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path: root/Lib/fontTools/pens/momentsPen.py
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-rw-r--r--Lib/fontTools/pens/momentsPen.py662
1 files changed, 434 insertions, 228 deletions
diff --git a/Lib/fontTools/pens/momentsPen.py b/Lib/fontTools/pens/momentsPen.py
index 8c90f70a..7cd87919 100644
--- a/Lib/fontTools/pens/momentsPen.py
+++ b/Lib/fontTools/pens/momentsPen.py
@@ -1,14 +1,19 @@
-"""Pen calculating 0th, 1st, and 2nd moments of area of glyph shapes.
-This is low-level, autogenerated pen. Use statisticsPen instead."""
-from fontTools.pens.basePen import BasePen
+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 OpenContourError(NotImplementedError):
- pass
+__all__ = ["MomentsPen"]
class MomentsPen(BasePen):
@@ -33,10 +38,26 @@ class MomentsPen(BasePen):
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
@@ -44,246 +65,431 @@ class MomentsPen(BasePen):
r0 = x1*y0
r1 = x1*y1
r2 = x1**2
- r3 = x0**2
- r4 = 2*y0
- r5 = y0 - y1
- r6 = r5*x0
- r7 = y0**2
- r8 = y1**2
- r9 = x1**3
- r10 = r4*y1
+ 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 - r2*y1/3 + r3*(r4 + y1)/6 - r6*x1/6
- self.momentY += -r0*y1/6 - r7*x1/6 - r8*x1/6 + x0*(r7 + r8 + y0*y1)/6
- self.momentXX += -r2*r6/12 - r3*r5*x1/12 - r9*y0/12 - r9*y1/4 + x0**3*(3*y0 + y1)/12
- self.momentXY += -r10*r2/24 - r2*r7/24 - r2*r8/8 + r3*(r10 + 3*r7 + r8)/24 - x0*x1*(r7 - r8)/12
- self.momentYY += -r0*r8/12 - r1*r7/12 - r11*x1/12 - r12*x1/12 + x0*(r11 + r12 + r7*y1 + r8*y0)/12
+ 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*x1
- r1 = r0*y2
- r2 = 2*y1
- r3 = r2*x2
- r4 = 3*y2
- r5 = r4*x2
- r6 = 3*y0
- r7 = x1**2
- r8 = 2*y2
- r9 = x2**2
- r10 = 4*y1
- r11 = 10*y2
- r12 = r0*x2
- r13 = x0**2
- r14 = 10*y0
- r15 = x2*y2
- r16 = r0*y1 + r15
- r17 = 4*x1
- r18 = x2*y0
- r19 = r10*r15
- r20 = y1**2
- r21 = 2*r20
- r22 = y2**2
- r23 = r22*x2
- r24 = 5*r23
- r25 = y0**2
- r26 = y0*y2
- r27 = 5*r25
- r28 = 8*x1**3
- r29 = x2**3
- r30 = 30*y1
- r31 = 6*y1
- r32 = 10*r9*x1
- r33 = 4*r7
- r34 = 5*y2
- r35 = 12*r7
- r36 = r5 + 20*x1*y1
- r37 = 30*x1
- r38 = 12*x1
- r39 = 20*r7
- r40 = 8*r7*y1
- r41 = r34*r9
- r42 = 60*y1
- r43 = 20*r20
- r44 = 4*r20
- r45 = 15*r22
- r46 = r38*x2
- r47 = y1*y2
- r48 = 8*r20*x1 + r24
- r49 = 6*x1
- r50 = 8*y1**3
- r51 = y2**3
