def getRadialPath(begin, center, end, path):
"Get radial path."
beginComplex = begin.dropAxis()
endComplex = end.dropAxis()
centerComplex = center.dropAxis()
beginMinusCenterComplex = beginComplex - centerComplex
endMinusCenterComplex = endComplex - centerComplex
beginMinusCenterComplexRadius = abs(beginMinusCenterComplex)
endMinusCenterComplexRadius = abs(endMinusCenterComplex)
if beginMinusCenterComplexRadius == 0.0 or endMinusCenterComplexRadius == 0.0:
return [begin]
beginMinusCenterComplex /= beginMinusCenterComplexRadius
endMinusCenterComplex /= endMinusCenterComplexRadius
angleDifference = euclidean.getAngleDifferenceByComplex(
endMinusCenterComplex, beginMinusCenterComplex)
radialPath = []
for point in path:
weightEnd = point.x
weightBegin = 1.0 - weightEnd
weightedRadius = beginMinusCenterComplexRadius * weightBegin + endMinusCenterComplexRadius * weightEnd * (
1.0 + point.y)
radialComplex = weightedRadius * euclidean.getWiddershinsUnitPolar(
angleDifference * point.x) * beginMinusCenterComplex
polygonPoint = center + Vector3(radialComplex.real, radialComplex.imag,
point.z)
radialPath.append(polygonPoint)
return radialPath
def getRadialPath(begin, end, path, segmentCenter):
"Get radial path."
beginComplex = begin.dropAxis()
endComplex = end.dropAxis()
segmentCenterComplex = segmentCenter.dropAxis()
beginMinusCenterComplex = beginComplex - segmentCenterComplex
endMinusCenterComplex = endComplex - segmentCenterComplex
beginMinusCenterComplexRadius = abs(beginMinusCenterComplex)
endMinusCenterComplexRadius = abs(endMinusCenterComplex)
if beginMinusCenterComplexRadius == 0.0 or endMinusCenterComplexRadius == 0.0:
return [begin]
beginMinusCenterComplex /= beginMinusCenterComplexRadius
endMinusCenterComplex /= endMinusCenterComplexRadius
angleDifference = euclidean.getAngleDifferenceByComplex(endMinusCenterComplex, beginMinusCenterComplex)
radialPath = []
for point in path:
weightEnd = point.x
weightBegin = 1.0 - weightEnd
weightedRadius = beginMinusCenterComplexRadius * weightBegin + endMinusCenterComplexRadius * weightEnd * (
1.0 + point.y
)
radialComplex = (
weightedRadius * euclidean.getWiddershinsUnitPolar(angleDifference * point.x) * beginMinusCenterComplex
)
polygonPoint = segmentCenter + Vector3(radialComplex.real, radialComplex.imag, point.z)
radialPath.append(polygonPoint)
return radialPath
def splitPointGetAfter(self, location, nextLocation):
"Fillet a point into arc segments and return the end of the last segment."
if self.filletRadius < 2.0 * self.minimumRadius:
return location
afterSegment = nextLocation - location
afterSegmentComplex = afterSegment.dropAxis(2)
thirdAfterSegmentLength = 0.333 * abs(afterSegmentComplex)
if thirdAfterSegmentLength < self.minimumRadius:
return location
beforeSegment = self.oldLocation - location
beforeSegmentComplex = beforeSegment.dropAxis(2)
thirdBeforeSegmentLength = 0.333 * abs(beforeSegmentComplex)
if thirdBeforeSegmentLength < self.minimumRadius:
return location
extruderOffReversalPoint = self.getExtruderOffReversalPoint(
afterSegment, afterSegmentComplex, beforeSegment,
beforeSegmentComplex, location)
if extruderOffReversalPoint != None:
return extruderOffReversalPoint
bevelRadius = min(thirdAfterSegmentLength, self.filletRadius)
bevelRadius = min(thirdBeforeSegmentLength, bevelRadius)
self.shouldAddLine = False
beforePoint = euclidean.getPointPlusSegmentWithLength(
bevelRadius * abs(beforeSegment) / abs(beforeSegmentComplex),
location, beforeSegment)
self.addLinearMovePoint(self.feedRateMinute, beforePoint)
afterPoint = euclidean.getPointPlusSegmentWithLength(
bevelRadius * abs(afterSegment) / abs(afterSegmentComplex),
location, afterSegment)
afterPointComplex = afterPoint.dropAxis(2)
beforePointComplex = beforePoint.dropAxis(2)
locationComplex = location.dropAxis(2)
