//calculate the vertical velocity at the moment of impact
private float Y_ImpactVelocity()
{// (V)^2 = (V°)^2 - 2 * g * X°
float Y_impactVelSquared = velocityPreviousFrame.getY() * velocityPreviousFrame.getY() -
2 * gravity.getY() * (position.DistanceFromPlane(ground) - radius);
if (Y_impactVelSquared < 0)
{
Y_impactVelSquared = 0;
}
return(Mathf.Sqrt(Y_impactVelSquared));
}
private void FixedUpdate()
{
//simulation starts upon pressing the spacebar
if (Input.GetKeyDown(KeyCode.Space) == true)
{
startSimulation = true;
}
if (!startSimulation)
{
return;
}
float t = Time.fixedDeltaTime;
MyVector3 previousLinearMomentum = linearMomentum;
MyVector3 linearMomentumVariation = linearMomentum.UnitVector().Scale(
-SnookerBall.NormalForce * SnookerBall.frictionCoeff * t);
if (linearMomentumVariation.Magnitude() >= linearMomentum.Magnitude())
{//the decrease in linear momentum is bigger than the linear momentum itself
linearMomentum = MyVector3.Zero();
}
else
{
linearMomentum = MyVector3.Add(linearMomentum, linearMomentumVariation);
}
MyVector3 avgLinearMomentum = MyVector3.Add(linearMomentum, previousLinearMomentum).Scale(0.5f);
MyVector3 avgVelocity = avgLinearMomentum.Scale(1 / SnookerBall.mass);
MyVector3 newPosition = MyVector3.Add(position, avgVelocity.Scale(t));
foreach (Plane plane in cushions)
{
float distanceFromPlane = newPosition.DistanceFromPlane(plane) - SnookerBall.radius;
if (distanceFromPlane < 0)
{//the ball has gone beyond the boundary
//collision detected: the collision has happened anytime between the previous frame and this one.
//find how much time has past since the collision
float impactTime =
ImpactTime(
MyVector3.Dot(previousLinearMomentum, plane.Normal()),
-MyVector3.Dot(avgLinearMomentum.UnitVector(), plane.Normal()) * SnookerBall.NormalForce * SnookerBall.frictionCoeff,
position.DistanceFromPlane(plane) - SnookerBall.radius);
linearMomentumVariation = previousLinearMomentum.UnitVector().Scale(
-SnookerBall.NormalForce * SnookerBall.frictionCoeff * impactTime);
//reflect the linear momentum along the normal of the plane
linearMomentum = MyVector3.Add(previousLinearMomentum, linearMomentumVariation).Reflect(plane.Normal());
//position ball just within the boundaries
newPosition = MyVector3.Add(newPosition, plane.Normal().Scale(-distanceFromPlane));
}
}
position = newPosition;
MoveGameObject();
}
//draw rays in the scene
private void Update()
{
int lines = 36;
MyVector3 normal = plane.Normal();
MyVector3 p = MyVector3.Subtract(vector, normal.Scale(vector.DistanceFromPlane(plane)));
for (int i = 0; i < lines; i++)
{
Vector3 v = new Vector3((float)Math.Cos(Math.PI * 2 * i / lines), 0, (float)Math.Sin(Math.PI * 2 * i / lines));
v = Quaternion.FromToRotation(Vector3.up, new Vector3(normal.getX(), normal.getY(), normal.getZ())) * v;
Debug.DrawRay(new Vector3(p.getX(), p.getY(), p.getZ()), 1000 * v, Color.magenta);
}
Debug.DrawRay(Vector3.zero, new Vector3(vector.getX(), vector.getY(), vector.getZ()), Color.black);
}
public void Calculate()
{
try
{//parse strings into floating point numbers
float v_x = Single.Parse(vect_inputs[0].text);
float v_y = Single.Parse(vect_inputs[1].text);
float v_z = Single.Parse(vect_inputs[2].text);
float plane_a = Single.Parse(plane_inputs[0].text);
float plane_b = Single.Parse(plane_inputs[1].text);
float plane_c = Single.Parse(plane_inputs[2].text);
float plane_d = Single.Parse(plane_inputs[3].text);
if (plane_a == 0 && plane_b == 0 && plane_c == 0)
{
throw new Exception("Coefficients cannot all be zero!");
}
float num = Single.Parse(scalar_input.text);
if (num < 0)
{
throw new Exception("Only positive tolerance allowed!");
}
vector = new MyVector3(v_x, v_y, v_z);
plane = new Plane(plane_a, plane_b, plane_c, plane_d);
tolerance = num;
}
catch (Exception e)
{//parsing failed
Debug.LogError(e.Message);
vect_inputs[0].text = "";
vect_inputs[1].text = "";
vect_inputs[2].text = "";
plane_inputs[0].text = "";
plane_inputs[1].text = "";
plane_inputs[2].text = "";
plane_inputs[3].text = "";
scalar_input.text = "";
return;
}
//printe vectors to the scene
distanceFromPlane.text = vector.DistanceFromPlane(plane).ToString("0.000");
isOnPlane.text = vector.IsOnPlane(plane, tolerance).ToString();
}
private void FixedUpdate()
{
//simulation start upon press of the spacebar
if (Input.GetKeyDown(KeyCode.Space) == true)
{
startSimulation = true;
}
if (!startSimulation)
{
return;
}
if (fullStop)
{
return; //simulation ended
}
float t = Time.fixedDeltaTime;
if (stopBouncing)
{
if (pureRolling)
{//case 1: the ball is rolling on the floor without sliding
float dumping = 1 -
(5 - 4 / (1 + mass)) *
(floorFriction / (4 * floorFriction + 6)) *
(1 + 49 / (1 + 10 * Mathf.Abs(velocityPreviousFrame.Magnitude()))) *
t; //arbitrary dumping factor. No real physical meaning.
