public override CartesianList <Point> Visit(Line line)
{
CartesianList <Point> intersections = new CartesianList <Point>();
// this = 0 line = 1
// x = v0 + t0 * i0 = v1 + t1 * i1
// k0.dot(x) = k0.dot(v1) + t1 * k0.dot(i1) = k0.dot(v0)
// k1.dot(x) = k1.dot(v0) + t0 * k1.dot(i0) = k1.dot(v1)
// t0 = k1.dot(v1 - v0) / k1.dot(i0)
// t1 = k0.dot(v0 - v1) / k0.dot(i1)
double den0 = line.KHat.Dot(this.IHat);
double den1 = this.KHat.Dot(line.IHat);
if (System.Math.Abs(den0) > Constants.tol)
{
double t0 = line.KHat.Dot(line.Vertex - this.Vertex) / den0;
double t1 = this.KHat.Dot(this.Vertex - line.Vertex) / den1;
if (this.Contains(t0) && line.Contains(t1))
{
intersections.Add(GetPoint(t0));
}
}
return(intersections);
}
private void AddSite(Point tail, Point head)
{
PointSite ps = new PointSite(tail, pointSitePrefab, spheres);
if (!pointSites.ContainsNear(ps))
{
pointSites.Add(ps);
sites.Add(ps);
}
LineSite ls = new LineSite(tail, head, lineSitePrefab, cylinders);
if (!lineSites.Contains(ls))
{
lineSites.Add(ls);
sites.Add(ls);
}
}
public override CartesianList <Point> Visit(Line line)
{
CartesianList <Point> intersections = new CartesianList <Point>();
List <double> solutions = new List <double>();
// p = v + x * ihat + z * khat
// n.dot(p) = n.dot(p0)
// n.dot(v + x*ihat + z*khat) = n.dot(p0)
// n.dot(ihat) * x + n.dot(khat) * z = n.dot(p0) - n.dot(v)
// a*x + b*z = c
Vector n = line.KHat;
double a = n.Dot(ihat);
double b = n.Dot(khat);
double c = n.Dot(line.Vertex - vertex);
// z = x^2 / r
// a*x + b*x^2/r = c
// t^2 + (a*r/b)*t - c*r/b = 0
// t^2 + a*r/b*t + a^2*r^2/4*b^2 = a^2*r^2/4*b^2 + c*r/b
// (t + a*r/2*b)^2 = (1/4*b^2)*(a^2*r^2 + 4*b*c*r)
// t + a*r/2*b = +- sqrt(r*(a^2*r + 4*b*c)) / 2*b
// t = (-a*r +- sqrt(r*(a^2*r + 4*b*c)) / 2*b
double discriminant = latusRectum * (a * a * latusRectum + 4.0 * b * c);
if (System.Math.Abs(b) > Constants.tol)
{
if (System.Math.Abs(discriminant) < Constants.tol)
{
double t = -0.5 * a * latusRectum / b;
solutions.Add(t);
}
else if (discriminant > Constants.tol)
{
double sqrt = System.Math.Sqrt(discriminant);
double t0 = -0.5 * (a * latusRectum - sqrt) / b;
double t1 = -0.5 * (a * latusRectum + sqrt) / b;
solutions.Add(t0);
solutions.Add(t1);
}
else
{
// no solution
}
}
else if (System.Math.Abs(a) > Constants.tol)
{
double t = c / a;
solutions.Add(t);
}
foreach (double t in solutions)
{
if (this.Contains(t))
{
Point p = GetPoint(t);
if (line.Contains(p))
{
intersections.Add(p);
}
}
}
return(intersections);
}
public void Generate()
{
wall2point = new Point[maze.Length, 4];
for (int iwall = 0; iwall < maze.Length; ++iwall)
{
Transform wall = maze[iwall];
for (int icorner = 0; icorner < 4; ++icorner)
{
Point p = Corner(wall, icorner);
if (points.ContainsNear(p))
{
p = points.GetNear(p);
}
else
{
points.Add(p);
List <WallIndex> walls = new List <WallIndex>();
point2wall.Add(p, walls);
}
point2wall[p].Add(new WallIndex(iwall, icorner));
wall2point[iwall, icorner] = p;
}
}
WallIndex currentWall = new WallIndex(0, 2);
Point current = vertices.AddNear(LookupPoint(currentWall));
Point first = current;
Point prev = null;
WallIndex peekWall = null;
Point peek = null;
for (int ii = 0; ii < 100; ++ii)
{
prev = current;
currentWall = FindNextWall(currentWall).Rotate;
current = LookupPoint(currentWall);
if (current.IsCoincident(first))
{
edges.Add(new PolygonEdge(prev, first));
break;
}
// combine parallel wall edges
for (int jj = 0; jj < 5; ++jj)
{
peekWall = FindNextWall(currentWall).Rotate;
peek = LookupPoint(peekWall);
Vector v0 = current - prev;
Vector v1 = peek - current;
if (v1.IsParallel(v0)) // (peek - current).IsParallel(current - prev))
{
currentWall = peekWall;
current = peek;
}
else
{
break;
}
}
current = vertices.AddNear(current);
edges.Add(new PolygonEdge(prev, current));
}
DetermineBounds();
}