midpoint = 0.5 * (afterPoint + beforePoint)
midpointComplex = midpoint.dropAxis(2)
midpointMinusLocationComplex = midpointComplex - locationComplex
midpointLocationLength = abs(midpointMinusLocationComplex)
if midpointLocationLength < 0.01 * self.filletRadius:
self.addLinearMovePoint(self.getCornerFeedRate(), afterPoint)
return afterPoint
midpointAfterPointLength = abs(midpointComplex - afterPointComplex)
midpointCenterLength = midpointAfterPointLength * midpointAfterPointLength / midpointLocationLength
radius = math.sqrt(midpointCenterLength * midpointCenterLength +
midpointAfterPointLength * midpointAfterPointLength)
centerComplex = midpointComplex + midpointMinusLocationComplex * midpointCenterLength / midpointLocationLength
center = Vector3(centerComplex.real, centerComplex.imag, midpoint.z)
afterCenterComplex = afterPointComplex - centerComplex
beforeCenter = beforePoint - center
angleDifference = euclidean.getAngleDifferenceByComplex(
afterCenterComplex, beforeCenter.dropAxis())
self.addArc(angleDifference, afterPoint, beforeCenter, beforePoint,
center)
return afterPoint
def splitPointGetAfter(self, location, nextLocation):
"Fillet a point into arc segments and return the end of the last segment."
if self.filletRadius < 2.0 * self.minimumRadius:
return location
afterSegment = nextLocation - location
afterSegmentComplex = afterSegment.dropAxis(2)
thirdAfterSegmentLength = 0.333 * abs(afterSegmentComplex)
if thirdAfterSegmentLength < self.minimumRadius:
return location
beforeSegment = self.oldLocation - location
beforeSegmentComplex = beforeSegment.dropAxis(2)
thirdBeforeSegmentLength = 0.333 * abs(beforeSegmentComplex)
if thirdBeforeSegmentLength < self.minimumRadius:
return location
extruderOffReversalPoint = self.getExtruderOffReversalPoint(
afterSegment, afterSegmentComplex, beforeSegment, beforeSegmentComplex, location
)
if extruderOffReversalPoint != None:
return extruderOffReversalPoint
bevelRadius = min(thirdAfterSegmentLength, self.filletRadius)
bevelRadius = min(thirdBeforeSegmentLength, bevelRadius)
self.shouldAddLine = False
beforePoint = euclidean.getPointPlusSegmentWithLength(
bevelRadius * abs(beforeSegment) / abs(beforeSegmentComplex), location, beforeSegment
)
self.addLinearMovePoint(self.feedRateMinute, beforePoint)
afterPoint = euclidean.getPointPlusSegmentWithLength(
bevelRadius * abs(afterSegment) / abs(afterSegmentComplex), location, afterSegment
)
afterPointComplex = afterPoint.dropAxis(2)
beforePointComplex = beforePoint.dropAxis(2)
locationComplex = location.dropAxis(2)
midpoint = 0.5 * (afterPoint + beforePoint)
midpointComplex = midpoint.dropAxis(2)
midpointMinusLocationComplex = midpointComplex - locationComplex
midpointLocationLength = abs(midpointMinusLocationComplex)
if midpointLocationLength < 0.01 * self.filletRadius:
self.addLinearMovePoint(self.getCornerFeedRate(), afterPoint)
return afterPoint
midpointAfterPointLength = abs(midpointComplex - afterPointComplex)
midpointCenterLength = midpointAfterPointLength * midpointAfterPointLength / midpointLocationLength
radius = math.sqrt(
midpointCenterLength * midpointCenterLength + midpointAfterPointLength * midpointAfterPointLength
)
centerComplex = midpointComplex + midpointMinusLocationComplex * midpointCenterLength / midpointLocationLength
center = Vector3(centerComplex.real, centerComplex.imag, midpoint.z)
afterCenterComplex = afterPointComplex - centerComplex
beforeCenter = beforePoint - center
angleDifference = euclidean.getAngleDifferenceByComplex(afterCenterComplex, beforeCenter.dropAxis())
self.addArc(angleDifference, afterPoint, beforeCenter, beforePoint, center)
return afterPoint
def getArcComplexes(begin, end, largeArcFlag, radius, sweepFlag, xAxisRotation):
'Get the arc complexes, procedure at http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes'