- r52 = y0**3
- r53 = 10*y1
- r54 = 12*y1
- r55 = 12*r20
+ 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 - r5/6 + x0*(r2 + r6 + y2)/6 - y0*(r0 + x2)/6
- self.momentX += -r10*r9/30 - r11*r9/30 - r12*(-r8 + y1)/30 + r13*(r10 + r14 + y2)/30 + r7*r8/30 + x0*(r1 + r16 - r17*y0 - r18)/30 - y0*(r12 + 2*r7 + r9)/30
- self.momentY += r1*(r8 + y1)/30 - r19/30 - r21*x2/30 - r24/30 - r25*(r17 + x2)/30 + x0*(r10*y0 + r2*y2 + r21 + r22 + r26 + r27)/30 - y0*(r16 + r3)/30
- self.momentXX += r13*(r11*x1 - 5*r18 + r3 + r36 - r37*y0)/420 + r28*y2/420 - r29*r30/420 - r29*y2/4 - r32*(r2 - r4)/420 - r33*x2*(r2 - r34)/420 + x0**3*(r31 + 21*y0 + y2)/84 - x0*(-r15*r38 + r18*r38 + r2*r9 - r35*y2 + r39*y0 - r40 - r41 + r6*r9)/420 - y0*(r28 + 5*r29 + r32 + r35*x2)/420
- self.momentXY += r13*(r14*y2 + 3*r22 + 105*r25 + r42*y0 + r43 + 12*r47)/840 - r17*x2*(r44 - r45)/840 - r22*r9/8 - r25*(r39 + r46 + 3*r9)/840 + r33*y2*(r10 + r34)/840 - r42*r9*y2/840 - r43*r9/840 + x0*(-r10*r18 + r17*r26 + r19 + r22*r49 - r25*r37 - r27*x2 + r38*r47 + r48)/420 - y0*(r15*r17 + r31*r9 + r40 + r41 + r46*y1)/420
- self.momentYY += r1*(r11*y1 + r44 + r45)/420 - r15*r43/420 - r23*r30/420 - r25*(r1 + r36 + r53*x2)/420 - r50*x2/420 - r51*x2/12 - r52*(r49 + x2)/84 + x0*(r22*r53 + r22*r6 + r25*r30 + r25*r34 + r26*r54 + r43*y0 + r50 + 5*r51 + 35*r52 + r55*y2)/420 - y0*(-r0*r22 + r15*r54 + r48 + r55*x2)/420
+ 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*x2
- r1 = r0*y3
- r2 = 6*y2
- r3 = 10*y3
- r4 = r3*x3
- r5 = 3*x1
- r6 = 3*y1
- r7 = 6*x1
- r8 = 3*x2
- r9 = 6*y1
- r10 = 3*y2
- r11 = x2**2
- r12 = r11*y3
- r13 = 45*r12
- r14 = x3**2
- r15 = r14*y2
- r16 = r14*y3
- r17 = x2*x3
- r18 = 15*r17
- r19 = 7*y3
- r20 = x1**2
- r21 = 9*r20
- r22 = x0**2
- r23 = 21*y1
- r24 = 9*r11
- r25 = 9*x2
- r26 = x2*y3
- r27 = 15*r26
- r28 = -r25*y1 + r27
- r29 = r25*y2
- r30 = r9*x3
- r31 = 45*x1
- r32 = x1*x3
- r33 = 45*r20
- r34 = 5*r14
- r35 = x2*y2
- r36 = 18*r35
- r37 = 5*x3
- r38 = r37*y3
- r39 = r31*y1 + r36 + r38
- r40 = x1*y0
- r41 = x1*y3
- r42 = x2*y0
- r43 = x3*y1
- r44 = r10*x3
- r45 = x3*y2*y3
- r46 = y2**2
- r47 = 45*r46
- r48 = r47*x3
- r49 = y3**2
+ 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 = y1**2
- r52 = 9*r51
- r53 = y0**2
- r54 = 21*x1
- r55 = x3*y2
- r56 = 15*r55
- r57 = 9*y2
- r58 = y2*y3
- r59 = 15*r58
