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|
from fontTools.pens.basePen import BasePen, OpenContourError
try:
import cython
except ImportError:
# if cython not installed, use mock module with no-op decorators and types
from fontTools.misc import cython
if cython.compiled:
# Yep, I'm compiled.
COMPILED = True
else:
# Just a lowly interpreted script.
COMPILED = False
__all__ = ["MomentsPen"]
class MomentsPen(BasePen):
def __init__(self, glyphset=None):
BasePen.__init__(self, glyphset)
self.area = 0
self.momentX = 0
self.momentY = 0
self.momentXX = 0
self.momentXY = 0
self.momentYY = 0
def _moveTo(self, p0):
self.__startPoint = p0
def _closePath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
self._lineTo(self.__startPoint)
def _endPath(self):
p0 = self._getCurrentPoint()
if p0 != self.__startPoint:
# Green theorem is not defined on open contours.
raise OpenContourError(
"Green theorem is not defined on open contours."
)
@cython.locals(r0=cython.double)
@cython.locals(r1=cython.double)
@cython.locals(r2=cython.double)
@cython.locals(r3=cython.double)
@cython.locals(r4=cython.double)
@cython.locals(r5=cython.double)
@cython.locals(r6=cython.double)
@cython.locals(r7=cython.double)
@cython.locals(r8=cython.double)
@cython.locals(r9=cython.double)
@cython.locals(r10=cython.double)
@cython.locals(r11=cython.double)
@cython.locals(r12=cython.double)
@cython.locals(x0=cython.double, y0=cython.double)
@cython.locals(x1=cython.double, y1=cython.double)
def _lineTo(self, p1):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
r0 = x1*y0
r1 = x1*y1
r2 = x1**2
r3 = r2*y1
r4 = y0 - y1
r5 = r4*x0
r6 = x0**2
r7 = 2*y0
r8 = y0**2
r9 = y1**2
r10 = x1**3
r11 = y0**3
r12 = y1**3
self.area += -r0/2 - r1/2 + x0*(y0 + y1)/2
self.momentX += -r2*y0/6 - r3/3 - r5*x1/6 + r6*(r7 + y1)/6
self.momentY += -r0*y1/6 - r8*x1/6 - r9*x1/6 + x0*(r8 + r9 + y0*y1)/6
self.momentXX += -r10*y0/12 - r10*y1/4 - r2*r5/12 - r4*r6*x1/12 + x0**3*(3*y0 + y1)/12
self.momentXY += -r2*r8/24 - r2*r9/8 - r3*r7/24 + r6*(r7*y1 + 3*r8 + r9)/24 - x0*x1*(r8 - r9)/12
self.momentYY += -r0*r9/12 - r1*r8/12 - r11*x1/12 - r12*x1/12 + x0*(r11 + r12 + r8*y1 + r9*y0)/12
@cython.locals(r0=cython.double)
@cython.locals(r1=cython.double)
@cython.locals(r2=cython.double)
@cython.locals(r3=cython.double)
@cython.locals(r4=cython.double)
@cython.locals(r5=cython.double)
@cython.locals(r6=cython.double)
@cython.locals(r7=cython.double)
@cython.locals(r8=cython.double)
@cython.locals(r9=cython.double)
@cython.locals(r10=cython.double)
@cython.locals(r11=cython.double)
@cython.locals(r12=cython.double)
@cython.locals(r13=cython.double)
@cython.locals(r14=cython.double)
@cython.locals(r15=cython.double)