xAxisRotationComplex = euclidean.getWiddershinsUnitPolar(xAxisRotation)
reverseXAxisRotationComplex = complex(xAxisRotationComplex.real, -xAxisRotationComplex.imag)
beginRotated = begin * reverseXAxisRotationComplex
beginTransformed = complex(beginRotated.real / radius.real, beginRotated.imag / radius.imag)
endRotated = end * reverseXAxisRotationComplex
endTransformed = complex(endRotated.real / radius.real, endRotated.imag / radius.imag)
midpointTransformed = 0.5 * (beginTransformed + endTransformed)
midMinusBeginTransformed = midpointTransformed - beginTransformed
midMinusBeginTransformedLength = abs(midMinusBeginTransformed)
midWiddershinsTransformed = complex(-midMinusBeginTransformed.imag, midMinusBeginTransformed.real)
midWiddershinsLengthSquared = 1.0 - midMinusBeginTransformedLength * midMinusBeginTransformedLength
if midWiddershinsLengthSquared < 0.0:
print('Warning, the radius is too small for getArcComplexes in svgReader')
print(begin)
print(end)
print(radius)
return []
midWiddershinsLength = midWiddershinsLengthSquared
midWiddershinsTransformed *= midWiddershinsLength / abs(midWiddershinsTransformed)
centerTransformed = midpointTransformed
if largeArcFlag == sweepFlag:
centerTransformed -= midWiddershinsTransformed
else:
centerTransformed += midWiddershinsTransformed
beginMinusCenterTransformed = beginTransformed - centerTransformed
beginMinusCenterTransformedLength = abs(beginMinusCenterTransformed)
if beginMinusCenterTransformedLength <= 0.0:
return end
beginAngle = math.atan2(beginMinusCenterTransformed.imag, beginMinusCenterTransformed.real)
endMinusCenterTransformed = endTransformed - centerTransformed
angleDifference = euclidean.getAngleDifferenceByComplex(endMinusCenterTransformed, beginMinusCenterTransformed)
if sweepFlag:
if angleDifference < 0.0:
angleDifference += 2.0 * math.pi
else:
if angleDifference > 0.0:
angleDifference -= 2.0 * math.pi
global globalSideAngle
sides = int(math.ceil(abs(angleDifference) / globalSideAngle))
sideAngle = angleDifference / float(sides)
arcComplexes = []
center = complex(centerTransformed.real * radius.real, centerTransformed.imag * radius.imag) * xAxisRotationComplex
for side in xrange(1, sides):
unitPolar = euclidean.getWiddershinsUnitPolar(beginAngle + float(side) * sideAngle)
circumferential = complex(unitPolar.real * radius.real, unitPolar.imag * radius.imag) * beginMinusCenterTransformedLength
point = center + circumferential * xAxisRotationComplex
arcComplexes.append(point)
arcComplexes.append(end)
return arcComplexes
def getArcComplexes(begin, end, largeArcFlag, radius, sweepFlag, xAxisRotation):
'Get the arc complexes, procedure at http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes'
xAxisRotationComplex = euclidean.getWiddershinsUnitPolar(xAxisRotation)
reverseXAxisRotationComplex = complex(xAxisRotationComplex.real, -xAxisRotationComplex.imag)
beginRotated = begin * reverseXAxisRotationComplex
beginTransformed = complex(beginRotated.real / radius.real, beginRotated.imag / radius.imag)
endRotated = end * reverseXAxisRotationComplex
endTransformed = complex(endRotated.real / radius.real, endRotated.imag / radius.imag)
midpointTransformed = 0.5 * (beginTransformed + endTransformed)
midMinusBeginTransformed = midpointTransformed - beginTransformed
midMinusBeginTransformedLength = abs(midMinusBeginTransformed)
midWiddershinsTransformed = complex(-midMinusBeginTransformed.imag, midMinusBeginTransformed.real)
midWiddershinsLengthSquared = 1.0 - midMinusBeginTransformedLength * midMinusBeginTransformedLength
if midWiddershinsLengthSquared < 0.0:
print('Warning, the radius is too small for getArcComplexes in svgReader')
print(begin)
print(end)
print(radius)
return []
midWiddershinsLength = midWiddershinsLengthSquared