- r60 = 9*r46
- r61 = 3*y3
- r62 = 45*y1
- r63 = r8*y3
- r64 = y0*y1
- r65 = y0*y2
- r66 = 30*r65
- r67 = 5*y3
- r68 = y1*y3
- r69 = 45*r51
- r70 = 5*r49
- r71 = x2**3
- r72 = x3**3
- r73 = 126*x3
- r74 = x1**3
- r75 = r14*x2
- r76 = 63*r11
- r77 = r76*x3
- r78 = 15*r35
- r79 = r19*x3
- r80 = x1*y1
- r81 = 63*r35
- r82 = r38 + 378*r80 + r81
- r83 = x1*y2
- r84 = x2*y1
- r85 = x3*y0
- r86 = x2*x3*y1
- r87 = x2*x3*y3
- r88 = r11*y2
- r89 = 27*r88
- r90 = 42*y3
- r91 = r14*r90
- r92 = 90*x1*x2
- r93 = 189*x2
- r94 = 30*x1*x3
- r95 = 14*r16 + 126*r20*y1 + 45*r88 + r94*y2
- r96 = x1*x2
- r97 = 252*r96
- r98 = x1*x2*y2
- r99 = 42*r32
- r100 = x1*x3*y1
- r101 = 30*r17
- r102 = 18*r17
- r103 = 378*r20
- r104 = 189*y2
- r105 = r20*y3
- r106 = r11*y1
- r107 = r14*y1
- r108 = 378*r46
- r109 = 252*y2
- r110 = y1*y2
- r111 = x2*x3*y2
- r112 = y0*y3
- r113 = 378*r51
- r114 = 63*r46
- r115 = 27*x2
- r116 = r115*r46 + 42*r50
- r117 = x2*y1*y3
- r118 = x3*y1*y2
- r119 = r49*x2
- r120 = r51*x3
- r121 = x3*y3
- r122 = 14*x3
- r123 = 30*r117 + r122*r49 + r47*x2 + 126*r51*x1
- r124 = x1*y1*y3
- r125 = x1*y2*y3
- r126 = x2*y1*y2
- r127 = 54*y3
- r128 = 21*r55
- r129 = 630*r53
- r130 = r46*x1
- r131 = r49*x1
- r132 = 126*r53
- r133 = y2**3
- r134 = y3**3
- r135 = 630*r49
- r136 = y1**3
- r137 = y0**3
- r138 = r114*y3 + r23*r49
- r139 = r49*y2
+ 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 - r2*x3/20 - r4/20 + r5*(y2 + y3)/20 - r6*(x2 + x3)/20 + x0*(r10 + r9 + 10*y0 + y3)/20 - y0*(r7 + r8 + x3)/20
- self.momentX += r13/840 - r15/8 - r16/3 - r18*(r10 - r19)/840 + r21*(r10 + 2*y3)/840 + r22*(r2 + r23 + 56*y0 + y3)/168 + r5*(r28 + r29 - r30 + r4)/840 - r6*(10*r14 + r18 + r24)/840 + x0*(12*r26 + r31*y2 - r37*y0 + r39 - 105*r40 + 15*r41 - 30*r42 - 3*r43 + r44)/840 - y0*(18*r11 + r18 + r31*x2 + 12*r32 + r33 + r34)/840
- self.momentY += r27*(r10 + r19)/840 - r45/8 - r48/840 + r5*(10*r49 + r57*y1 + r59 + r60 + r9*y3)/840 - r50/6 - r52*(r8 + 2*x3)/840 - r53*(r0 + r54 + x3)/168 - r6*(r29 + r4 + r56)/840 + x0*(18*r46 + 140*r53 + r59 + r62*y2 + 105*r64 + r66 + r67*y0 + 12*r68 + r69 + r70)/840 - y0*(r39 + 15*r43 + 12*r55 - r61*x1 + r62*x2 + r63)/840
