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path: root/Lib/fontTools/pens/momentsPen.py
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-rw-r--r--Lib/fontTools/pens/momentsPen.py1339
1 files changed, 859 insertions, 480 deletions
diff --git a/Lib/fontTools/pens/momentsPen.py b/Lib/fontTools/pens/momentsPen.py
index 7cd87919..dab0d10e 100644
--- a/Lib/fontTools/pens/momentsPen.py
+++ b/Lib/fontTools/pens/momentsPen.py
@@ -1,503 +1,882 @@
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
+ import cython
+
+ COMPILED = cython.compiled
+except (AttributeError, 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
+ 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 __init__(self, glyphset=None):
- BasePen.__init__(self, glyphset)
+ def _moveTo(self, p0):
+ self.__startPoint = p0
- self.area = 0
- self.momentX = 0
- self.momentY = 0
- self.momentXX = 0
- self.momentXY = 0
- self.momentYY = 0
+ def _closePath(self):
+ p0 = self._getCurrentPoint()
+ if p0 != self.__startPoint:
+ self._lineTo(self.__startPoint)
- def _moveTo(self, p0):
- self.__startPoint = p0
+ 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.")
- def _closePath(self):
- p0 = self._getCurrentPoint()
- if p0 != self.__startPoint:
- self._lineTo(self.__startPoint)
+ @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
- 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."
- )
+ 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
- @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
+ 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
+ )
- 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
+ @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
- 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
+ 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
- @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
+ 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
+ )
- 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
+ @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
- 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
+ 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
- @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
+ 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
+ )
- 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
-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),
- ])
+ printGreenPen(
+ "MomentsPen",
+ [
+ ("area", 1),
+ ("momentX", x),
+ ("momentY", y),
+ ("momentXX", x**2),
+ ("momentXY", x * y),
+ ("momentYY", y**2),
+ ],
+ )
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-08 06:21:32 +0000