midWiddershinsTransformed *= midWiddershinsLength / abs(midWiddershinsTransformed)
centerTransformed = midpointTransformed
if largeArcFlag == sweepFlag:
centerTransformed -= midWiddershinsTransformed
else:
centerTransformed += midWiddershinsTransformed
beginMinusCenterTransformed = beginTransformed - centerTransformed
beginMinusCenterTransformedLength = abs(beginMinusCenterTransformed)
if beginMinusCenterTransformedLength <= 0.0:
return end
beginAngle = math.atan2(beginMinusCenterTransformed.imag, beginMinusCenterTransformed.real)
endMinusCenterTransformed = endTransformed - centerTransformed
angleDifference = euclidean.getAngleDifferenceByComplex(endMinusCenterTransformed, beginMinusCenterTransformed)
if sweepFlag:
if angleDifference < 0.0:
angleDifference += 2.0 * math.pi
else:
if angleDifference > 0.0:
angleDifference -= 2.0 * math.pi
global globalSideAngle
sides = int(math.ceil(abs(angleDifference) / globalSideAngle))
sideAngle = angleDifference / float(sides)
arcComplexes = []
center = complex(centerTransformed.real * radius.real, centerTransformed.imag * radius.imag) * xAxisRotationComplex
for side in xrange(1, sides):
unitPolar = euclidean.getWiddershinsUnitPolar(beginAngle + float(side) * sideAngle)
circumferential = complex(unitPolar.real * radius.real, unitPolar.imag * radius.imag) * beginMinusCenterTransformedLength
point = center + circumferential * xAxisRotationComplex
arcComplexes.append(point)
arcComplexes.append(end)
return arcComplexes
def getRoundPath(begin, center, close, end, radius, sidesPerRadian):
"Get round path."
beginComplex = begin.dropAxis()
centerComplex = center.dropAxis()
endComplex = end.dropAxis()
beginComplexSegmentLength = abs(centerComplex - beginComplex)
endComplexSegmentLength = abs(centerComplex - endComplex)
minimumRadius = lineation.getMinimumRadius(beginComplexSegmentLength,
endComplexSegmentLength, radius)
if minimumRadius <= close:
return [center]
beginBevel = center + minimumRadius / beginComplexSegmentLength * (begin -
center)
endBevel = center + minimumRadius / endComplexSegmentLength * (end -
center)
beginBevelComplex = beginBevel.dropAxis()
endBevelComplex = endBevel.dropAxis()
midpointComplex = 0.5 * (beginBevelComplex + endBevelComplex)
if radius < 0.0:
centerComplex = midpointComplex + midpointComplex - centerComplex
midpointMinusCenterComplex = midpointComplex - centerComplex
midpointCenterLength = abs(midpointMinusCenterComplex)
midpointEndLength = abs(midpointComplex - endBevelComplex)
midpointCircleCenterLength = midpointEndLength * midpointEndLength / midpointCenterLength
circleRadius = math.sqrt(midpointCircleCenterLength *
midpointCircleCenterLength +
midpointEndLength * midpointEndLength)
circleCenterComplex = midpointComplex + midpointMinusCenterComplex * midpointCircleCenterLength / midpointCenterLength
circleCenter = Vector3(circleCenterComplex.real, circleCenterComplex.imag,
center.z)
endMinusCircleCenterComplex = endBevelComplex - circleCenterComplex
beginMinusCircleCenter = beginBevel - circleCenter
beginMinusCircleCenterComplex = beginMinusCircleCenter.dropAxis()
angleDifference = euclidean.getAngleDifferenceByComplex(
endMinusCircleCenterComplex, beginMinusCircleCenterComplex)
steps = int(math.ceil(abs(angleDifference) * sidesPerRadian))
stepPlaneAngle = euclidean.getWiddershinsUnitPolar(angleDifference /
float(steps))
deltaZStep = (end.z - begin.z) / float(steps)
roundPath = [beginBevel]
for step in xrange(1, steps):
beginMinusCircleCenterComplex = beginMinusCircleCenterComplex * stepPlaneAngle
arcPointComplex = circleCenterComplex + beginMinusCircleCenterComplex
arcPoint = Vector3(arcPointComplex.real, arcPointComplex.imag,
begin.z + deltaZStep * step)
roundPath.append(arcPoint)
return roundPath + [endBevel]
def getRoundPath(begin, center, close, end, radius, sidesPerRadian):
"Get round path."