velocityCurrentFrame = velocityPreviousFrame.Scale(dumping);
if (velocityCurrentFrame.Magnitude() < 0.01f)
{//the velocity is low enough to be neglectable
velocityCurrentFrame = MyVector3.Zero();
fullStop = true;
}
//calculate the avarage velocity between two consecutive frames and use it to calculate the new position
MyVector3 avgVelocity = MyVector3.Lerp(velocityPreviousFrame, velocityCurrentFrame, 0.5f);
MyVector3 displacement = avgVelocity.Scale(t);
position = MyVector3.Add(position, displacement);
MoveGameObject();
angularMomentumCurrentFrame = MyVector3.Cross(velocityCurrentFrame, new MyVector3(0, -1, 0)).Scale(momentOfInertia / radius);
RotateGameObject(t);
velocityPreviousFrame = velocityCurrentFrame;
angularMomentumPreviousFrame = angularMomentumCurrentFrame;
}
else
{//case 2: the ball is rolling on the floor with sliding
velocityCurrentFrame = HorizontalVelocityAfterSliding(t);
//calculate the avarage velocity between two consecutive frames and use it to calculate the new position
MyVector3 avgVelocity = MyVector3.Lerp(velocityPreviousFrame, velocityCurrentFrame, 0.5f);
MyVector3 displacement = avgVelocity.Scale(t);
position = MyVector3.Add(position, displacement);
MoveGameObject();
//angularMomentumCurrentFrame set in the X_VelocityAfterSliding() function
RotateGameObject(t);
velocityPreviousFrame = velocityCurrentFrame;
angularMomentumPreviousFrame = angularMomentumCurrentFrame;
}
}
else
{//the ball is still bouncing
MyVector3 deltaVel = gravity.Scale(t);
velocityCurrentFrame = MyVector3.Add(velocityPreviousFrame, deltaVel);
//calculate the avarage velocity between two consecutive frames and use it to calculate the new position
MyVector3 avgVelocity = MyVector3.Lerp(velocityPreviousFrame, velocityCurrentFrame, 0.5f);
MyVector3 displacement = avgVelocity.Scale(t);
MyVector3 newPosition = MyVector3.Add(position, displacement);
float distanceFromGround = newPosition.DistanceFromPlane(ground) - radius;
if (distanceFromGround < 0)
{ //case 3: the ball is bouncing and has partially fallen balow the plane of the ground
float impactVel_y = Y_ImpactVelocity();
float velocityCurrentFrame_y = impactVel_y * restitution; //upwards speed after bounce
if (velocityCurrentFrame_y < tresholdStopBouncing)
{ //the speed after the bounce is small enough to be ignored
stopBouncing = true;
velocityCurrentFrame_y = 0;
}
MyVector3 horzVelocityCurrentFrame = HorizontalVelocityAfterSliding(t + 0.001f * impactVel_y + 8 * t * (1 - 1 / Mathf.Sqrt(1 + mass)));
//position ball on top of the ground
position = MyVector3.Add(newPosition, ground.Normal().Scale(-distanceFromGround));
MoveGameObject();
//angularMomentumCurrentFrame set in the X_VelocityAfterSliding() function
RotateGameObject(t);
angularMomentumPreviousFrame = angularMomentumCurrentFrame;
velocityPreviousFrame = new MyVector3(horzVelocityCurrentFrame.getX(), velocityCurrentFrame_y, horzVelocityCurrentFrame.getZ());
}
else
{//case 4: the ball is bouncing and is in mid-air
velocityPreviousFrame = velocityCurrentFrame;
position = newPosition;
MoveGameObject();
RotateGameObject(t);
}
}
}
