv;
if (tca >= 0) {
Eigen::Vector3d s = tca*v;
double bb = r0.dot(r0) - s.dot(s);
double radius = std::max(left.radius, right.radius);
if (bb < 4*radius*radius)
result = tca;
}
}
return result;
}
int main()
{
Eigen::Vector3d vp1 {0,0,0};
Eigen::Vector3d vv1 {1,0,0};
Eigen::Vector3d vp2 {12,0,0};
Eigen::Vector3d vv2 {-1,0,0};
Particle p1 {1, vp1, vv1};
Particle p2 {1, vp2, vv2};
std::cout << timeToCollision(p1, p2) << '\n';
}

Answer 2

My apologies for a very poorly worded question that was to long and bulky to make much sense of. Luckily I have found my own answer to be much easier then initially anticipated.
double Particle::timeToCollision(const Particle particle){
Vector r2=particle.getPosition();
Vector r1=p;
Vector v2=particle.getVelocity();
Vector v1=v;
Vector r0=r2-r1;
Vector v=v2-v1;
double modv;
double tca = ((--r0).dot(v)) / v.modulusSqr();
double bsqr;
double result=0;
double rColTestx=r0.GetX()+v.GetX()*tca;
double rColTesty=r0.GetY()+v.GetY()*tca;
double rColTestz=r0.GetZ()+v.GetZ()*tca;
Vector rtColTest(rColTestx, rColTesty, rColTestz);
modv=getVelocity().modulus();
cout << "start " << endl;
if(modv<0.0000001){
cout << "a" << endl;
result=FLT_MAX;
}else{
cout << "b" << endl;
if (tca < 0) {
cout << "c" << endl;
result=FLT_MAX;
}else{
cout << "d" << endl;
Vector s(v.GetX(), v.GetY(), v.GetZ());
s.Scale(tca);
cout << getVelocity().GetX() << endl;
cout << getVelocity().GetY() << endl;
cout << getVelocity().GetZ() << endl;
double radsqr= radius*radius;
bsqr=rtColTest.modulusSqr();
if (bsqr < 4*radsqr) {
cout << "e" << endl;
cout << "collision occurs" << endl;
result = FLT_MAX;
} else {
cout << "collision does not occurs" << endl;
}
}
}
cout << "fin" << endl;
return result;
}
Sorry its a large section of code. Also FLT_MAX is from the cfloat lib. I didn't stat this in my question. I found this to work for several examples I calculated on paper to check.
To be Clear, the return resultand result=0 were arbitrary. I later edit to return time but for this part didn't need or want that.