# Sphere for Spherical Collision (C ++)

I am implementing some basic 3D physics engine. For ball collision, I am following this tutorial . I have problems with two moving spheres. I am guessing there may be some problem with how I find the "cut speed"

``````bool collidingDSmove(Sphere sphere){
// Early Escape test: if the length of the movevec is less
// than distance between the centers of these circles minus
// their radii, there no way they can hit.
```

```

In my test environment, the motion velocity vectors are (-2, -4, -2) and (1,2,1). Therefore, "shortVel" actually becomes larger than the original speeds.

``````    vec3 shortVel = sphere.velocity.substract(velocity);
vec3 fromAtoBCenter = position.substract(sphere.position);
float distSquare = fromAtoBCenter.getLengthSquare();
if (shortVel.getLengthSquare() < distSquare){
return false;
}

// Normalize the movevec
vec3 N = shortVel.normalize();

// Find C, the vector from the center of the moving
// circle A to the center of B
vec3 C = sphere.position.substract(position);

// D = N . C = ||C|| * cos(angle between N and C)
float D = N.dot(C);

// Another early escape: Make sure that A is moving
// towards B! If the dot product between the movevec and
// B.center - A.center is less that or equal to 0,
// A isn't isn't moving towards B
if (D <= 0){
return false;
}
// Find the length of the vector C
float lengthCSquare = C.getLengthSquare();

float F = (lengthCSquare)-(D * D);

// Escape test: if the closest that A will get to B
// is more than the sum of their radii, there no
// way they are going collide
return false;
}

// We now have F and sumRadii, two sides of a right triangle.
// Use these to find the third side, sqrt(T)
double T = sumRadiiSquared - F;

// If there is no such right triangle with sides length of
// sumRadii and sqrt(f), T will probably be less than 0.
// Better to check now than perform a square root of a
// negative number.
if (T < 0){
return false;
}

// Therefore the distance the circle has to travel along
// movevec is D - sqrt(T)
float distance = D - sqrt(T);

// Get the magnitude of the movement vector
float mag = velocity.getLength();

// Finally, make sure that the distance A has to move
// to touch B is not greater than the magnitude of the
// movement vector.
if (mag < distance){
return false;
}
```

```

// *** the amount is not between 0 and 1

``````    float amount = shortVel.normalize().getLength() / velocity.getLength();
// Set the length of the movevec so that the circles will just
// touch
velocity = velocity.normalize().times(amount);
sphere.velocity = sphere.velocity.normalize().times(amount);

return true;
}
```

```

My vec3 class looks like this:

``````class vec3 {
public:
float x; float y; float z;
vec3() : x(0), y(0), z(0) { }
vec3 substract(vec3 v){
vec3 sub;
sub.x = x - v.x;
sub.y = y - v.y;
sub.z = z - v.z;
return sub;
}
float getLength() {
return sqrt(x*x + y*y + z*z);
}
float getLengthSquare() {
return x*x + y*y + z*z;
}
vec3 normalize(){
vec3 n;
n.x = x / getLength();
n.y = y / getLength();
n.z = z / getLength();
return n;
}
float dot(vec3 v) {
return x*v.x + y*v.y + z*v.z;
}
}
```

```

Could you please explain to me what I am doing wrong here?

Here is my update function. Where deltaT is the time elapsed between 2 frames

``````void updateVelocity(double deltaT){
velocity.x = velocity.x + acceleration.x*deltaT;
velocity.y = velocity.y + acceleration.y*deltaT;
velocity.z = velocity.z + acceleration.z*deltaT;
}
void updatePosition(double deltaT){
position.x = position.x + velocity.x * deltaT + 0.5 * acceleration.x * deltaT * deltaT;
position.y = position.y + velocity.y * deltaT + 0.5 * acceleration.y * deltaT * deltaT;
position.z = position.z + velocity.z * deltaT + 0.5 * acceleration.z * deltaT * deltaT;
}
void update(double deltaT){
updateVelocity(deltaT);
updatePosition(deltaT);

}
```

```
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First create add and time functions in vec3.

If sphere s1 and sphere s2 at position p (vec3), velocity v (vec3), radius r (float) and mass m (float) collide, you can do:

``````// from s1 to s2
vec3 pDiff = s2.p.subtract(s1.p);
// collision detection
if (pDiff.getLength() >= s1.r + s2.r) {
return;
}
// find direction from s1 to s2
vec3 dir = pDiff.normalize();
vec3 vDiff = s2.v.subtract(s1.v);
float fellingSpeed = vDiff.dot(dir);
// don't collide in this case
if (fellingSpeed >= 0) {
return;
}
// perfect spheric collision
float speed1 = (2 * s2.m * fellingSpeed) / (s1.m + s2.m);
float speed2 = (fellingSpeed * (s2.m - s1.m)) / (s1.m + s2.m);
```

```

Hope this helps.

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