public void TestDisconnectReturnsNull()
{
GeometryCollection geometry = new GeometryCollection();
Line line = new Line(new Vector2(-1, 0), new Vector2(1, 0));
geometry.Add(line);
geometry.Add(new Vector2(2, 0));
BoundParticle particle = new BoundParticle(line, false, 0.5, 0, 0);
Path path = PathFinding.PathTo(particle, new Vector2(2, 0), geometry, 0.1f, 0.1f);
Assert.IsNull(path);
}
public void TestBowlSwing()
{
GeometryCollection geometry = new GeometryCollection();
Line line = new Line(new Vector2(1, 0), new Vector2(-1, 0));
geometry.Add(line);
geometry.Add(new Line(new Vector2(-2, 1), new Vector2(-1, 0)));
geometry.Add(new Line(new Vector2(2, 1), new Vector2(1, 0)));
// Shape looks like \_._/*
BoundParticle particle = new BoundParticle(line, false, 0.5, 0, 0);
Path path = PathFinding.PathTo(particle, new Vector2(2, 1), geometry, 0.1f, -0.2f);
Assert.IsNotNull(path);
}
public void TestBowlSlowdown()
{
GeometryCollection geometry = new GeometryCollection();
Line line = new Line(new Vector2(1, 0), new Vector2(-1, 0));
geometry.Add(line);
geometry.Add(new Line(new Vector2(-2, 1), new Vector2(-1, 0)));
geometry.Add(new Line(new Vector2(2, 1), new Vector2(1, 0)));
// Shape looks like \_._/*
BoundParticle particle = new BoundParticle(line, false, 0.5, 0, 0);
Path path = PathFinding.PathTo(particle, new Vector2(2, 1), geometry, 0.1f, -0.1f);
// Exact answer: √(80+120√2)-√40
AssertExtra.AreApproximate(9.4775213623, path.totalTime);
}
public static Path PathTo(BoundParticle start, Point end, GeometryCollection geometry, float accel, float gravity)
{
// construct a new critical point
Point newPoint = start.position();
Line line1 = new Line(newPoint, start.boundTo.p1);
Line line2 = new Line(newPoint, start.boundTo.p2);
geometry.Add(line1);
geometry.Add(line2);
geometry.Remove(start.boundTo);
Queue<PathCriticalPoint> bfs = new Queue<PathCriticalPoint>();
// map time function for two attached points
Dictionary<PathCriticalPoint, PointFunction> dict = new Dictionary<PathCriticalPoint, PointFunction>();
PathCriticalPoint state1 = new PathCriticalPoint(line1, true);
PathCriticalPoint state2 = new PathCriticalPoint(line2, true);
dict[state1] = new PointFunction(0);
dict[state2] = new PointFunction(0);
bfs.Enqueue(state1);
bfs.Enqueue(state2);
// bfs will simply search through steps, and will not continue a branch if it doesn't improve anything
while (bfs.Count > 0)
{
var head = bfs.Dequeue();
// TODO: currently not going back to previously visited points, as the logic isn't correct for it
var currPoint = head.firstPoint ? head.line.p1 : head.line.p2;
foreach (var nextLine in geometry.LinesAttachedTo(currPoint).Where(l => !l.Equals(head.line)))
{
var nextPoint = (nextLine.p1.Equals(currPoint)) ? nextLine.p2 : nextLine.p1;
var nextState = new PathCriticalPoint(nextLine, nextLine.p1.Equals(nextPoint));
PointFunction timings = new PointFunction(currPoint, nextPoint, dict[head], accel, gravity);
WorkWithTimings(end, geometry, bfs, dict, nextState, timings);
// also attempt to return along that path
var nextState2 = new PathCriticalPoint(nextLine, nextLine.p1.Equals(currPoint));
