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el.py
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el.py
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#! /usr/bin/env python3
# coding: utf-8
import math
import numbers
import collections
class Point:
# and Vector as well
def __init__(self, x, y):
self.x = x
self.y = y
def norm(self):
return math.sqrt(self.x**2 + self.y**2)
def unit(self):
norm = self.norm()
return Point(self.x / norm, self.y / norm)
def __add__(self, other):
if not isinstance(other, Point): return NotImplemented
return Point(self.x+other.x, self.y+other.y)
def __sub__(self, other):
if not isinstance(other, Point): return NotImplemented
return Point(self.x-other.x, self.y-other.y)
def __neg__(self):
return Point(-self.x, -self.y)
def __mul__(self, mul):
# if isinstance(mul, numbers.Number):
# return Point(mul*self.x, mul*self.y)
if isinstance(mul, Point):
return self.x*mul.x + self.y*mul.y
else:
return NotImplemented
def __rmul__(self, mul):
if not isinstance(mul, numbers.Number): return NotImplemented
return Point(mul*self.x, mul*self.y)
def __truediv__(self, div):
if not isinstance(div, numbers.Number): return NotImplemented
return Point(self.x/div, self.y/div)
def rotate(self, alpha):
cosalpha = math.cos(alpha)
sinalpha = math.sin(alpha)
return Point(
cosalpha*self.x-sinalpha*self.y,
sinalpha*self.x+cosalpha*self.y)
def rotatepi2(self):
return Point(-self.y,self.x)
@staticmethod
def det(v, w):
return v.x * w.y - v.y * w.x
@staticmethod
def convergence(A,v,B,w):
# A and B point
# v and w vectors
# returns intersection I of (A,v) (B,w) if:
# - I exists
# - AI and v goes in the same direction
# - BI and w goes in the same direction
det = Point.det(v,w)
if abs(det)/(v.norm()*w.norm()) < 0.01:
return None
a = Point.det(w, A-B) / det
b = Point.det(v, A-B) / det
if a <= 0 or b <=0:
return None
return B + b * w
# return A + a * v
class Node:
def __init__(self, x, y):
self.pos = Point(x,y)
self.vertices = []
def addvertex(self, othernode, vertex):
assert (vertex.node1==self and othernode==vertex.node2) or (vertex.node2==self and othernode==vertex.node1)
self.vertices.append((othernode,vertex))
self.vertices.sort(key=self.orient)
def orient(self, ov):
# this function helps sorting vertices by angle
# it is a increasing function of that angle
# from -3pi/4 (-4) to 5pi/4 (+4)
#
# 2 0
# \ o=1-X/Y /
# \ /
# X<-Y\ /X>=Y
# \ /
# \ /
# o=3+Y/X + o=-1+Y/X
# / \
# / \
# X<Y/ \X>=-Y
# / \
# / o=-3-X/Y\
# +-4 -2
othernode,vertex = ov
X = othernode.pos.x - self.pos.x
Y = othernode.pos.y - self.pos.y
if X>=Y:
if X>=-Y:
o=-1+Y/X
else:
o=-3-X/Y
else:
if X>=-Y:
o=1-X/Y
else:
o=3+Y/X
return o
class Vertex:
def __new__(cls, node1, node2, symbol, params):
if symbol == '*':
return object.__new__(StarVertex)
if symbol == '+':
return object.__new__(PlusVertex)
if symbol == '=':
return object.__new__(EqualVertex)
raise Exception("Unknown symbol {!r}".format(symbol))
def __init__(self, node1, node2, symbol, params):
self.params = params
self.node1 = node1
self.node2 = node2
self.node1.addvertex(node2, self)
self.node2.addvertex(node1, self)
self.reset()
def reset(self):
self._NW, self._NE, self._SW, self._SE = self.computepoints()
@property
def NW(self):
return self._NW
@property
def NE(self):
return self._NE
@property
def SW(self):
return self._SW
@property
def SE(self):
return self._SE
def begin(self, relativeto):
if relativeto == self.node1:
return self.SW
elif relativeto == self.node2:
return self.NE
else:
assert True
def end(self, relativeto):
if relativeto == self.node1:
return self.SE
elif relativeto == self.node2:
return self.NW
else:
assert True
def direction(self, alpha):
v = self.node2.pos - self.node1.pos
return v.rotate(alpha)
class StarVertex(Vertex):
def computepoints(self):
# node2
# +
# |
# alpha | -alpha
# NW | NE
# *
# SW | SE
# pi-alpha | -pi+alpha
# |
# +
# node1
mid = (self.node1.pos + self.node2.pos) / 2
alpha = math.pi/180*self.params['alpha']
NW = (mid, self.direction( alpha), (self, False))
NE = (mid, self.direction( -alpha), (self, True ))
SW = (mid, self.direction( math.pi-alpha), (self, True ))
SE = (mid, self.direction(-math.pi+alpha), (self, False))
return NW, NE, SW, SE
class PlusVertex(Vertex):
def computepoints(self):
# node2
# +
# |
# pi/2 NW * NE -pi/2 ^
# | |
# | | plusgap
# | |
# pi/2 SW * SE -pi/2 v
# |
# +
# node1
gap = (self.params['plusgap']/2) * (self.node2.pos-self.node1.pos).unit()
mid1 = (self.node1.pos + self.node2.pos) / 2 - gap
mid2 = (self.node1.pos + self.node2.pos) / 2 + gap
alpha = math.pi/2
NW = (mid2, self.direction( math.pi/2), (self, True ))
NE = (mid2, self.direction(-math.pi/2), (self, True ))
SW = (mid1, self.direction( math.pi/2), (self, False))
SE = (mid1, self.direction(-math.pi/2), (self, False))
return NW, NE, SW, SE
class EqualVertex(Vertex):
def computepoints(self):
# node2
# +
# |
# 0 | 0
# NW | NE
# * | *
# SW | SE
# pi | -pi
# |
# +
# node1
gap = (self.params['equalgap']/2) * (self.node2.pos-self.node1.pos).rotate(math.pi/2).unit()
mid1 = (self.node1.pos + self.node2.pos) / 2 - gap
mid2 = (self.node1.pos + self.node2.pos) / 2 + gap
NW = (mid2, self.direction(0), (self, True ))
NE = (mid1, self.direction(0), (self, False ))
SW = (mid2, self.direction(math.pi), (self, True))
SE = (mid1, self.direction(math.pi), (self, False))
return NW, NE, SW, SE
class EL:
def __init__(self, nodes, vertices, params):
