public Isometry(Isometry i)
{
Mobius = i.Mobius;
if (i.Reflection != null)
{
Reflection = i.Reflection.Clone();
}
}
/// <summary>
/// Returns an isometry which represents a reflection across the x axis.
/// </summary>
public static Isometry ReflectX()
{
Isometry i = new Isometry();
Circle reflection = new Circle(new Vector3D(), new Vector3D(1, 0));
i.Reflection = reflection;
return(i);
}
/// <summary>
/// Simple helper to transform an array of vertices using an isometry.
/// Warning! Allocates a new array.
/// </summary>
public static Vector3D[] TransformVertices(Vector3D[] vertices, Isometry isometry)
{
List <Vector3D> result = new List <Vector3D>();
for (int i = 0; i < vertices.Length; i++)
{
Vector3D transformed = isometry.Apply(vertices[i]);
result.Add(transformed);
}
return(result.ToArray());
}
/// <summary>
/// Composition operator.
/// </summary>>
public static Isometry operator *(Isometry i1, Isometry i2)
{
// ZZZ - Probably a better way.
// We'll just apply both isometries to a canonical set of points,
// Then calc which isometry makes that.
Complex p1 = new Complex(1, 0);
Complex p2 = new Complex(-1, 0);
Complex p3 = new Complex(0, 1);
Complex w1 = p1, w2 = p2, w3 = p3;
// Compose (apply in reverse order).
w1 = i2.Apply(w1);
w2 = i2.Apply(w2);
w3 = i2.Apply(w3);
w1 = i1.Apply(w1);
w2 = i1.Apply(w2);
w3 = i1.Apply(w3);
Mobius m = new Mobius();
m.MapPoints(p1, p2, p3, w1, w2, w3);
Isometry result = new Isometry();
result.Mobius = m;
// Need to reflect at end?
bool r1 = i1.Reflection != null;
bool r2 = i2.Reflection != null;
if (r1 ^ r2) // One and only one reflection.
{
result.Reflection = new Circle(
Vector3D.FromComplex(w1),
Vector3D.FromComplex(w2),
Vector3D.FromComplex(w3));
}
return(result);
}
public void Transform( Isometry i )
{
Boundary.Transform( i );
Drawn.Transform( i );
VertexCircle.Transform( i );
}
public Tile()
{
Isometry = new Isometry();
EdgeIncidences = new List<Tile>();
VertexIndicences = new List<Tile>();
}
/// <summary>
/// Composition operator.
/// </summary>>
public static Isometry operator *( Isometry i1, Isometry i2 )
{
// ZZZ - Probably a better way.
// We'll just apply both isometries to a canonical set of points,
// Then calc which isometry makes that.
Complex p1 = new Complex( 1, 0 );
Complex p2 = new Complex( -1, 0 );
Complex p3 = new Complex( 0, 1 );
Complex w1 = p1, w2 = p2, w3 = p3;
// Compose (apply in reverse order).
w1 = i2.Apply( w1 );
w2 = i2.Apply( w2 );
w3 = i2.Apply( w3 );
w1 = i1.Apply( w1 );
w2 = i1.Apply( w2 );
w3 = i1.Apply( w3 );
Mobius m = new Mobius();
m.MapPoints( p1, p2, p3, w1, w2, w3 );
Isometry result = new Isometry();
result.Mobius = m;
// Need to reflect at end?
bool r1 = i1.Reflection != null;
bool r2 = i2.Reflection != null;
if( r1 ^ r2 ) // One and only one reflection.
{
result.Reflection = new Circle(
Vector3D.FromComplex( w1 ),
Vector3D.FromComplex( w2 ),
Vector3D.FromComplex( w3 ) );
}
return result;
}
public Isometry( Isometry i )
{
Mobius = i.Mobius;
if( i.Reflection != null )
Reflection = i.Reflection.Clone();
}
/// <summary>
/// Simple helper to transform an array of vertices using an isometry.
/// Warning! Allocates a new array.
/// </summary>
public static Vector3D[] TransformVertices( Vector3D[] vertices, Isometry isometry )
{
List<Vector3D> result = new List<Vector3D>();
for( int i = 0; i < vertices.Length; i++ )
{
Vector3D transformed = isometry.Apply( vertices[i] );
result.Add( transformed );
}
return result.ToArray();
}
/// <summary>
/// Returns an isometry which represents a reflection across the x axis.
/// </summary>
public static Isometry ReflectX()
{
Isometry i = new Isometry();
Circle reflection = new Circle( new Vector3D(), new Vector3D( 1, 0 ) );
i.Reflection = reflection;
return i;
}