- self.momentXX += -r11*r73*(-r61 + y2)/9240 + r21*(r28 - r37*y1 + r44 + r78 + r79)/9240 + r22*(21*r26 - 630*r40 + 42*r41 - 126*r42 + r57*x3 + r82 + 210*r83 + 42*r84 - 14*r85)/9240 - r5*(r11*r62 + r14*r23 + 14*r15 - r76*y3 + 54*r86 - 84*r87 - r89 - r91)/9240 - r6*(27*r71 + 42*r72 + 70*r75 + r77)/9240 + 3*r71*y3/220 - 3*r72*y2/44 - r72*y3/4 + 3*r74*(r57 + r67)/3080 - r75*(378*y2 - 630*y3)/9240 + x0**3*(r57 + r62 + 165*y0 + y3)/660 + x0*(-18*r100 - r101*y0 - r101*y1 + r102*y2 - r103*y0 + r104*r20 + 63*r105 - 27*r106 - 9*r107 + r13 - r34*y0 - r76*y0 + 42*r87 + r92*y3 + r94*y3 + r95 - r97*y0 + 162*r98 - r99*y0)/9240 - y0*(135*r11*x1 + r14*r54 + r20*r93 + r33*x3 + 45*r71 + 14*r72 + 126*r74 + 42*r75 + r77 + r92*x3)/9240
- self.momentXY += -r108*r14/18480 + r12*(r109 + 378*y3)/18480 - r14*r49/8 - 3*r14*r58/44 - r17*(252*r46 - 1260*r49)/18480 + r21*(18*r110 + r3*y1 + 15*r46 + 7*r49 + 18*r58)/18480 + r22*(252*r110 + 28*r112 + r113 + r114 + 2310*r53 + 30*r58 + 1260*r64 + 252*r65 + 42*r68 + r70)/18480 - r52*(r102 + 15*r11 + 7*r14)/18480 - r53*(r101 + r103 + r34 + r76 + r97 + r99)/18480 + r7*(-r115*r51 + r116 + 18*r117 - 18*r118 + 42*r119 - 15*r120 + 28*r45 + r81*y3)/18480 - r9*(63*r111 + 42*r15 + 28*r87 + r89 + r91)/18480 + x0*(r1*y0 + r104*r80 + r112*r54 + 21*r119 - 9*r120 - r122*r53 + r123 + 54*r124 + 60*r125 + 54*r126 + r127*r35 + r128*y3 - r129*x1 + 81*r130 + 15*r131 - r132*x2 - r2*r85 - r23*r85 + r30*y3 + 84*r40*y2 - 84*r42*y1 + r60*x3)/9240 - y0*(54*r100 - 9*r105 + 81*r106 + 15*r107 + 54*r111 + r121*r7 + 21*r15 + r24*y3 + 60*r86 + 21*r87 + r95 + 189*r96*y1 + 54*r98)/9240
- self.momentYY += -r108*r121/9240 - r133*r73/9240 - r134*x3/12 - r135*r55/9240 - 3*r136*(r25 + r37)/3080 - r137*(r25 + r31 + x3)/660 + r26*(r135 + 126*r46 + 378*y2*y3)/9240 + r5*(r110*r127 + 27*r133 + 42*r134 + r138 + 70*r139 + r46*r62 + 27*r51*y2 + 15*r51*y3)/9240 - r52*(r56 + r63 + r78 + r79)/9240 - r53*(r128 + r25*y3 + 42*r43 + r82 + 42*r83 + 210*r84)/9240 - r6*(r114*x3 + r116 - 14*r119 + 84*r45)/9240 + x0*(r104*r51 + r109*r64 + 90*r110*y3 + r113*y0 + r114*y0 + r129*y1 + r132*y2 + 45*r133 + 14*r134 + 126*r136 + 770*r137 + r138 + 42*r139 + 135*r46*y1 + 14*r53*y3 + r64*r90 + r66*y3 + r69*y3 + r70*y0)/9240 - y0*(90*r118 + 63*r120 + r123 - 18*r124 - 30*r125 + 162*r126 - 27*r130 - 9*r131 + r36*y3 + 30*r43*y3 + 42*r45 + r48 + r51*r93)/9240
+ 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
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-08 10:35:34 +0000