PointFunction timings2 = PointFunction.Return(currPoint, nextPoint, dict[head], accel, gravity);
WorkWithTimings(end, geometry, bfs, dict, nextState2, timings2);
}
}
Path answer = null;
if (ContainsAnyState(dict, end, geometry, 0))
{
answer = BestOfAnyState(dict, end, geometry, 0);
}
geometry.Remove(newPoint);
geometry.Add(start.boundTo);
return answer;
}
public BoundParticle FirstCollision(Particle particle)
{
var v = particle.velocity;
var p = particle.position;
if (v.X == 0 && v.Y == 0) return null;
BoundParticle collidedWith = null;
double minT = Double.MaxValue;
foreach (Line line in lines)
{
// calculate t, the amount of time it would take to collide
// p+v*t=line.p1+(line.p2-line.p1)*g
// p.x+v.x*t=line.p1.x+(line.p2.x-line.p1.x)*g
// p.y+v.y*t=line.p1.y+(line.p2.y-line.p1.y)*g
// (line.p1.x+(line.p2.x-line.p1.x)*g)*v.y-(line.p1.y+(line.p2.y-line.p1.y)*g)*v.x=p.x*v.y-p.y*v*x
// g=(p.x*v.y-p.y*v.x-v.y*line.p1.x+line.p1.y*v.x)/((line.p2.x-line.p1.x)*v.y-(line.p2.y-line.p1.y)*v.x)
double g = (p.X*v.Y-p.Y*v.X-v.Y*line.p1.v.Position.X+line.p1.v.Position.Y*v.X)/((line.p2.v.Position.X-line.p1.v.Position.X)*v.Y-(line.p2.v.Position.Y-line.p1.v.Position.Y)*v.X);
double t = (line.p1.v.Position.Y + (line.p2.v.Position.Y - line.p1.v.Position.Y) * g - p.Y) / v.Y;
if(t>=0 && g>=0 && g<=1 && t<minT && t<=1)
{
minT = t;
double gv = Vector2.Dot(v, (Vector2)line.p2 - line.p1) / (((Vector2)line.p2 - line.p1).LengthSquared());
double ga = Vector2.Dot(particle.gravity, line) / ((Vector2)line).LengthSquared();
collidedWith = new BoundParticle(line, v.CrossProduct(line) > 0, g, gv, ga);
}
}
return collidedWith;
}
internal void Update()
{
mouseListener.Update();
var keystate = Keyboard.GetState();
if(keystate.IsKeyDown(Keys.Z) && !playback && isBound) // TODO: we can improve this to work even when unbound
{
var target = geometry.SnapToClosePoint(mouseListener.Transform(Mouse.GetState()));
recording = PathFinding.PathTo(player2, target, geometry, ACCEL, GRAVITY);
if (recording != null)
{
timeInRecording = 0;
recordingPointer = new Particle(recording.absolutePosAt(0), Vector2.Zero, Vector2.Zero);
playback = true;
}
}
if (!playback)
{
if (!isBound)
{
var collision = geometry.FirstCollision(player);
if (collision != null)
{
isBound = true;
player2 = collision;
}
}
if (isBound)
{
bool upsideDown = (((Vector2)player2.boundTo).X < 0) != player2.onCW;
if (upsideDown)
{
isBound = false;
player.position = player2.boundTo.p1 + Vector2.Multiply(player2.boundTo, (float)player2.g);
player.velocity = Vector2.Multiply(player2.boundTo, (float)player2.gv) + player.gravity;
player.position += player.velocity;
player.velocity += player.gravity;
}
else
{
player2.g += player2.gv;
player2.gv += player2.ga;
if (keystate.IsKeyDown(Keys.A))
{
player2.gv += ACCEL * ((player2.onCW) ? 1 : -1) / ((Vector2)player2.boundTo).Length();
}
if (keystate.IsKeyDown(Keys.D))
{
player2.gv -= ACCEL * ((player2.onCW) ? 1 : -1) / ((Vector2)player2.boundTo).Length();
}
if (player2.g > 1 || player2.g < 0)
{
var exitingPoint = (player2.g < 0) ? player2.boundTo.p1 : player2.boundTo.p2;
var nextList = geometry.LinesAttachedTo(exitingPoint).Where(l => l != player2.boundTo);
