#
# $Id: geometry.py,v 1.24 2003/05/12 22:13:11 mrnolta Exp $
#
# Copyright (C) 2000-2001 Mike Nolta <mrnolta@users.sourceforge.net>
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public
# License along with this program; if not, write to the
# Free Software Foundation, Inc., 59 Temple Place - Suite 330,
# Boston, MA  02111-1307, USA.
#

import math, Numeric

# pt_* functions --------------------------------------------------------------

def pt_add( u, v ):
	return u[0] + v[0], u[1] + v[1]

def pt_sub( u, v ):
	return u[0] - v[0], u[1] - v[1]

def pt_mul( a, u ):
	return a * u[0], a * u[1]

def pt_rot( u, angle ):
	c, s = math.cos(angle), math.sin(angle)
	return c*u[0] - s*u[1], s*u[0] + c*u[1]

def pt_len( u ):
	return math.hypot( u[0], u[1] )

def pt_angle( u ):
	return math.atan2( u[1], u[0] )

def pt_unit( u ):
	r = pt_len(u)
	return u[0]/r, u[1]/r

def pt_min( a, b ):
	if a is None: return b
	if b is None: return a
	return min(a[0],b[0]), min(a[1],b[1])

def pt_max( a, b ):
	if a is None: return b
	if b is None: return a
	x = max( a[0], b[0] )
	if x is None:
		x = min( a[0], b[0] )
	y = max( a[1], b[1] )
	if y is None:
		y = min( a[1], b[1] )
	return x, y

# BoundingBox -----------------------------------------------------------------

class BoundingBox:

	def __init__( self, *args ):
		if len(args) > 0:
			self.p0 = reduce( pt_min, args )
			self.p1 = reduce( pt_max, args )
		else:
			self.p0 = None
			self.p1 = None

	def __str__( self ):
		return "(%s,%s)" % (str(self.p0), str(self.p1))

	def copy( self ):
		return BoundingBox( self.p0, self.p1 )

	def is_null( self ):
		return self.p0 is None or self.p1 is None

	def width( self ):
		if self.is_null():
			return None
		else:
			return abs( self.p0[0] - self.p1[0] )

	def height( self ):
		if self.is_null():
			return None
		else:
			return abs( self.p0[1] - self.p1[1] )

	def diagonal( self ):
		if self.is_null():
			return None
		else:
			return math.hypot( self.width(), self.height() )

	def aspect_ratio( self ):
		if self.is_null():
			return None
		else:
			return self.height()/self.width()

	def xrange( self ):
		if self.is_null():
			return None
		else:
			return self.p0[0], self.p1[0]

	def yrange( self ):
		if self.is_null():
			return None
		else:
			return self.p0[1], self.p1[1]

	def lowerleft( self ):
		if self.is_null():
			return None
		else:
			return self.p0

	def upperleft( self ):
		if self.is_null():
			return None
		else:
			return self.p0[0], self.p1[1]

	def upperright( self ):
		if self.is_null():
			return None
		else:
			return self.p1

	def lowerright( self ):
		if self.is_null():
			return None
		else:
			return self.p1[0], self.p0[1]

	def center( self ):
		x = self.xrange()
		y = self.yrange()
		return (x[0]+x[1])/2., (y[0]+y[1])/2.

	def union( self, other ):
		self.p0 = pt_min( self.p0, other.p0 )
		self.p1 = pt_max( self.p1, other.p1 )

	def deform( self, dt, db, dl, dr ):
		self.p0 = pt_sub( self.p0, (dl,db) )
		self.p1 = pt_add( self.p1, (dr,dt) )

	def shift( self, dp ):
		self.p0 = pt_add( self.p0, dp )
		self.p1 = pt_add( self.p1, dp )

	def expand( self, factor ):
		dp = pt_mul( factor/2., (self.width(), self.height()) )
		self.p0 = pt_sub( self.p0, dp )
		self.p1 = pt_add( self.p1, dp )

	def rotate( self, angle, p ):
		a = pt_add(pt_rot(pt_sub( self.lowerleft(), p), angle), p)
		b = pt_add(pt_rot(pt_sub(self.lowerright(), p), angle), p)
		c = pt_add(pt_rot(pt_sub( self.upperleft(), p), angle), p)
		d = pt_add(pt_rot(pt_sub(self.upperright(), p), angle), p)
		self.p0 = pt_min( a, pt_min( b, pt_min( c, d ) ) )
		self.p1 = pt_max( a, pt_max( b, pt_max( c, d ) ) )

	def make_aspect_ratio( self, ratio ):
		if ratio < self.aspect_ratio():
			dh = self.height() - ratio * self.width()
			self.p0 = self.p0[0], self.p0[1] + dh/2
			self.p1 = self.p1[0], self.p1[1] - dh/2
		else:
			dw = self.width() - self.height() / ratio
			self.p0 = self.p0[0] + dw/2, self.p0[1]
			self.p1 = self.p1[0] - dw/2, self.p1[1]

	def contains( self, q ):
		if self.p0[0] <= q[0] and \
		   q[0] <= self.p1[0] and \
		   self.p0[1] <= q[1] and \
		   q[1] <= self.p1[1]:
			return 1
		else:
			return 0

# AffineTransform -------------------------------------------------------------

def _matrix_multipy( A, B ):
	C00 = A[0][0] * B[0][0] + A[0][1] * B[1][0]
	C01 = A[0][0] * B[0][1] + A[0][1] * B[1][1]
	C10 = A[1][0] * B[0][0] + A[1][1] * B[1][0]
	C11 = A[1][0] * B[0][1] + A[1][1] * B[1][1]
	return (C00, C01), (C10, C11)

class AffineTransform:

	def __init__( self ):
		self.t = 0., 0.
		self.m = (1., 0.), (0., 1.)

	def __call__( self, x, y ):
		p = self.t[0] + self.m[0][0] * x + self.m[0][1] * y
		q = self.t[1] + self.m[1][0] * x + self.m[1][1] * y
		return p, q

	def call_vec( self, x, y ):
		x_ = Numeric.asarray( x )
		y_ = Numeric.asarray( y )
		p = self.t[0] + self.m[0][0] * x_ + self.m[0][1] * y_
		q = self.t[1] + self.m[1][0] * x_ + self.m[1][1] * y_
		return p, q

	def compose( self, other ):
		self.t = self( other.t[0], other.t[1] )
		self.m = _matrix_multiply( self.m, other.m )

class RectilinearMap( AffineTransform ):

	def __init__( self, src, dest ):
		AffineTransform.__init__( self )
		sx = dest.width() / src.width()
		sy = dest.height() / src.height()
		p, q = dest.lowerleft(), src.lowerleft()
		tx = p[0] - sx * q[0]
		ty = p[1] - sy * q[1]
		self.t = tx, ty
		self.m = ( sx, 0. ), ( 0., sy )