"""
This file is part of the 'Elements' Project
Elements is a 2D Physics API for Python (supporting Box2D2)

Copyright (C) 2008, The Elements Team, <elements@linuxuser.at>

Home:  http://elements.linuxuser.at
IRC:   #elements on irc.freenode.org

Code:  http://www.assembla.com/wiki/show/elements
       svn co http://svn2.assembla.com/svn/elements                     

License:  GPLv3 | See LICENSE for the full text
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 3 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, see <http://www.gnu.org/licenses/>.              
"""
from functools import partial

from math import fabs
from math import sqrt
from math import atan
from math import atan2
from math import degrees
from math import acos

from locals import *
from elements import box2d

def ComputeCentroid(pd):
    count = pd.vertexCount

    if count < 3:
        return False

    c = box2d.b2Vec2(0, 0)
    area = 0.0

    # pRef is the reference point for forming triangles.
    # It's location doesn't change the result (except for rounding error).
    pRef = box2d.b2Vec2(0.0, 0.0)

    inv3 = 1.0 / 3.0

    for i in range(count):
        # Triangle vertices.
        p1 = pRef
        p2 = pd.getVertex(i)
        if i + 1 < count: 
            p3 = pd.getVertex(i+1)
        else: p3 = pd.getVertex(0)

        e1 = p2 - p1
        e2 = p3 - p1

        D = box2d.b2Cross(e1, e2)

        triangleArea = 0.5 * D
        area += triangleArea

        # Area weighted centroid
        c += triangleArea * inv3 * (p1 + p2 + p3)

	# Centroid
 #   if area < FLT_EPSILON:
        #raise ValueError, "ComputeCentroid: area < FLT_EPSILON"

    return c / area

def checkDef(pd):
    """Check the polygon definition for invalid vertices, etc.

       Return: True if valid, False if invalid
    """

#    if pd.vertexCount < 3 or pd.vertexCount > box2d.b2_maxPolygonVertices:
        #raise ValueError, "Invalid vertexCount"

    threshold = FLT_EPSILON * FLT_EPSILON
    verts = pd.getVertices_b2Vec2()
    normals = []
    v0 = verts[0]
    for i in range(pd.vertexCount):
        if i == pd.vertexCount-1:
            v1 = verts[0]
        else: v1 = verts[i+1]
        edge=v1 - v0
#        if edge.LengthSquared() < threshold:
#           raise ValueError, "edge.LengthSquared < FLT_EPSILON**2" 
        normals.append( box2d.b2Cross(edge, 1.0) )
        normals[-1].Normalize()
        v0=v1

    centroid = ComputeCentroid(pd)

    d=box2d.b2Vec2()
    for i in range(pd.vertexCount):
        i1 = i - 1 
        if i1 < 0: i1 = pd.vertexCount - 1
        i2 = i
        n1 = normals[i1]
        n2 = normals[i2]
        v = verts[i] - centroid

        d.x = box2d.b2Dot(n1, v) - box2d.b2_toiSlop
        d.y = box2d.b2Dot(n2, v) - box2d.b2_toiSlop

		# Shifting the edge inward by b2_toiSlop should
		# not cause the plane to pass the centroid.

		# Your shape has a radius/extent less than b2_toiSlop.
#        if d.x < 0.0 or d.y <= 0.0: 
#            raise ValueError, "Your shape has a radius/extent less than b2_toiSlop."

        A = box2d.b2Mat22()
        A.col1.x = n1.x; A.col2.x = n1.y
        A.col1.y = n2.x; A.col2.y = n2.y
		#coreVertices[i] = A.Solve(d) + m_centroid

    return True

def calc_center(points):
    """ Calculate the center of a polygon
    
        Return: The center (x,y)
    """
    tot_x, tot_y = 0,0
    for p in points:
        tot_x += p[0]
        tot_y += p[1]
    n = len(points)
    return (tot_x/n, tot_y/n)
    
def poly_center_vertices(pointlist):
    """ Rearranges vectors around the center
    
        Return: pointlist ([(x, y), ...])
    """    
    poly_points_center = []
    center = cx, cy = calc_center(pointlist)
    
    for p in pointlist:
        x = p[0] - cx
        y = cy - p[1]
        poly_points_center.append((x, y))
    
    return poly_points_center
    
def is_line(vertices, tolerance=25.0):
    """ Check if passed vertices are a line. Done by comparing
        the angles of all vectors and check tolerance.
        