# TODO: verification on validity
# -proper structure
# -at least one vertex
# -raisonable dimensions
# ...
self.params = params
self.nodes = [Node(*node) for node in nodes]
self.vertices = [Vertex(self.nodes[n1], self.nodes[n2], symbol, params) for n1,n2,symbol in vertices]
self._paths = None
def reset(self):
self._paths = None
for vertex in self.vertices:
vertex.reset()
def dump(self):
nodes = [(node.pos.x, node.pos.y) for node in self.nodes]
vertices = [(self.nodes.index(vertex.node1), self.nodes.index(vertex.node2)) for vertex in self.vertices]
return nodes,vertices,self.params
@property
def bounds(self):
if not self._paths:
dummy = self.paths
return self.left, self.right, self.top, self.bottom
@property
def paths(self):
if self._paths:
return self._paths
# There is an arc between each middle of adjacent joining segments
# an arc is displayed as a Bezier curve and thus described by its two
# end points and its two control points
# Two examples: *C1
# n2 C2* n /
# + | + /
# \ | /|/
# \ C2 |/ *M1
# M2 *--* C1 M2* |
# \ * / +
# \ \ / n1
# +-----*-----+ n1 +
# n M1 n2
# Vertices v1(n,n1) and v2(n,n2) are joining in node n
# There is no vertex between v1 and v2 and angle n1/n/n2 is positive.
# Node n keeps its joining vertices sorted like that.
# The control points are computed as C = M + a * D
# where:
# - M - middle point
# - D - direction (oriented tangent of arc)
# M and D are given by Vertex.begin(n) and Vertex.end(n)
# - a is tune so as to draw a nice curve without loop or cusp
self._paths = []
Curve = collections.namedtuple('Curve', 'idend arcs')
curves = {}
for n in self.nodes:
for i,(n1,v1) in enumerate(n.vertices):
n2,v2 = n.vertices[(i+1)%len(n.vertices)]
M1,D1,id1 = v1.begin(n)
M2,D2,id2 = v2.end(n)
if n1==n2 or Point.det(n1.pos-n.pos, n2.pos-n.pos) < 0: #convexe
A= n.pos+self.params['peak']*((n.pos-n1.pos).unit() + (n.pos-n2.pos).unit())
C1 = M1+0.3*D1
C2 = A+0.3*D1.norm()*(D1.unit()+D2.unit()).unit().rotate(-math.pi/2)
arc1 = (M1,C1,C2,A)
C1 = A+0.3*D2.norm()*(D1.unit()+D2.unit()).unit().rotate(math.pi/2)
C2 = M2+0.3*D2
arc2 = (A,C1,C2,M2)
else:
c = (1.3 + (n1.pos-n.pos).unit() * (n.pos-n2.pos).unit())/4
C1 = M1+c*D1
C2 = M2+c*D2
arc1, arc2 = self.splitarc(M1,C1,C2,M2)
idbegin = id1
curve = Curve(id2, [arc1, arc2])
while idbegin in curves:
idend,arcs = curves.pop(idbegin)
idbegin = curve.idend
curve.arcs.reverse()
arcs = [*curve.arcs, *arcs]
curve = Curve(idend, arcs)
curves[idbegin] = curve
while curves:
idbegin,(idend,arcs) = curves.popitem()
if idbegin == idend:
self._paths.append(arcs)
elif idend in curves:
curve = curves.pop(idend)
curves[idbegin] = Curve(curve.idend, [*arcs, *curve.arcs])
else:
arcs.reverse()
curves[idend] = Curve(curve.idbegin, arcs)
self.left = self.right = self.nodes[0].pos.x
self.top = self.bottom = self.nodes[0].pos.y
for path in self._paths:
for P1,C1,C2,P2 in path:
self.left = min(self.left, P1.x, C1.x, C2.x, P2.x)
self.right = max(self.right, P1.x, C1.x, C2.x, P2.x)
self.bottom = min(self.bottom, P1.y, C1.y, C2.y, P2.y)
self.top = max(self.top, P1.y, C1.y, C2.y, P2.y)
return self._paths
def splitarc(self, P1,C1,C2,P2):
return (P1,(P1+C1)/2,(P1+2*C1+C2)/4,(P1+3*C1+3*C2+P2)/8),\
((P1+3*C1+3*C2+P2)/8,(C1+2*C2+P2)/4,(C2+P2)/2,P2)