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#! /usr/bin/env python
"""
Converts a cubic bezier curve to a quadratic spline with
exactly two off curve points.
"""
import numpy
from numpy import array,cross,dot
from fontTools.misc import bezierTools
from FL import *
def calcIntersect(a,b,c,d):
numpy.seterr(all='raise')
e = b-a
f = d-c
p = array([-e[1], e[0]])
try:
h = dot((a-c),p) / dot(f,p)
except:
print a,b,c,d
raise
return c + dot(f,h)
def simpleConvertToQuadratic(p0,p1,p2,p3):
p = [array(i.x,i.y) for i in [p0,p1,p2,p3]]
off = calcIntersect(p[0],p[1],p[2],p[3])
# OFFCURVE_VECTOR_CORRECTION = -.015
OFFCURVE_VECTOR_CORRECTION = 0
def convertToQuadratic(p0,p1,p2,p3):
# TODO: test for accuracy and subdivide further if needed
p = [(i.x,i.y) for i in [p0,p1,p2,p3]]
# if p[0][0] == p[1][0] and p[0][0] == p[2][0] and p[0][0] == p[2][0] and p[0][0] == p[3][0]:
# return (p[0],p[1],p[2],p[3])
# if p[0][1] == p[1][1] and p[0][1] == p[2][1] and p[0][1] == p[2][1] and p[0][1] == p[3][1]:
# return (p[0],p[1],p[2],p[3])
seg1,seg2 = bezierTools.splitCubicAtT(p[0], p[1], p[2], p[3], .5)
pts1 = [array([i[0], i[1]]) for i in seg1]
pts2 = [array([i[0], i[1]]) for i in seg2]
on1 = seg1[0]
on2 = seg2[3]
try:
off1 = calcIntersect(pts1[0], pts1[1], pts1[2], pts1[3])
off2 = calcIntersect(pts2[0], pts2[1], pts2[2], pts2[3])
except:
return (p[0],p[1],p[2],p[3])
off1 = (on1 - off1) * OFFCURVE_VECTOR_CORRECTION + off1
off2 = (on2 - off2) * OFFCURVE_VECTOR_CORRECTION + off2
return (on1,off1,off2,on2)
def cubicNodeToQuadratic(g,nid):
node = g.nodes[nid]
if (node.type != nCURVE):
print "Node type not curve"
return
#pNode,junk = getPrevAnchor(g,nid)
pNode = g.nodes[nid-1] #assumes that a nCURVE type will always be proceeded by another point on the same contour
points = convertToQuadratic(pNode[0],node[1],node[2],node[0])
points = [Point(p[0],p[1]) for p in points]
curve = [
Node(nOFF, points[1]),
Node(nOFF, points[2]),
Node(nLINE,points[3]) ]
return curve
def glyphCurvesToQuadratic(g):
nodes = []
for i in range(len(g.nodes)):
n = g.nodes[i]
if n.type == nCURVE:
try:
newNodes = cubicNodeToQuadratic(g, i)
nodes = nodes + newNodes
except Exception:
print g.name, i
raise
else:
nodes.append(Node(g.nodes[i]))
g.Clear()
g.Insert(nodes)
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