/// <summary>
/// Reflect a point in us.
/// </summary>
public Vector3D ReflectPoint(Vector3D p)
{
if (IsPlane)
{
// We used to call ProjectOntoPlane, but optimized it away.
// This is faster because we already know our normal is normalized,
// and it avoids some extra Vector3D operations.
double dist = Euclidean3D.DistancePointPlane(this.Normal, this.Offset, p);
Vector3D offset = this.Normal * dist * -2;
return(p + offset);
}
else
{
if (p == Center)
{
return(Infinity.InfinityVector);
}
if (Infinity.IsInfinite(p))
{
return(Center);
}
Vector3D v = p - Center;
double d = v.Abs();
v.Normalize();
return(Center + v * (Radius * Radius / d));
}
}
/// <summary>
/// Reflect a point in us.
/// </summary>
public Vector3D ReflectPoint(Vector3D p)
{
if (IsPlane)
{
//Debug.Assert( !Infinity.IsInfinite( p ) );
Vector3D v = Euclidean3D.ProjectOntoPlane(this.Normal, this.Offset, p);
v = p + (v - p) * 2;
return(v);
}
else
{
if (p == Center)
{
return(Infinity.InfinityVector);
}
if (Infinity.IsInfinite(p))
{
return(Center);
}
Vector3D v = p - Center;
double d = v.Abs();
v.Normalize();
return(Center + v * (Radius * Radius / d));
}
}
public bool IsPointOn(Vector3D test)
{
if (IsPlane)
{
double dist = Euclidean3D.DistancePointPlane(this.Normal, this.Offset, test);
return(Tolerance.Zero(dist));
}
return(Tolerance.Equal((test - Center).Abs(), Radius));
}
/// <summary>
/// Calculate a normal after a transformation function is applied
/// to the points of the polygon.
/// </summary>
public Vector3D NormalAfterTransform(System.Func <Vector3D, Vector3D> transform)
{
if (this.NumSides < 1)
{
return(new Vector3D(0, 0, 1));
}
return(Euclidean3D.NormalFrom3Points(
this.Segments[0].P1, this.Segments[0].P2, this.Center, transform));
}
public static void TranslateSphere(Sphere s, Vector3D t)
{
if (s.IsPlane)
{
Vector3D offsetAlongNormal = Euclidean3D.ProjectOntoLine(s.Normal, new Vector3D(), t);
s.Offset += offsetAlongNormal;
}
else
{
s.Center += t;
}
}
/// <summary>
/// Radially project a point onto our surface.
/// </summary>
public Vector3D ProjectToSurface(Vector3D p)
{
if (this.IsPlane)
{
return(Euclidean3D.ProjectOntoPlane(this.Normal, this.Offset, p));
}
Vector3D direction = p - Center;
direction.Normalize();
direction *= Radius;
return(Center + direction);
}
/// <summary>
/// Reflect ourselves about another sphere.
/// </summary>
public void Reflect(Sphere sphere)
{
// An interior point used to calculate whether we get inverted.
Vector3D interiorPoint;
if (IsPlane)
{
Debug.Assert(!this.Normal.IsOrigin);
interiorPoint = this.Offset - this.Normal;
}
else
{
// We don't want it to be the center, because that will reflect to infinity.
interiorPoint = (this.Center + new Vector3D(this.Radius / 2, 0));
}
if (Invert)
{
interiorPoint = ReflectPoint(interiorPoint);
}
Debug.Assert(IsPointInside(interiorPoint));
interiorPoint = sphere.ReflectPoint(interiorPoint);
Debug.Assert(!interiorPoint.DNE);
if (this.Equals(sphere))
{
if (IsPlane)
{
//this.Center = -this.Center; // Same as inverting, but we need to do it this way because of Pov-Ray
this.Invert = !this.Invert;
}
else
{
this.Invert = !this.Invert;
}
Debug.Assert(this.IsPointInside(interiorPoint));
return;
}
// Both planes?
if (IsPlane && sphere.IsPlane)
{
// XXX - not general, but I know the planes I'll be dealing with go through the origin.
//if( !sphere.Offset.IsOrigin )
// throw new System.NotImplementedException();
/*Vector3D p1 = this.Normal.Cross( sphere.Normal );
* if( !p1.Normalize() )
* {
* this.Center *= -1;
* return;
* }
*
* Vector3D p2 = p1.Cross( this.Normal );
* p2.Normalize();
* p1 = sphere.ReflectPoint( p1 );
* p2 = sphere.ReflectPoint( p2 );
* Vector3D newNormal = p2.Cross( p1 );
* if( !newNormal.Normalize() )
* throw new System.Exception( "Reflection impl" );
* this.Center = newNormal;*/
// Reflect the normal relative to the plane (conjugate with sphere.Offset).
Vector3D newNormal = this.Normal + sphere.Offset;
newNormal = sphere.ReflectPoint(newNormal);
newNormal -= sphere.Offset;
newNormal.Normalize();
this.Center = newNormal;
// Calc the new offset (so far we have considered planes through origin).
this.Offset = sphere.ReflectPoint(this.Offset);
//Debug.Assert( Offset.IsOrigin ); // XXX - should handle more generality.
Debug.Assert(this.IsPointInside(interiorPoint));
return;
}
// We are a plane and reflecting in a sphere.
if (IsPlane)
{
// Think of 2D case here (circle and line)...
Vector3D projected = Euclidean3D.ProjectOntoPlane(this.Normal, this.Offset, sphere.Center);
Vector3D p = sphere.ReflectPoint(projected);
if (Infinity.IsInfinite(p))
{
// This can happen if we go through sphere.Center.
// This reflection does not change our orientation (does not invert us).
return;
}
Center = sphere.Center + (p - sphere.Center) / 2;
Radius = Center.Dist(sphere.Center);
// Did this invert us?
if (!this.IsPointInside(interiorPoint))
{
Invert = !Invert;
}
return;
}
// Is mirror a plane?
if (sphere.IsPlane)
{
Vector3D projected = Euclidean3D.ProjectOntoPlane(sphere.Normal, sphere.Offset, Center);
Vector3D diff = Center - projected;
Center -= 2 * diff;
// Radius remains unchanged.
// NOTE: This does not invert us.
Debug.Assert(this.IsPointInside(interiorPoint));
return;
}
//
// Now sphere reflecting in a sphere.
//
// Reflecting to a plane?
if (IsPointOn(sphere.Center))
{
// Concentric spheres?
if (Center == sphere.Center)
{
throw new System.Exception();
}
// Center
Vector3D center = Center - sphere.Center;
// Offset
Vector3D direction = center;
direction.Normalize();
Vector3D offset = direction * Radius * 2;
offset = sphere.ReflectPoint(offset);
// We are a line now.
Center = center;
//Offset = offset; // Not working?? Caused issues in old generation code for 435.
Radius = double.PositiveInfinity;
// Did this invert us?
if (!this.IsPointInside(interiorPoint))
{
this.Invert = !this.Invert;
}
Debug.Assert(this.IsPointInside(interiorPoint));
return;
}
// XXX - Could try to share code below with Circle class.
// NOTE: We can't just reflect the center.
// See http://mathworld.wolfram.com/Inversion.html
double a = Radius;
double k = sphere.Radius;
Vector3D v = Center - sphere.Center;
double s = k * k / (v.MagSquared() - a * a);
Center = sphere.Center + v * s;
Radius = Math.Abs(s) * a;
// Did this invert us?
if (!this.IsPointInside(interiorPoint))
{
Invert = !Invert;
}
}