@cython.locals(r16=cython.double)
@cython.locals(r17=cython.double)
@cython.locals(r18=cython.double)
@cython.locals(r19=cython.double)
@cython.locals(r20=cython.double)
@cython.locals(r21=cython.double)
@cython.locals(r22=cython.double)
@cython.locals(r23=cython.double)
@cython.locals(r24=cython.double)
@cython.locals(r25=cython.double)
@cython.locals(r26=cython.double)
@cython.locals(r27=cython.double)
@cython.locals(r28=cython.double)
@cython.locals(r29=cython.double)
@cython.locals(r30=cython.double)
@cython.locals(r31=cython.double)
@cython.locals(r32=cython.double)
@cython.locals(r33=cython.double)
@cython.locals(r34=cython.double)
@cython.locals(r35=cython.double)
@cython.locals(r36=cython.double)
@cython.locals(r37=cython.double)
@cython.locals(r38=cython.double)
@cython.locals(r39=cython.double)
@cython.locals(r40=cython.double)
@cython.locals(r41=cython.double)
@cython.locals(r42=cython.double)
@cython.locals(r43=cython.double)
@cython.locals(r44=cython.double)
@cython.locals(r45=cython.double)
@cython.locals(r46=cython.double)
@cython.locals(r47=cython.double)
@cython.locals(r48=cython.double)
@cython.locals(r49=cython.double)
@cython.locals(r50=cython.double)
@cython.locals(r51=cython.double)
@cython.locals(r52=cython.double)
@cython.locals(r53=cython.double)
@cython.locals(x0=cython.double, y0=cython.double)
@cython.locals(x1=cython.double, y1=cython.double)
@cython.locals(x2=cython.double, y2=cython.double)
def _qCurveToOne(self, p1, p2):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
r0 = 2*y1
r1 = r0*x2
r2 = x2*y2
r3 = 3*r2
r4 = 2*x1
r5 = 3*y0
r6 = x1**2
r7 = x2**2
r8 = 4*y1
r9 = 10*y2
r10 = 2*y2
r11 = r4*x2
r12 = x0**2
r13 = 10*y0
r14 = r4*y2
r15 = x2*y0
r16 = 4*x1
r17 = r0*x1 + r2
r18 = r2*r8
r19 = y1**2
r20 = 2*r19
r21 = y2**2
r22 = r21*x2
r23 = 5*r22
r24 = y0**2
r25 = y0*y2
r26 = 5*r24
r27 = x1**3
r28 = x2**3
r29 = 30*y1
r30 = 6*y1
r31 = 10*r7*x1
r32 = 5*y2
r33 = 12*r6
r34 = 30*x1
r35 = x1*y1
r36 = r3 + 20*r35
r37 = 12*x1
r38 = 20*r6
r39 = 8*r6*y1
r40 = r32*r7
r41 = 60*y1
r42 = 20*r19
r43 = 4*r19
r44 = 15*r21
r45 = 12*x2
r46 = 12*y2
r47 = 6*x1
r48 = 8*r19*x1 + r23
r49 = 8*y1**3
r50 = y2**3
r51 = y0**3
r52 = 10*y1
r53 = 12*y1
self.area += -r1/6 - r3/6 + x0*(r0 + r5 + y2)/6 + x1*y2/3 - y0*(r4 + x2)/6
self.momentX += -r11*(-r10 + y1)/30 + r12*(r13 + r8 + y2)/30 + r6*y2/15 - r7*r8/30 - r7*r9/30 + x0*(r14 - r15 - r16*y0 + r17)/30 - y0*(r11 + 2*r6 + r7)/30
self.momentY += -r18/30 - r20*x2/30 - r23/30 - r24*(r16 + x2)/30 + x0*(r0*y2 + r20 + r21 + r25 + r26 + r8*y0)/30 + x1*y2*(r10 + y1)/15 - y0*(r1 + r17)/30
