351 lines
12 KiB
Python
351 lines
12 KiB
Python
|
import numpy
|
||
|
|
import sys
|
||
|
|
from shaperrec import geometric
|
||
|
|
from shaperrec import miscellaneous
|
||
|
|
|
||
|
|
# *************************************************************
|
||
|
|
# debugging
|
||
|
|
def void(*l):
|
||
|
|
pass
|
||
|
|
def debug_on(*l):
|
||
|
|
sys.stderr.write(' '.join(str(i) for i in l) +'\n')
|
||
|
|
debug = void
|
||
|
|
#debug = debug_on
|
||
|
|
|
||
|
|
# *************************************************************
|
||
|
|
# Internal Objects
|
||
|
|
class Path(object):
|
||
|
|
"""Private representation of a sequence of points.
|
||
|
|
A SVG node of type 'path' is splitted in several of these Path objects.
|
||
|
|
"""
|
||
|
|
next = None # next Path in the sequence of path corresponding to a SVG node
|
||
|
|
prev = None # previous Path in the sequence of path corresponding to a SVG node
|
||
|
|
sourcepoints = None # the full list of points from which this path is a subset
|
||
|
|
|
||
|
|
normalv = None # normal vector to this Path
|
||
|
|
|
||
|
|
def __init__(self, points):
|
||
|
|
"""points an array of points """
|
||
|
|
self.points = points
|
||
|
|
self.init()
|
||
|
|
|
||
|
|
def init(self):
|
||
|
|
self.effectiveNPoints = len(self.points)
|
||
|
|
if self.effectiveNPoints>1:
|
||
|
|
self.length, self.univ = geometric.dirAndLength(self.points[0], self.points[-1])
|
||
|
|
else:
|
||
|
|
self.length, self.univ = 0, numpy.array([0, 0])
|
||
|
|
if self.effectiveNPoints>0:
|
||
|
|
self.pointN=self.points[-1]
|
||
|
|
self.point1=self.points[0]
|
||
|
|
|
||
|
|
def isSegment(self):
|
||
|
|
return False
|
||
|
|
|
||
|
|
def quality(self):
|
||
|
|
return 1000
|
||
|
|
|
||
|
|
def dump(self):
|
||
|
|
n = len(self.points)
|
||
|
|
if n>0:
|
||
|
|
return 'path at '+str(self.points[0])+ ' to '+ str(self.points[-1])+' npoints=%d / %d (eff)'%(n, self.effectiveNPoints)
|
||
|
|
else:
|
||
|
|
return 'path Void !'
|
||
|
|
|
||
|
|
def setNewLength(self, l):
|
||
|
|
self.newLength = l
|
||
|
|
|
||
|
|
def removeLastPoints(self, n):
|
||
|
|
self.points = self.points[:-n]
|
||
|
|
self.init()
|
||
|
|
def removeFirstPoints(self, n):
|
||
|
|
self.points = self.points[n:]
|
||
|
|
self.init()
|
||
|
|
|
||
|
|
def costheta(self, seg):
|
||
|
|
return self.unitv.dot(seg.unitv)
|
||
|
|
|
||
|
|
def translate(self, tr):
|
||
|
|
"""Translate this path by tr"""
|
||
|
|
self.points = self.points + tr
|
||
|
|
|
||
|
|
def asSVGCommand(self, firstP=False):
|
||
|
|
svgCommands = []
|
||
|
|
com = 'M' if firstP else 'L'
|
||
|
|
for p in self.points:
|
||
|
|
svgCommands.append( [com, [p[0], p[1]] ] )
|
||
|
|
com='L'
|
||
|
|
return svgCommands
|
||
|
|
|
||
|
|
|
||
|
|
def setIntersectWithNext(self, next=None):
|
||
|
|
pass
|
||
|
|
|
||
|
|
def mergedWithNext(self, newPath=None):
|
||
|
|
""" Returns the combination of self and self.next.
