882 lines
25 KiB
Python
882 lines
25 KiB
Python
|
from fontTools.pens.basePen import BasePen, OpenContourError
|
||
|
|
|
||
|
|
try:
|
||
|
|
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
|
||
|
|
|
||
|
|
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:
|
||
|
|
raise OpenContourError("Glyph statistics 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),
|
||
|
|
],
|
||
|
|
)
|