self.momentXX += r12*(r1 - 5*r15 - r34*y0 + r36 + r9*x1)/420 + 2*r27*y2/105 - r28*r29/420 - r28*y2/4 - r31*(r0 - 3*y2)/420 - r6*x2*(r0 - r32)/105 + x0**3*(r30 + 21*y0 + y2)/84 - x0*(r0*r7 + r15*r37 - r2*r37 - r33*y2 + r38*y0 - r39 - r40 + r5*r7)/420 - y0*(8*r27 + 5*r28 + r31 + r33*x2)/420
self.momentXY += r12*(r13*y2 + 3*r21 + 105*r24 + r41*y0 + r42 + r46*y1)/840 - r16*x2*(r43 - r44)/840 - r21*r7/8 - r24*(r38 + r45*x1 + 3*r7)/840 - r41*r7*y2/840 - r42*r7/840 + r6*y2*(r32 + r8)/210 + x0*(-r15*r8 + r16*r25 + r18 + r21*r47 - r24*r34 - r26*x2 + r35*r46 + r48)/420 - y0*(r16*r2 + r30*r7 + r35*r45 + r39 + r40)/420
self.momentYY += -r2*r42/420 - r22*r29/420 - r24*(r14 + r36 + r52*x2)/420 - r49*x2/420 - r50*x2/12 - r51*(r47 + x2)/84 + x0*(r19*r46 + r21*r5 + r21*r52 + r24*r29 + r25*r53 + r26*y2 + r42*y0 + r49 + 5*r50 + 35*r51)/420 + x1*y2*(r43 + r44 + r9*y1)/210 - y0*(r19*r45 + r2*r53 - r21*r4 + r48)/420
@cython.locals(r0=cython.double)
@cython.locals(r1=cython.double)
@cython.locals(r2=cython.double)
@cython.locals(r3=cython.double)
@cython.locals(r4=cython.double)
@cython.locals(r5=cython.double)
@cython.locals(r6=cython.double)
@cython.locals(r7=cython.double)
@cython.locals(r8=cython.double)
@cython.locals(r9=cython.double)
@cython.locals(r10=cython.double)
@cython.locals(r11=cython.double)
@cython.locals(r12=cython.double)
@cython.locals(r13=cython.double)
@cython.locals(r14=cython.double)
@cython.locals(r15=cython.double)
@cython.locals(r16=cython.double)
@cython.locals(r17=cython.double)
@cython.locals(r18=cython.double)
@cython.locals(r19=cython.double)
@cython.locals(r20=cython.double)
@cython.locals(r21=cython.double)
@cython.locals(r22=cython.double)
@cython.locals(r23=cython.double)
@cython.locals(r24=cython.double)
@cython.locals(r25=cython.double)
@cython.locals(r26=cython.double)
@cython.locals(r27=cython.double)
@cython.locals(r28=cython.double)
@cython.locals(r29=cython.double)
@cython.locals(r30=cython.double)
@cython.locals(r31=cython.double)
@cython.locals(r32=cython.double)
@cython.locals(r33=cython.double)
@cython.locals(r34=cython.double)
@cython.locals(r35=cython.double)
@cython.locals(r36=cython.double)
@cython.locals(r37=cython.double)
@cython.locals(r38=cython.double)
@cython.locals(r39=cython.double)
@cython.locals(r40=cython.double)
@cython.locals(r41=cython.double)
@cython.locals(r42=cython.double)
@cython.locals(r43=cython.double)
@cython.locals(r44=cython.double)
@cython.locals(r45=cython.double)
@cython.locals(r46=cython.double)
@cython.locals(r47=cython.double)
@cython.locals(r48=cython.double)
@cython.locals(r49=cython.double)
@cython.locals(r50=cython.double)
@cython.locals(r51=cython.double)
@cython.locals(r52=cython.double)
@cython.locals(r53=cython.double)
@cython.locals(r54=cython.double)
@cython.locals(r55=cython.double)
@cython.locals(r56=cython.double)