beginComplex = begin.dropAxis()
centerComplex = center.dropAxis()
endComplex = end.dropAxis()
beginComplexSegmentLength = abs(centerComplex - beginComplex)
endComplexSegmentLength = abs(centerComplex - endComplex)
minimumRadius = lineation.getMinimumRadius(beginComplexSegmentLength, endComplexSegmentLength, radius)
if minimumRadius <= close:
return [center]
beginBevel = center + minimumRadius / beginComplexSegmentLength * (begin - center)
endBevel = center + minimumRadius / endComplexSegmentLength * (end - center)
beginBevelComplex = beginBevel.dropAxis()
endBevelComplex = endBevel.dropAxis()
midpointComplex = 0.5 * (beginBevelComplex + endBevelComplex)
if radius < 0.0:
centerComplex = midpointComplex + midpointComplex - centerComplex
midpointMinusCenterComplex = midpointComplex - centerComplex
midpointCenterLength = abs(midpointMinusCenterComplex)
midpointEndLength = abs(midpointComplex - endBevelComplex)
midpointCircleCenterLength = midpointEndLength * midpointEndLength / midpointCenterLength
circleRadius = math.sqrt(
midpointCircleCenterLength * midpointCircleCenterLength + midpointEndLength * midpointEndLength
)
circleCenterComplex = (
midpointComplex + midpointMinusCenterComplex * midpointCircleCenterLength / midpointCenterLength
)
circleCenter = Vector3(circleCenterComplex.real, circleCenterComplex.imag, center.z)
endMinusCircleCenterComplex = endBevelComplex - circleCenterComplex
beginMinusCircleCenter = beginBevel - circleCenter
beginMinusCircleCenterComplex = beginMinusCircleCenter.dropAxis()
angleDifference = euclidean.getAngleDifferenceByComplex(endMinusCircleCenterComplex, beginMinusCircleCenterComplex)
steps = int(math.ceil(abs(angleDifference) * sidesPerRadian))
stepPlaneAngle = euclidean.getWiddershinsUnitPolar(angleDifference / float(steps))
deltaZStep = (end.z - begin.z) / float(steps)
roundPath = [beginBevel]
for step in xrange(1, steps):
beginMinusCircleCenterComplex = beginMinusCircleCenterComplex * stepPlaneAngle
arcPointComplex = circleCenterComplex + beginMinusCircleCenterComplex
arcPoint = Vector3(arcPointComplex.real, arcPointComplex.imag, begin.z + deltaZStep * step)
roundPath.append(arcPoint)
return roundPath + [endBevel]
def getArcComplexes( begin, end, largeArcFlag, radius, sweepFlag, xAxisRotation ): 'Get the arc complexes, procedure at http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes' beginTransformed = complex( begin.real / radius.real, begin.imag / radius.imag ) endTransformed = complex( end.real / radius.real, end.imag / radius.imag ) midpointTransformed = 0.5 * ( beginTransformed + endTransformed ) midMinusBeginTransformed = midpointTransformed - beginTransformed midMinusBeginTransformedLength = abs( midMinusBeginTransformed ) midWiddershinsTransformed = complex( - midMinusBeginTransformed.imag, midMinusBeginTransformed.real ) midWiddershinsLength = math.sqrt( 1.0 - midMinusBeginTransformedLength * midMinusBeginTransformedLength ) midWiddershinsTransformed *= midWiddershinsLength / abs( midWiddershinsTransformed ) centerTransformed = midpointTransformed if largeArcFlag == sweepFlag: centerTransformed -= midWiddershinsTransformed else: centerTransformed += midWiddershinsTransformed beginMinusCenterTransformed = beginTransformed - centerTransformed beginAngle = math.atan2( beginMinusCenterTransformed.imag, beginMinusCenterTransformed.real ) endMinusCenterTransformed = endTransformed - centerTransformed angleDifference = euclidean.getAngleDifferenceByComplex( endMinusCenterTransformed, beginMinusCenterTransformed ) if sweepFlag: if angleDifference < 0.0: angleDifference += 2.0 * math.pi else: if angleDifference > 0.0: angleDifference -= 2.0 * math.pi global globalSideAngle sides = int( math.ceil( abs( angleDifference ) / globalSideAngle ) ) sideAngle = angleDifference / sides arcComplexes = [] center = complex(centerTransformed.real * radius.real, centerTransformed.imag * radius.imag) for side in xrange( 1, sides ): unitPolar = euclidean.getWiddershinsUnitPolar( beginAngle + float(side) * sideAngle ) point = center + complex( unitPolar.real * radius.real, unitPolar.imag * radius.imag ) arcComplexes.append( point ) arcComplexes.append( end ) return arcComplexes