        Parameters:
          vertices ... a list of vertices (x, y)
          tolerance .. how many degrees should be allowed max to be a line
          
        Returns: True if line, False if no line
    """
    if len(vertices) <= 2:        
        return True

    # Step 1: Points -> Vectors
    p_old = vertices[0]
    alphas = []
    

    for p in vertices[1:]:
        x1, y1 = p_old
        x2, y2 = p
        p_old = p

        # Create Vector        
        vx, vy = (x2-x1, y2-y1)
        
        # Check Length
        l = sqrt((vx*vx) + (vy*vy))
        if l == 0.0: continue

        # Normalize vector
        vx /= l
        vy /= l
        
        # Append angle
        if fabs(vx) < 0.2: alpha = 90.0
        else: alpha = degrees(atan(vy / vx))

        alphas.append(fabs(alpha))
        
    # Sort angles
    alphas.sort()
    
    # Get maximum difference
    alpha_diff = fabs(alphas[-1] - alphas[0])
    print "alpha difference:", alpha_diff
    
    if alpha_diff < tolerance:
        return True
    else:
        return False
    
def reduce_poly_by_angle(vertices, tolerance=10.0, minlen=20):
    """ This function reduces a poly by the angles of the vectors (detect lines)
        If the angle difference from one vector to the last > tolerance: use last point
        If the angle is quite the same, it's on the line
        
        Parameters:
          vertices ... a list of vertices (x, y)
          tolerance .. how many degrees should be allowed max
          
        Returns: (1) New Pointlist, (2) Soft reduced pointlist (reduce_poly())
    """
    v_last = vertices[-1]
    vertices = vxx = reduce_poly(vertices, minlen)
    
    p_new =  []
    p_new.append(vertices[0])
    
    dir = None 
    is_convex = True
    
    for i in xrange(len(vertices)-1):
        if i == 0:
            p_old = vertices[i]
            continue
        
        x1, y1 = p_old
        x2, y2 = vertices[i]
        x3, y3 = vertices[i+1]
        p_old = vertices[i]
        
        # Create Vectors
        v1x = (x2 - x1) * 1.0
        v1y = (y2 - y1) * 1.0
        
        v2x = (x3 - x2) * 1.0
        v2y = (y3 - y2) * 1.0

        # Calculate angle
        a = ((v1x * v2x) + (v1y * v2y))
        b = sqrt((v1x*v1x) + (v1y*v1y))
        c = sqrt((v2x*v2x) + (v2y*v2y))

        # No Division by 0 :)        
        if (b*c) == 0.0: continue
        
        # Get the current degrees
        # We have a bug here sometimes...
        try:
            angle = degrees(acos(a / (b*c)))
        except:
            # cos=1.0
            print "cos=", a/(b*c)
            continue
            
        # Check if inside tolerance
        if fabs(angle) > tolerance:
            p_new.append(vertices[i])        
            # print "x", 180-angle, is_left(vertices[i-1], vertices[i], vertices[i+1])
            
            # Check if convex:
            if dir == None:
                dir = is_left(vertices[i-1], vertices[i], vertices[i+1])
            else:
                if dir != is_left(vertices[i-1], vertices[i], vertices[i+1]):
                    is_convex = False
                    
    # We also want to append the last point :)
    p_new.append(v_last)
    
    # Returns: (1) New Pointlist, (2) Soft reduced pointlist (reduce_poly())
    return p_new, is_convex

    """ OLD FUNCTION: """    
    # Wipe all points too close to each other
    vxx = vertices = reduce_poly(vertices, minlen)
    
    # Create Output List
    p_new = []
    p_new.append(vertices[0])
    
    # Set the starting vertice
    p_old = vertices[0]
    alpha_old = None

    # For each vector, compare the angle difference to the last one
    for i in range(1, len(vertices)):
        x1, y1 = p_old
        x2, y2 = vertices[i]
        p_old = (x2, y2)