@cython.locals(r57=cython.double)
@cython.locals(r58=cython.double)
@cython.locals(r59=cython.double)
@cython.locals(r60=cython.double)
@cython.locals(r61=cython.double)
@cython.locals(r62=cython.double)
@cython.locals(r63=cython.double)
@cython.locals(r64=cython.double)
@cython.locals(r65=cython.double)
@cython.locals(r66=cython.double)
@cython.locals(r67=cython.double)
@cython.locals(r68=cython.double)
@cython.locals(r69=cython.double)
@cython.locals(r70=cython.double)
@cython.locals(r71=cython.double)
@cython.locals(r72=cython.double)
@cython.locals(r73=cython.double)
@cython.locals(r74=cython.double)
@cython.locals(r75=cython.double)
@cython.locals(r76=cython.double)
@cython.locals(r77=cython.double)
@cython.locals(r78=cython.double)
@cython.locals(r79=cython.double)
@cython.locals(r80=cython.double)
@cython.locals(r81=cython.double)
@cython.locals(r82=cython.double)
@cython.locals(r83=cython.double)
@cython.locals(r84=cython.double)
@cython.locals(r85=cython.double)
@cython.locals(r86=cython.double)
@cython.locals(r87=cython.double)
@cython.locals(r88=cython.double)
@cython.locals(r89=cython.double)
@cython.locals(r90=cython.double)
@cython.locals(r91=cython.double)
@cython.locals(r92=cython.double)
@cython.locals(r93=cython.double)
@cython.locals(r94=cython.double)
@cython.locals(r95=cython.double)
@cython.locals(r96=cython.double)
@cython.locals(r97=cython.double)
@cython.locals(r98=cython.double)
@cython.locals(r99=cython.double)
@cython.locals(r100=cython.double)
@cython.locals(r101=cython.double)
@cython.locals(r102=cython.double)
@cython.locals(r103=cython.double)
@cython.locals(r104=cython.double)
@cython.locals(r105=cython.double)
@cython.locals(r106=cython.double)
@cython.locals(r107=cython.double)
@cython.locals(r108=cython.double)
@cython.locals(r109=cython.double)
@cython.locals(r110=cython.double)
@cython.locals(r111=cython.double)
@cython.locals(r112=cython.double)
@cython.locals(r113=cython.double)
@cython.locals(r114=cython.double)
@cython.locals(r115=cython.double)
@cython.locals(r116=cython.double)
@cython.locals(r117=cython.double)
@cython.locals(r118=cython.double)
@cython.locals(r119=cython.double)
@cython.locals(r120=cython.double)
@cython.locals(r121=cython.double)
@cython.locals(r122=cython.double)
@cython.locals(r123=cython.double)
@cython.locals(r124=cython.double)
@cython.locals(r125=cython.double)
@cython.locals(r126=cython.double)
@cython.locals(r127=cython.double)
@cython.locals(r128=cython.double)
@cython.locals(r129=cython.double)
@cython.locals(r130=cython.double)
@cython.locals(r131=cython.double)
@cython.locals(r132=cython.double)
@cython.locals(x0=cython.double, y0=cython.double)
