| 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), |
| ], |
| ) |
