# Autore: Maurizio Paolini (2005)
# Licenza: GPL
#
# seguono alcune costruzioni basate sullo scripting python
# di 'kig' e l'interfaccia 'pykig.py' di Daniele Zambelli
# per operare con il modello del semipiano di Poincare'
#
# Le costruzioni particolari ottenute possono essere utilizzate
# per ottenere delle macro
#
# ROTAZIONE:
# la rotazione nel semipiano di Poincare' non e' ottenuta

scriptsegment='''def calc( arg1, arg2 ):
	# Construct the hyperbolic segment (arc) connecting the two points
        a=arg1.coordinate();
        b=arg2.coordinate();
        ax=a.x
        ay=a.y
        if ay < 0:
           return InvalidObject()

        bx=b.x
        by=b.y
        if by < 0:
           return InvalidObject()

        asq=ax*ax + ay*ay
        bsq=bx*bx + by*by

        den = 2*(bx - ax)
        if den == 0:
          return Segment(a,b)

        x = (bsq - asq)/den
        c = Coordinate(x,0)
        rsq = asq + x*x - 2*x*ax
        r = sqrt (rsq)

        if rsq > 1000*asq:
          return Segment(a,b)

        alfa = atan2(ay, ax-x)
        beta = atan2(by, bx-x)

        return Arc(c,r,alfa,beta-alfa)
'''

def HyperbolicSegment ( a, b ):
  return PythonScript (scriptsegment, [a, b])

scriptline='''def calc( arg1, arg2 ):
	# Construct the hyperbolic line (semicircle) through two points
        a=arg1.coordinate();
        b=arg2.coordinate();
        ax=a.x
        ay=a.y
        if ay < 0:
           return InvalidObject()

        bx=b.x
        by=b.y
        if by < 0:
           return InvalidObject()

        asq=ax*ax + ay*ay
        bsq=bx*bx + by*by

        den = 2*(bx - ax)
        if den == 0:
          return Ray(Coordinate(ax,0.),b)

        x = (bsq - asq)/den
        c = Coordinate(x,0)
        rsq = asq + x*x - 2*x*ax
        r = sqrt (rsq)

        if rsq > 100000*asq:
          return Ray(Coordinate(ax,0.),b)

        alfa = atan2(ay, ax-x)
        beta = atan2(by, bx-x)

        return Arc(c,r,0.,atan2(0.,-1.))
'''

def HyperbolicLine ( a, b ):
  return PythonScript (scriptline, [a, b])

scriptcircle='''def calc( arg1, arg2 ):
	# Construct the hyperbolic circle centered in arg1 through arg2
        a=arg1.coordinate();
        b=arg2.coordinate();
        ax=a.x
        ay=a.y
        if ay < 0:
           return InvalidObject()

        bx=b.x
        by=b.y
        if by <= 0:
           return InvalidObject()

        asq=ax*ax + ay*ay
        bsq=bx*bx + by*by

        den = 2*(bx - ax)

        num2 = bsq - asq - den*bx
        dby2 = num2/by
        dy = by - dby2/2.
        d = Coordinate(ax,dy)
	r2 = sqrt( den*den + dby2*dby2 )
        return Circle(d,r2/2.)
'''

def HyperbolicCircle ( a, b ):
  return PythonScript (scriptcircle, [a, b])

scriptlinebyvector='''def calc( arg1, arg2 ):
	# Construct the hyperbolic line through arg1 and direction arg2
        a=arg1.coordinate()
        dir=arg2.dir()
        ax=a.x
        ay=a.y
        if ay < 0:
           return InvalidObject()

        dirx=dir.x
        diry=dir.y

	cx=ax + ay*diry/dirx

	r = sqrt ((cx-ax)*(cx-ax) + ay*ay)

        c = Coordinate(cx,0.)
        return Arc(c,r,0.,atan2(0.,-1.))
'''