@cython.locals(x1=cython.double, y1=cython.double)
@cython.locals(x2=cython.double, y2=cython.double)
@cython.locals(x3=cython.double, y3=cython.double)
def _curveToOne(self, p1, p2, p3):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
x3,y3 = p3
r0 = 6*y2
r1 = r0*x3
r2 = 10*y3
r3 = r2*x3
r4 = 3*y1
r5 = 6*x1
r6 = 3*x2
r7 = 6*y1
r8 = 3*y2
r9 = x2**2
r10 = 45*r9
r11 = r10*y3
r12 = x3**2
r13 = r12*y2
r14 = r12*y3
r15 = 7*y3
r16 = 15*x3
r17 = r16*x2
r18 = x1**2
r19 = 9*r18
r20 = x0**2
r21 = 21*y1
r22 = 9*r9
r23 = r7*x3
r24 = 9*y2
r25 = r24*x2 + r3
r26 = 9*x2
r27 = x2*y3
r28 = -r26*y1 + 15*r27
r29 = 3*x1
r30 = 45*x1
r31 = 12*x3
r32 = 45*r18
r33 = 5*r12
r34 = r8*x3
r35 = 105*y0
r36 = 30*y0
r37 = r36*x2
r38 = 5*x3
r39 = 15*y3
r40 = 5*y3
r41 = r40*x3
r42 = x2*y2
r43 = 18*r42
r44 = 45*y1
r45 = r41 + r43 + r44*x1
r46 = y2*y3
r47 = r46*x3
r48 = y2**2
r49 = 45*r48
r50 = r49*x3
r51 = y3**2
r52 = r51*x3
r53 = y1**2
r54 = 9*r53
r55 = y0**2
r56 = 21*x1
r57 = 6*x2
r58 = r16*y2
r59 = r39*y2
r60 = 9*r48
r61 = r6*y3
r62 = 3*y3
r63 = r36*y2
r64 = y1*y3
r65 = 45*r53
r66 = 5*r51
r67 = x2**3
r68 = x3**3
r69 = 630*y2
r70 = 126*x3
r71 = x1**3
r72 = 126*x2
r73 = 63*r9
r74 = r73*x3
r75 = r15*x3 + 15*r42
r76 = 630*x1
r77 = 14*x3
r78 = 21*r27
r79 = 42*x1
r80 = 42*x2
r81 = x1*y2
r82 = 63*r42
r83 = x1*y1
r84 = r41 + r82 + 378*r83
r85 = x2*x3
r86 = r85*y1
r87 = r27*x3
r88 = 27*r9
r89 = r88*y2
r90 = 42*r14
r91 = 90*x1
r92 = 189*r18
r93 = 378*r18
r94 = r12*y1
r95 = 252*x1*x2
r96 = r79*x3
r97 = 30*r85
r98 = r83*x3
r99 = 30*x3
r100 = 42*x3
r101 = r42*x1
r102 = r10*y2 + 14*r14 + 126*r18*y1 + r81*r99
r103 = 378*r48
r104 = 18*y1
r105 = r104*y2
r106 = y0*y1
r107 = 252*y2
r108 = r107*y0
r109 = y0*y3
r110 = 42*r64
r111 = 378*r53
r112 = 63*r48
r113 = 27*x2
r114 = r27*y2
r115 = r113*r48 + 42*r52
r116 = x3*y3
r117 = 54*r42
r118 = r51*x1
r119 = r51*x2
r120 = r48*x1
r121 = 21*x3
r122 = r64*x1
r123 = r81*y3
r124 = 30*r27*y1 + r49*x2 + 14*r52 + 126*r53*x1
r125 = y2**3
r126 = y3**3
r127 = y1**3
r128 = y0**3
r129 = r51*y2
r130 = r112*y3 + r21*r51
r131 = 189*r53
r132 = 90*y2
self.area += -r1/20 - r3/20 - r4*(x2 + x3)/20 + x0*(r7 + r8 + 10*y0 + y3)/20 + 3*x1*(y2 + y3)/20 + 3*x2*y3/10 - y0*(r5 + r6 + x3)/20
self.momentX += r11/840 - r13/8 - r14/3 - r17*(-r15 + r8)/840 + r19*(r8 + 2*y3)/840 + r20*(r0 + r21 + 56*y0 + y3)/168 + r29*(-r23 + r25 + r28)/840 - r4*(10*r12 + r17 + r22)/840 + x0*(12*r27 + r30*y2 + r34 - r35*x1 - r37 - r38*y0 + r39*x1 - r4*x3 + r45)/840 - y0*(r17 + r30*x2 + r31*x1 + r32 + r33 + 18*r9)/840
self.momentY += -r4*(r25 + r58)/840 - r47/8 - r50/840 - r52/6 - r54*(r6 + 2*x3)/840 - r55*(r56 + r57 + x3)/168 + x0*(r35*y1 + r40*y0 + r44*y2 + 18*r48 + 140*r55 + r59 + r63 + 12*r64 + r65 + r66)/840 + x1*(r24*y1 + 10*r51 + r59 + r60 + r7*y3)/280 + x2*y3*(r15 + r8)/56 - y0*(r16*y1 + r31*y2 + r44*x2 + r45 + r61 - r62*x1)/840