        # Make Vector
        vx, vy = (x2-x1, y2-y1)
    
        # Vector length
        l = sqrt((vx*vx) + (vy*vy))
        
        # normalize
        vx /= l
        vy /= l
        
        # Get Angle
        if fabs(vx) < 0.2:
            alpha = 90
        else: 
            alpha = degrees(atan(vy * 1.0) / (vx*1.0))

        if alpha_old == None:
            alpha_old = alpha
            continue
        
        # Get difference to previous angle
        alpha_diff = fabs(alpha - alpha_old)        
        alpha_old = alpha
        
        # If the new vector differs from the old one, we add the old point
        # to the output list, as the line changed it's way :)
        if alpha_diff > tolerance:
            #print ">",alpha_diff, "\t", vx, vy, l
            p_new.append(vertices[i-1])

    # We also want to append the last point :)
    p_new.append(vertices[-1])
    
    # Returns: (1) New Pointlist, (2) Soft reduced pointlist (reduce_poly())
    return p_new, vxx
    
        
# The following functions is_left, reduce_poly and convex_hull are 
# from the pymunk project (http://code.google.com/p/pymunk/)
def is_left(p0, p1, p2):
    """Test if p2 is left, on or right of the (infinite) line (p0,p1).
    
    :return: > 0 for p2 left of the line through p0 and p1
        = 0 for p2 on the line
        < 0 for p2 right of the line
    """
    sorting = (p1[0] - p0[0])*(p2[1]-p0[1]) - (p2[0]-p0[0])*(p1[1]-p0[1])
    if sorting > 0: return 1
    elif sorting < 0: return -1 
    else: return 0

def is_convex(points):
    """Test if a polygon (list of (x,y)) is strictly convex or not.
    
    :return: True if the polygon is convex, False otherwise
    """
    #assert len(points) > 2, "not enough points to form a polygon"
    
    p0 = points[0]
    p1 = points[1]
    p2 = points[2]

    xc, yc = 0, 0
    is_same_winding = is_left(p0, p1, p2)
    for p2 in points[2:] + [p0] + [p1]:
        if is_same_winding != is_left(p0, p1, p2): 
            return False
        a = p1[0] - p0[0], p1[1] - p0[1] # p1-p0
        b = p2[0] - p1[0], p2[1] - p1[1] # p2-p1
        if sign(a[0]) != sign(b[0]): xc +=1
        if sign(a[1]) != sign(b[1]): yc +=1
        p0, p1 = p1, p2
   
    return xc <= 2 and yc <= 2

def sign(x): 
    if x < 0: return -1 
    else: return 1


def reduce_poly(points, tolerance=50):
    """Remove close points to simplify a polyline
    tolerance is the min distance between two points squared.
    
    :return: The reduced polygon as a list of (x,y)
    """
    curr_p = points[0]
    reduced_ps = [points[0]]
    
    for p in points[1:]:
        x1, y1 = curr_p
        x2, y2 = p
        dx = fabs(x2 - x1)
        dy = fabs(y2 - y1)
        l = sqrt((dx*dx) + (dy*dy))
        if l > tolerance:
            curr_p = p
            reduced_ps.append(p)
            
    return reduced_ps

def convex_hull(points):
    """Create a convex hull from a list of points.
    This function uses the Graham Scan Algorithm.
    
    :return: Convex hull as a list of (x,y)
    """
    ### Find lowest rightmost point
    p0 = points[0]
    for p in points[1:]:
        if p[1] < p0[1]:
            p0 = p
        elif p[1] == p0[1] and p[0] > p0[0]:
            p0 = p
    points.remove(p0)
    
    ### Sort the points angularly about p0 as center
    f = partial(is_left, p0)
    points.sort(cmp = f)
    points.reverse()
    points.insert(0, p0)
    
    ### Find the hull points
    hull = [p0, points[1]]
    
    for p in points[2:]:
        
        pt1 = hull[-1]
        pt2 = hull[-2]
        l = is_left(pt2, pt1, p) 
        if l > 0:
            hull.append(p)
        else:
            while l <= 0 and len(hull) > 2:
                hull.pop()
                pt1 = hull[-1]
                pt2 = hull[-2]
                l = is_left(pt2, pt1, p)
            hull.append(p)
    return hull