|
||
|
|
sourcepoints has to be set
|
||
|
|
"""
|
||
|
|
if newPath is None: newPath = Path( numpy.concatenate([self.points, self.next.points]) )
|
||
|
|
|
||
|
|
newPath.sourcepoints = self.sourcepoints
|
||
|
|
newPath.prev = self.prev
|
||
|
|
if self.prev : newPath.prev.next = newPath
|
||
|
|
newPath.next = self.next.__next__
|
||
|
|
if newPath.__next__:
|
||
|
|
newPath.next.prev = newPath
|
||
|
|
return newPath
|
||
|
|
|
||
|
|
# *************************************************************
|
||
|
|
#
|
||
|
|
class Segment(Path):
|
||
|
|
""" A segment. Defined by its line equation ax+by+c=0 and the points from orignal paths
|
||
|
|
it is ensured that a**2+b**2 = 1
|
||
|
|
"""
|
||
|
|
QUALITYCUT = 0.9
|
||
|
|
|
||
|
|
newAngle = None # temporary angle set during the "parralelization" step
|
||
|
|
newLength = None # temporary lenght set during the "parralelization" step
|
||
|
|
|
||
|
|
# Segment Builders
|
||
|
|
@staticmethod
|
||
|
|
def from2Points( p1, p2, refPoints = None):
|
||
|
|
dirV = p2-p1
|
||
|
|
center = 0.5*(p2+p1)
|
||
|
|
return Segment.fromCenterAndDir(center, dirV, refPoints)
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
def fromCenterAndDir( center, dirV, refPoints=None):
|
||
|
|
b = dirV[0]
|
||
|
|
a = -dirV[1]
|
||
|
|
c = - (a*center[0]+b*center[1])
|
||
|
|
|
||
|
|
if refPoints is None:
|
||
|
|
refPoints = numpy.array([ center-0.5*dirV, center+0.5*dirV] )
|
||
|
|
s = Segment( a, b, c, refPoints)
|
||
|
|
return s
|
||
|
|
|
||
|
|
|
||
|
|
def __init__(self, a,b,c, points, doinit=True):
|
||
|
|
"""a,b,c: the line parameters.
|
||
|
|
points : the array of 2D points represented by this Segment
|
||
|
|
doinit : if true will compute additionnal parameters to this Segment (first/last points, unit vector,...)
|
||
|
|
"""
|
||
|
|
self.a = a
|
||
|
|
self.b = b
|
||
|
|
self.c = c
|
||
|
|
|
||
|
|
self.points = points
|
||
|
|
d = numpy.sqrt(a**2+b**2)
|
||
|
|
if d != 1. :
|
||
|
|
self.a /= d
|
||
|
|
self.b /= d
|
||
|
|
self.c /= d
|
||
|
|
|
||
|
|
if doinit :
|
||
|
|
self.init()
|
||
|
|
|
||
|
|
|
||
|
|
def init(self):
|
||
|
|
a, b, c = self.a, self.b, self.c
|
||
|
|
x, y = self.points[0]
|
||
|
|
self.point1 = numpy.array( [ b*(x*b-y*a) - c*a, a*(y*a-x*b) - c*b ] )
|
||
|
|
x, y = self.points[-1]
|
||
|
|
self.pointN = numpy.array( [ b*(x*b-y*a) - c*a, a*(y*a-x*b) - c*b ] )
|
||
|
|
uv = self.computeDirLength()
|
||
|
|
self.distancesToLine = self.computeDistancesToLine(self.points)
|
||
|
|
self.normalv = numpy.array( [ a, b ])
|
||
|
|
|
||
|
|
self.angle = numpy.arccos( uv[0] )*numpy.sign(uv[1] )
|
||
|
|
|
||
|
|
|
||
|
|
def computeDirLength(self):
|
||
|
|
"""re-compute and set unit vector and length """
|
||
|
|
self.length, uv = geometric.dirAndLength(self.pointN, self.point1)
|
||
|
|
self.unitv = uv
|
||
|
|
return uv
|
||
|
|
|
||
|
|
def isSegment(self):
|
||
|
|
return True
|
||
|
|
|
||
|
|
def recomputeEndPoints(self):
|
||
|
|
a, b, c = self.a, self.b, self.c
|
||
|
|
x, y = self.points[0]
|
||
|
|
self.point1 = numpy.array( [ b*(x*b-y*a) - c*a, a*(y*a-x*b) - c*b ] )
|
||
|
|
x, y = self.points[-1]
|
||
|
|
|
||
|
|
self.pointN = numpy.array( [ b*(x*b-y*a) - c*a, a*(y*a-x*b) - c*b ] )
|
||
|
|
|
||
|
|
self.length = numpy.sqrt( geometric.D2(self.pointN, self.point1) )
|
||
|
|
|
||
|
|
def projectPoint(self, p):
|
||
|
|
""" return the point projection of p onto this segment"""
|
||
|
|
a, b, c = self.a, self.b, self.c
|
||
|
|
x, y = p
|
||
|
|
return numpy.array( [ b*(x*b-y*a) - c*a, a*(y*a-x*b) - c*b ] )
|
||
|
|
|
||
|
|
|
||
|
|
def intersect(self, seg):
|
||
|
|
"""Returns the intersection of this line with the line seg"""
|
||
|
|
nu, nv = self.normalv, seg.normalv
|
||
|
|