scriptlineend1='''def calc( arg1 ):
	# Construct the first endpoint of a line
        if arg1.inherits( Ray.stype() ):
	  ld = arg1.data()
	  return Point( ld.a )

        return Point (arg1.secondEndPoint())
'''

scriptlineend2='''def calc( arg1 ):
	# Construct the second endpoint of a line
        if arg1.inherits( Ray.stype() ):
	  return InvalidObject()

        return Point (arg1.firstEndPoint())
'''

scriptsegmentdir1='''def calc( arg1, arg2 ):
	# Construct the vector tangent in A to the hyp segment AB
	# A (arg1) and B (arg2) are the two endpoints
        a=arg1.coordinate();
        b=arg2.coordinate();
        ax=a.x
        ay=a.y
        if ay < 0:
           return InvalidObject()

        bx=b.x
        by=b.y
        if by < 0:
           return InvalidObject()

        asq=ax*ax + ay*ay
        bsq=bx*bx + by*by

        den = 2*(bx - ax)
        if den == 0:
          return Segment(a,b)

        cx = (bsq - asq)/den
        dirort = Coordinate( ay, cx - ax)
	dirortnorm = dirort.length()
	if den < 0:
	  dirortnorm = -dirortnorm

	return Vector (a, a + dirort/dirortnorm)
'''

scriptcirclelineradical='''def calc( arg1, arg2 ):
        if arg2.inherits( Ray.stype() ):
          # by now...
	  line = Ray.data()
	  return Line(line)

	a = arg1.center()
	ax = a.x
	ay = a.y
	#return Point (a)
        r1sq = arg1.squareRadius()

        c = arg2.center()
        cx = c.x
        r2 = arg2.radius()
        r2sq = r2*r2
	dirx = ax - cx
	diry = ay

        if c.y != 0:
          return InvalidObject()

        num = r2sq - r1sq
	dirsq = dirx*dirx + diry*diry
	lam = num/(2*dirsq)
        #lam = (ax*ax + ay*ay - cx*cx - r1sq + r2sq)/(2*((ax - cx)*(ax - cx) + ay*ay))
        #lam = 0.5
	mx = (ax + cx)/2
	my = ay/2
	dir = Coordinate(dirx, diry)

	point = Coordinate (mx + lam*dirx, my + lam*diry)
	dirort = Coordinate (-diry, dirx)
        return Line (point, point + dirort)
	#return Point (a)
'''

assoluto = Line(Point(-1.,0.,internal=True),Point(1.,0.,internal=True))

#
# ROTAZIONE del punto B attorno ad A di angolo "Angle".
# basata su una riflessione attorno all'asse verticale per A
# seguita da una inversione circolare rispetto ad un cerchio
# passante per A e centro sull'asse delle ascisse costruito in
# modo che l'angolo che forma in A rispetto all'asse verticale
# sia la meta' dell'angolo "Angle".
#

def HyperbolicRotation (B, A, Angle):
  reflectionaxis = Orthogonal (assoluto, A, HIDDEN)
  Breflected = AxialSymmetry (B, reflectionaxis, HIDDEN)
  projection = LineLineIntersection (reflectionaxis, assoluto, HIDDEN)
  rotatedprojection = Rotate (projection, A, Angle, HIDDEN)

  # angleatA = Angle (projection, A, rotatedprojection)
  # ... non proseguo in questo modo perche' al momento pykig non
  # permette di costruire la bisettrice

  pushdown = Vector (A, projection, HIDDEN)
  pusheddown = Translate (rotatedprojection, pushdown, HIDDEN)
  ltangent = Line (A, pusheddown, HIDDEN)
  ortoline = Orthogonal (ltangent, A, HIDDEN)
  inversioncenter = LineLineIntersection (ortoline, assoluto, HIDDEN)
  inversioncircle = Circle (inversioncenter, A, HIDDEN)
  return InvertPoint (Breflected, inversioncircle)