def getArcComplexes(begin, end, largeArcFlag, radius, sweepFlag, xAxisRotation):
'Get the arc complexes, procedure at http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes'
if begin == end:
print('Warning, begin equals end in getArcComplexes in svgReader')
print(begin)
print(end)
return []
if radius.imag < 0.0:
print('Warning, radius.imag is less than zero in getArcComplexes in svgReader')
print(radius)
radius = complex(radius.real, abs(radius.imag))
if radius.real < 0.0:
print('Warning, radius.real is less than zero in getArcComplexes in svgReader')
print(radius)
radius = complex(abs(radius.real), radius.imag)
if radius.imag <= 0.0:
print('Warning, radius.imag is too small for getArcComplexes in svgReader')
print(radius)
return [end]
if radius.real <= 0.0:
print('Warning, radius.real is too small for getArcComplexes in svgReader')
print(radius)
return [end]
xAxisRotationComplex = euclidean.getWiddershinsUnitPolar(xAxisRotation)
reverseXAxisRotationComplex = complex(xAxisRotationComplex.real, -xAxisRotationComplex.imag)
beginRotated = begin * reverseXAxisRotationComplex
endRotated = end * reverseXAxisRotationComplex
beginTransformed = complex(beginRotated.real / radius.real, beginRotated.imag / radius.imag)
endTransformed = complex(endRotated.real / radius.real, endRotated.imag / radius.imag)
midpointTransformed = 0.5 * (beginTransformed + endTransformed)
midMinusBeginTransformed = midpointTransformed - beginTransformed
midMinusBeginTransformedLength = abs(midMinusBeginTransformed)
if midMinusBeginTransformedLength > 1.0:
print('The ellipse radius is too small for getArcComplexes in svgReader.')
print('So the ellipse will be scaled to fit, according to the formulas in "Step 3: Ensure radii are large enough" of:')
print('http://www.w3.org/TR/SVG/implnote.html#ArcCorrectionOutOfRangeRadii')
print('')
radius *= midMinusBeginTransformedLength
beginTransformed /= midMinusBeginTransformedLength
endTransformed /= midMinusBeginTransformedLength
midpointTransformed /= midMinusBeginTransformedLength
midMinusBeginTransformed /= midMinusBeginTransformedLength
midMinusBeginTransformedLength = 1.0
midWiddershinsTransformed = complex(-midMinusBeginTransformed.imag, midMinusBeginTransformed.real)
midWiddershinsLengthSquared = 1.0 - midMinusBeginTransformedLength * midMinusBeginTransformedLength
if midWiddershinsLengthSquared < 0.0:
midWiddershinsLengthSquared = 0.0
midWiddershinsLength = math.sqrt(midWiddershinsLengthSquared)
midWiddershinsTransformed *= midWiddershinsLength / abs(midWiddershinsTransformed)
centerTransformed = midpointTransformed
if largeArcFlag == sweepFlag:
centerTransformed -= midWiddershinsTransformed
else:
centerTransformed += midWiddershinsTransformed
beginMinusCenterTransformed = beginTransformed - centerTransformed
beginMinusCenterTransformedLength = abs(beginMinusCenterTransformed)
if beginMinusCenterTransformedLength <= 0.0:
return end
beginAngle = math.atan2(beginMinusCenterTransformed.imag, beginMinusCenterTransformed.real)
endMinusCenterTransformed = endTransformed - centerTransformed
angleDifference = euclidean.getAngleDifferenceByComplex(endMinusCenterTransformed, beginMinusCenterTransformed)
if sweepFlag:
if angleDifference < 0.0:
angleDifference += 2.0 * math.pi
else:
if angleDifference > 0.0:
angleDifference -= 2.0 * math.pi
global globalSideAngle
sides = int(math.ceil(abs(angleDifference) / globalSideAngle))
sideAngle = angleDifference / float(sides)