u = numpy.array([[-self.c], [-seg.c]])
|
||
|
|
doRotation = min(nu.min(), nv.min()) <1e-4
|
||
|
|
if doRotation:
|
||
|
|
# rotate to avoid numerical issues
|
||
|
|
nu = numpy.array(geometric.rotMat.dot(nu))[0]
|
||
|
|
nv = numpy.array(geometric.rotMat.dot(nv))[0]
|
||
|
|
m = numpy.matrix( (nu, nv) )
|
||
|
|
|
||
|
|
i = (m**-1).dot(u)
|
||
|
|
i=numpy.array( i).swapaxes(0, 1)[0]
|
||
|
|
debug(' intersection ', nu, nv, self.angle, seg.angle, ' --> ', i)
|
||
|
|
if doRotation:
|
||
|
|
i = geometric.unrotMat.dot(i).A1
|
||
|
|
debug(' ', i)
|
||
|
|
|
||
|
|
|
||
|
|
return i
|
||
|
|
|
||
|
|
def setIntersectWithNext(self, next=None):
|
||
|
|
"""Modify self such as self.pointN is the intersection with next segment """
|
||
|
|
if next is None:
|
||
|
|
next = self.__next__
|
||
|
|
if next and next.isSegment():
|
||
|
|
if abs(self.normalv.dot(next.unitv)) < 1e-3:
|
||
|
|
return
|
||
|
|
debug(' Intersect', self, next, ' from ', self.point1, self.pointN, ' to ', next.point1, next.pointN,)
|
||
|
|
inter = self.intersect(next)
|
||
|
|
debug(' --> ', inter, ' d=', geometric.D(self.pointN, inter) )
|
||
|
|
next.point1 = inter
|
||
|
|
self.pointN = inter
|
||
|
|
self.computeDirLength()
|
||
|
|
next.computeDirLength()
|
||
|
|
|
||
|
|
def computeDistancesToLine(self, points):
|
||
|
|
"""points: array of points.
|
||
|
|
returns the array of distances to this segment"""
|
||
|
|
return abs(self.a*points[:, 0]+self.b*points[:, 1]+self.c)
|
||
|
|
|
||
|
|
|
||
|
|
def distanceTo(self, point):
|
||
|
|
return abs(self.a*point[0]+self.b*point[1]+self.c)
|
||
|
|
|
||
|
|
def inverse(self):
|
||
|
|
"""swap all x and y values. """
|
||
|
|
def inv(v):
|
||
|
|
v[0], v[1] = v[1], v[0]
|
||
|
|
for v in [self.point1, self.pointN, self.unitv, self.normalv]:
|
||
|
|
inv(v)
|
||
|
|
|
||
|
|
self.points = numpy.roll(self.points, 1, axis=1)
|
||
|
|
self.a, self.b = self.b, self.a
|
||
|
|
self.angle = numpy.arccos( self.unitv[0] )*numpy.sign(self.unitv[1] )
|
||
|
|
return
|
||
|
|
|
||
|
|
def dumpShort(self):
|
||
|
|
return 'seg '+' '+str(self.point1 )+'to '+str(self.pointN)+ ' npoints=%d | angle,offset=(%.2f,%.2f )'%(len(self.points), self.angle, self.c)+' ', self.normalv
|
||
|
|
|
||
|
|
def dump(self):
|
||
|
|
v = self.variance()
|
||
|
|
n = len(self.points)
|
||
|
|
return 'seg '+str(self.point1 )+' , '+str(self.pointN)+ ' v/l=%.2f / %.2f = %.2f r*numpy.sqrt(n)=%.2f npoints=%d | angle,offset=(%.2f,%.2f )'%(v, self.length, v/self.length, v/self.length*numpy.sqrt(n), n, self.angle, self.c)
|
||
|
|
|
||
|
|
def variance(self):
|
||
|
|
d = self.distancesToLine
|
||
|
|
return numpy.sqrt( (d**2).sum()/len(d) )
|
||
|
|
|
||
|
|
def quality(self):
|
||
|
|
n = len(self.points)
|
||
|
|
return min(self.variance()/self.length*numpy.sqrt(n), 1000)
|
||
|
|
|
||
|
|
def formatedSegment(self, firstP=False):
|
||
|
|
return self.asSVGCommand(firstP)
|
||
|
|
|
||
|
|
def asSVGCommand(self, firstP=False):
|
||
|
|
|
||
|
|
if firstP:
|
||
|
|
segment = [ ['M', [self.point1[0], self.point1[1] ] ],
|
||
|
|
['L', [self.pointN[0], self.pointN[1] ] ]
|
||
|
|
]
|
||
|
|
else:
|
||
|
|
segment = [ ['L', [self.pointN[0], self.pointN[1] ] ] ]
|
||
|
|
#debug("Segment, format : ", segment)
|
||
|
|
return segment
|
||
|
|
|
||
|
|
def replaceInList(self, startPos, fullList):
|
||
|
|
code0 = fullList[startPos][0]
|
||
|
|
segment = [ [code0, [self.point1[0], self.point1[1] ] ],
|
||
|
|
['L', [self.pointN[0], self.pointN[1] ] ]
|
||
|
|
]
|
||
|
|
l = fullList[:startPos]+segment+fullList[startPos+len(self.points):]
|
||
|
|
return l
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
def mergedWithNext(self, doRefit=True):
|
||
|
|
""" Returns the combination of self and self.next.