self.momentXX += -r12*r72*(-r40 + r8)/9240 + 3*r18*(r28 + r34 - r38*y1 + r75)/3080 + r20*(r24*x3 - r72*y0 - r76*y0 - r77*y0 + r78 + r79*y3 + r80*y1 + 210*r81 + r84)/9240 - r29*(r12*r21 + 14*r13 + r44*r9 - r73*y3 + 54*r86 - 84*r87 - r89 - r90)/9240 - r4*(70*r12*x2 + 27*r67 + 42*r68 + r74)/9240 + 3*r67*y3/220 - r68*r69/9240 - r68*y3/4 - r70*r9*(-r62 + y2)/9240 + 3*r71*(r24 + r40)/3080 + x0**3*(r24 + r44 + 165*y0 + y3)/660 + x0*(r100*r27 + 162*r101 + r102 + r11 + 63*r18*y3 + r27*r91 - r33*y0 - r37*x3 + r43*x3 - r73*y0 - r88*y1 + r92*y2 - r93*y0 - 9*r94 - r95*y0 - r96*y0 - r97*y1 - 18*r98 + r99*x1*y3)/9240 - y0*(r12*r56 + r12*r80 + r32*x3 + 45*r67 + 14*r68 + 126*r71 + r74 + r85*r91 + 135*r9*x1 + r92*x2)/9240
self.momentXY += -r103*r12/18480 - r12*r51/8 - 3*r14*y2/44 + 3*r18*(r105 + r2*y1 + 18*r46 + 15*r48 + 7*r51)/6160 + r20*(1260*r106 + r107*y1 + r108 + 28*r109 + r110 + r111 + r112 + 30*r46 + 2310*r55 + r66)/18480 - r54*(7*r12 + 18*r85 + 15*r9)/18480 - r55*(r33 + r73 + r93 + r95 + r96 + r97)/18480 - r7*(42*r13 + r82*x3 + 28*r87 + r89 + r90)/18480 - 3*r85*(r48 - r66)/220 + 3*r9*y3*(r62 + 2*y2)/440 + x0*(-r1*y0 - 84*r106*x2 + r109*r56 + 54*r114 + r117*y1 + 15*r118 + 21*r119 + 81*r120 + r121*r46 + 54*r122 + 60*r123 + r124 - r21*x3*y0 + r23*y3 - r54*x3 - r55*r72 - r55*r76 - r55*r77 + r57*y0*y3 + r60*x3 + 84*r81*y0 + 189*r81*y1)/9240 + x1*(r104*r27 - r105*x3 - r113*r53 + 63*r114 + r115 - r16*r53 + 28*r47 + r51*r80)/3080 - y0*(54*r101 + r102 + r116*r5 + r117*x3 + 21*r13 - r19*y3 + r22*y3 + r78*x3 + 189*r83*x2 + 60*r86 + 81*r9*y1 + 15*r94 + 54*r98)/9240
self.momentYY += -r103*r116/9240 - r125*r70/9240 - r126*x3/12 - 3*r127*(r26 + r38)/3080 - r128*(r26 + r30 + x3)/660 - r4*(r112*x3 + r115 - 14*r119 + 84*r47)/9240 - r52*r69/9240 - r54*(r58 + r61 + r75)/9240 - r55*(r100*y1 + r121*y2 + r26*y3 + r79*y2 + r84 + 210*x2*y1)/9240 + x0*(r108*y1 + r110*y0 + r111*y0 + r112*y0 + 45*r125 + 14*r126 + 126*r127 + 770*r128 + 42*r129 + r130 + r131*y2 + r132*r64 + 135*r48*y1 + 630*r55*y1 + 126*r55*y2 + 14*r55*y3 + r63*y3 + r65*y3 + r66*y0)/9240 + x1*(27*r125 + 42*r126 + 70*r129 + r130 + r39*r53 + r44*r48 + 27*r53*y2 + 54*r64*y2)/3080 + 3*x2*y3*(r48 + r66 + r8*y3)/220 - y0*(r100*r46 + 18*r114 - 9*r118 - 27*r120 - 18*r122 - 30*r123 + r124 + r131*x2 + r132*x3*y1 + 162*r42*y1 + r50 + 63*r53*x3 + r64*r99)/9240
if __name__ == '__main__':
from fontTools.misc.symfont import x, y, printGreenPen
printGreenPen('MomentsPen', [
('area', 1),
('momentX', x),
('momentY', y),
('momentXX', x**2),
('momentXY', x*y),
('momentYY', y**2),
])
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