nextList = nextList.Where(l => (((((Vector2)player2.boundTo).CrossProduct(l) < 0) != player2.onCW) != (player2.boundTo.p1 == exitingPoint)) != ((exitingPoint == l.p1) == (exitingPoint == player2.boundTo.p1)));
if (nextList.Count() > 0)
{
var next = nextList.OrderBy(l => Math.Abs(((Vector2)player2.boundTo).CrossProduct(l)) / ((Vector2)l).Length()).Last();
var multiplier = Vector2.Dot(next, player2.boundTo) / (((Vector2)next).Length() * ((Vector2)player2.boundTo).Length()) * ((Vector2)player2.boundTo).Length() / ((Vector2)next).Length();
if ((exitingPoint == next.p1) == (exitingPoint == player2.boundTo.p1))
{
player2.onCW = !player2.onCW;
}
player2.boundTo = next;
player2.g = (next.p1 == exitingPoint) ? 0 : 1;
player2.gv *= multiplier;
player2.ga = Vector2.Dot(player.gravity, (Vector2)next) / (((Vector2)next).LengthSquared());
}
else
{
isBound = false;
player.position = player2.boundTo.p1 + Vector2.Multiply(player2.boundTo, (float)player2.g);
player.velocity = Vector2.Multiply(player2.boundTo, (float)player2.gv);
}
}
}
}
else
{
// order of this matters
player.position += player.velocity;
player.velocity += player.gravity;
}
}
}
public void TestMultipleFlatLines()
{
int n = 10; // half the total number of points
GeometryCollection geometry = new GeometryCollection();
Line line = new Line(new Vector2(-1, 0), new Vector2(1, 0));
geometry.Add(line);
MathExp.Geometry.Point target = null;
for(int i=1; i<n; i++)
{
MathExp.Geometry.Point rightMostPoint = new Vector2(i + 1, 0);
Line leftLine = new Line(new Vector2(i, 0), rightMostPoint);
Line rightLine = new Line(new Vector2(-i, 0), new Vector2(-i - 1, 0));
geometry.Add(leftLine);
geometry.Add(rightLine);
target = rightMostPoint;
}
BoundParticle particle = new BoundParticle(line, false, 0.5, 0, 0);
Path path = PathFinding.PathTo(particle, target, geometry, 0.1f, 0.1f);
AssertExtra.AreApproximate(path.totalTime, 2 * Math.Sqrt(10 * n));
for (float t = 0; t < path.totalTime; t += 0.01f)
{
Vector2 pos = path.absolutePosAt(t);
AssertExtra.AreApproximate(0, pos.Y);
if (t < Math.Sqrt(10*n))
{
// when speeding up to approach
AssertExtra.AreApproximate(0.1 * t * t / 2, pos.X);
}
else
{
// when slowing down to stop
double g = t - Math.Sqrt(10*n);
AssertExtra.AreApproximate(-0.1 * g * g / 2 + Math.Sqrt(10*n) * 0.1 * g + 0.5*n, pos.X);
}
}
}
public void TestSingleFlatLine()
{
GeometryCollection geometry = new GeometryCollection();
Line line = new Line(new Vector2(-1, 0), new Vector2(1, 0));
geometry.Add(line);
BoundParticle particle = new BoundParticle(line, false, 0.5, 0, 0);
Path path = PathFinding.PathTo(particle, new Vector2(1, 0), geometry, 0.1f, 0.1f);
AssertExtra.AreApproximate(2 * Math.Sqrt(10), path.totalTime);
for (float t = 0; t < path.totalTime; t += 0.01f)
{
Vector2 pos = path.absolutePosAt(t);
AssertExtra.AreApproximate(0, pos.Y);
if (t < Math.Sqrt(10))
{
// when speeding up to approach
AssertExtra.AreApproximate(0.1 * t * t / 2, pos.X);
}else
{
// when slowing down to stop
double g = t - Math.Sqrt(10);
AssertExtra.AreApproximate(-0.1 * g * g / 2 + Math.Sqrt(10)*0.1*g+0.5, pos.X);
}
}
}