|
||
|
|
sourcepoints has to be set
|
||
|
|
"""
|
||
|
|
spoints = numpy.concatenate([self.points, self.next.points])
|
||
|
|
|
||
|
|
if doRefit:
|
||
|
|
newSeg = fitSingleSegment(spoints)
|
||
|
|
else:
|
||
|
|
newSeg = Segment.fromCenterAndDir(geometric.barycenter(spoints), self.unitv, spoints)
|
||
|
|
|
||
|
|
newSeg = Path.mergedWithNext(self, newSeg)
|
||
|
|
return newSeg
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
def center(self):
|
||
|
|
return 0.5*(self.point1+self.pointN)
|
||
|
|
|
||
|
|
def box(self):
|
||
|
|
return geometric.computeBox(self.points)
|
||
|
|
|
||
|
|
|
||
|
|
def translate(self, tr):
|
||
|
|
"""Translate this segment by tr """
|
||
|
|
c = self.c -self.a*tr[0] -self.b*tr[1]
|
||
|
|
self.c =c
|
||
|
|
self.pointN = self.pointN+tr
|
||
|
|
self.point1 = self.point1+tr
|
||
|
|
self.points +=tr
|
||
|
|
|
||
|
|
def adjustToNewAngle(self):
|
||
|
|
"""reset all parameters so that self.angle is change to self.newAngle """
|
||
|
|
|
||
|
|
self.a, self.b, self.c = miscellaneous.parametersFromPointAngle( 0.5*(self.point1+self.pointN), self.newAngle)
|
||
|
|
|
||
|
|
#print 'adjustToNewAngle ', self, self.angle, self.newAngle
|
||
|
|
self.angle = self.newAngle
|
||
|
|
self.normalv = numpy.array( [ self.a, self.b ])
|
||
|
|
self.unitv = numpy.array( [ self.b, -self.a ])
|
||
|
|
if abs(self.angle) > numpy.pi/2 :
|
||
|
|
if self.b > 0: self.unitv *= -1
|
||
|
|
elif self.b<0 : self.unitv *= -1
|
||
|
|
|
||
|
|
self.point1 = self.projectPoint(self.point1) # reset point1
|
||
|
|
if not hasattr(self, "__next__") or not self.next.isSegment():
|
||
|
|
# move the last point (no intersect with next)
|
||
|
|
|
||
|
|
pN = self.projectPoint(self.pointN)
|
||
|
|
dirN = pN - self.point1
|
||
|
|
lN = geometric.length(pN, self.point1)
|
||
|
|
self.pointN = dirN/lN*self.length + self.point1
|
||
|
|
#print ' ... adjusting last seg angle ',p.dump() , ' normalv=', p.normalv, 'unitv ', p.unitv
|
||
|
|
else:
|
||
|
|
self.setIntersectWithNext()
|
||
|
|
|
||
|
|
def adjustToNewDistance(self):
|
||
|
|
self.pointN = self.newLength* self.unitv + self.point1
|
||
|
|
self.length = self.newLength
|
||
|
|
|
||
|
|
def tempLength(self):
|
||
|
|
if self.newLength : return self.newLength
|
||
|
|
else : return self.length
|
||
|
|
|
||
|
|
def tempAngle(self):
|
||
|
|
if self.newAngle: return self.newAngle
|
||
|
|
return self.angle
|