public bool ClosestPoints(Line3D b, out Point3D pa, out Point3D pb)
{
pa = null;
pb = null;
if (Vector == b.Vector || Vector == -b.Vector) return false;
Vector3D p0 = Point.ToVector();
Vector3D p1 = b.Point.ToVector();
Vector3D d0 = Vector;
Vector3D d1 = b.Vector;
Vector3D d0n = d0.Normalize();
Vector3D c = new Vector3D();
Vector3D d = new Vector3D();
d.X = d1.X - d0n.X * (d0.X * d1.X + d0.Y * d1.Y + d0.Z * d1.Z);
c.X = p1.X - p0.X + d0n.X * (d0.X * p0.X + d0.Y * p0.Y + d0.Z * p0.Z);
d.Y = d1.Y - d0n.Y * (d0.X * d1.X + d0.Y * d1.Y + d0.Z * d1.Z);
c.Y = p1.Y - p0.Y + d0n.Y * (d0.X * p0.X + d0.Y * p0.Y + d0.Z * p0.Z);
d.Z = d1.Z - d0n.Z * (d0.X * d1.X + d0.Y * d1.Y + d0.Z * d1.Z);
c.Z = p1.Z - p0.Z + d0n.Z * (d0.X * p0.X + d0.Y * p0.Y + d0.Z * p0.Z);
double t = -(c.X * d.X + c.Y * d.Y + c.Z * d.Z) / (d.X * d.X + d.Y * d.Y + d.Z * d.Z);
pb = b.Point + (b.Vector * t);
pa = ClosestPoint(pb);
return true;
}
public Slice3D(Vector3D normal, Point3D topLeft, double width, double height)
{
Vector3D right = normal.Rotate(Vector3D.AxisY, -90.0);
Vector3D down = normal.Rotate(Vector3D.AxisX, -90.0);
_topLeft = topLeft;
_topRight = _topLeft + (right * width);
_bottomLeft = _topLeft + (down * height);
_bottomRight = _bottomLeft + (right * width);
_normal = normal;
_width = width;
_height = height;
_plane = new Plane3D(normal, _topLeft);
}
public Point3D ClosestPoint(Point3D point)
{
Vector3D pv = point.ToVector();
double d = Normal.DotProduct(pv - Point.ToVector());
return (pv - (Normal * d)).ToPoint();
}
public bool Intersect(Plane3D b, out Line3D intersection)
{
intersection = null;
if (IsParallel(b)) return false;
Point3D p;
Vector3D v1 = Normal.CrossProduct(b.Normal);
Vector3D v2 = new Vector3D(v1.X * v1.X, v1.Y * v1.Y, v1.Z * v1.Z);
double w1 = -Distance;
double w2 = -b.Distance;
double id;
if ((v2.Z > v2.Y) && (v2.Z > v2.X) && (v2.Z > Double.Epsilon))
{
// point on XY plane
id = 1.0 / v1.Z;
p = new Point3D(Normal.Y * w2 - b.Normal.Y * w1, b.Normal.X * w1 - Normal.X * w2, 0.0);
}
else if ((v2.Y > v2.X) && (v2.Y > Double.Epsilon))
{
// point on XZ plane
id = -1.0 / v1.Y;
p = new Point3D(Normal.Z * w2 - b.Normal.Z * w1, 0.0, b.Normal.Y * w1 - Normal.Y * w2);
}
else if (v2.X > Double.Epsilon)
{
// point on YZ plane
id = 1.0 / v1.X;
p = new Point3D(0.0, Normal.Z * w2 - b.Normal.Z * w1, b.Normal.Y * w1 - Normal.Y * w2);
}
else return false;
p = (p.ToVector() * id).ToPoint();
id = 1.0 / Math.Sqrt(v2.X + v2.Y + v2.Z);
v1 *= id;
intersection = new Line3D(p, p.ToVector() + v1);
return true;
}
public bool Intersect(Line3D line, out Point3D intersection)
{
if (IsParallel(line))
{
intersection = null;
return false;
}
double t = (Distance - Normal.DotProduct(line.Point.ToVector())) / Normal.DotProduct(line.Vector);
intersection = line.Point + (t * line.Vector);
return true;
}
public Plane3D(Point3D a, Point3D b, Point3D c)
{
Vector3D av = a.ToVector();
Vector3D bv = b.ToVector();
Vector3D cv = c.ToVector();
_normal = (bv - av).CrossProduct(cv - av).Normalize();
_point = a;
}
public Plane3D(Vector3D normal, Point3D point)
{
_normal = normal;
_point = point;
}
public Segment3D(Point3D a, Point3D b)
{
_a = a.Clone();
_b = b.Clone();
}
public Segment3D()
{
_a = Point3D.Zero.Clone();
_b = Point3D.Zero.Clone();
}
public Point3D ClosestPoint(Point3D point)
{
double n = (point.ToVector() - Point.ToVector()).DotProduct(Vector);
double d = Vector.Length();
return Point + (Vector * (n / d));
}
public Line3D(Line3D line)
{
_point = line.Point.Clone();
_vector = line.Vector.Clone();
}
public Line3D(Point3D p, Vector3D v)
{
_point = p.Clone();
_vector = v.Clone();
}
public Line3D()
{
_point = Point3D.Zero.Clone();
_vector = Vector3D.Zero.Clone();
}
public double Distance(Point3D b)
{
return Math.Sqrt((X - b.X) * (X - b.X) + (Y - b.Y) * (Y - b.Y) + (Z - b.Z) * (Z - b.Z));
}
public Point3D(Point3D v)
{
_x = v.X;
_y = v.Y;
_z = v.Z;
}
public Point3D Project(Point3D point)
{
Point3D p = Plane.ClosestPoint(point);
//normal vector?
throw new NotImplementedException();
//return p;
}