arcComplexes = []
center = complex(centerTransformed.real * radius.real, centerTransformed.imag * radius.imag) * xAxisRotationComplex
for side in xrange(1, sides):
unitPolar = euclidean.getWiddershinsUnitPolar(beginAngle + float(side) * sideAngle)
circumferential = complex(unitPolar.real * radius.real, unitPolar.imag * radius.imag) * beginMinusCenterTransformedLength
point = center + circumferential * xAxisRotationComplex
arcComplexes.append(point)
arcComplexes.append(end)
return arcComplexes
def getArcComplexes(begin, end, largeArcFlag, radius, sweepFlag,
xAxisRotation):
'Get the arc complexes, procedure at http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes'
if begin == end:
print('Warning, begin equals end in getArcComplexes in svgReader')
print(begin)
print(end)
return []
if radius.imag < 0.0:
print(
'Warning, radius.imag is less than zero in getArcComplexes in svgReader'
)
print(radius)
radius = complex(radius.real, abs(radius.imag))
if radius.real < 0.0:
print(
'Warning, radius.real is less than zero in getArcComplexes in svgReader'
)
print(radius)
radius = complex(abs(radius.real), radius.imag)
if radius.imag <= 0.0:
print(
'Warning, radius.imag is too small for getArcComplexes in svgReader'
)
print(radius)
return [end]
if radius.real <= 0.0:
print(
'Warning, radius.real is too small for getArcComplexes in svgReader'
)
print(radius)
return [end]
xAxisRotationComplex = euclidean.getWiddershinsUnitPolar(xAxisRotation)
reverseXAxisRotationComplex = complex(xAxisRotationComplex.real,
-xAxisRotationComplex.imag)
beginRotated = begin * reverseXAxisRotationComplex
endRotated = end * reverseXAxisRotationComplex
beginTransformed = complex(beginRotated.real / radius.real,
beginRotated.imag / radius.imag)
endTransformed = complex(endRotated.real / radius.real,
endRotated.imag / radius.imag)
midpointTransformed = 0.5 * (beginTransformed + endTransformed)
midMinusBeginTransformed = midpointTransformed - beginTransformed
midMinusBeginTransformedLength = abs(midMinusBeginTransformed)
if midMinusBeginTransformedLength > 1.0:
print(
'The ellipse radius is too small for getArcComplexes in svgReader.'
)
print(
'So the ellipse will be scaled to fit, according to the formulas in "Step 3: Ensure radii are large enough" of:'
)
print(
'http://www.w3.org/TR/SVG/implnote.html#ArcCorrectionOutOfRangeRadii'
)
print('')
radius *= midMinusBeginTransformedLength
beginTransformed /= midMinusBeginTransformedLength
endTransformed /= midMinusBeginTransformedLength
midpointTransformed /= midMinusBeginTransformedLength
midMinusBeginTransformed /= midMinusBeginTransformedLength
midMinusBeginTransformedLength = 1.0
midWiddershinsTransformed = complex(-midMinusBeginTransformed.imag,
midMinusBeginTransformed.real)
midWiddershinsLengthSquared = 1.0 - midMinusBeginTransformedLength * midMinusBeginTransformedLength
if midWiddershinsLengthSquared < 0.0:
midWiddershinsLengthSquared = 0.0
midWiddershinsLength = math.sqrt(midWiddershinsLengthSquared)
midWiddershinsTransformed *= midWiddershinsLength / abs(
midWiddershinsTransformed)
centerTransformed = midpointTransformed
if largeArcFlag == sweepFlag:
centerTransformed -= midWiddershinsTransformed
else:
centerTransformed += midWiddershinsTransformed
beginMinusCenterTransformed = beginTransformed - centerTransformed
beginMinusCenterTransformedLength = abs(beginMinusCenterTransformed)
if beginMinusCenterTransformedLength <= 0.0:
return end
beginAngle = math.atan2(beginMinusCenterTransformed.imag,
beginMinusCenterTransformed.real)
endMinusCenterTransformed = endTransformed - centerTransformed
angleDifference = euclidean.getAngleDifferenceByComplex(
endMinusCenterTransformed, beginMinusCenterTransformed)
if sweepFlag:
if angleDifference < 0.0:
angleDifference += 2.0 * math.pi
else:
if angleDifference > 0.0:
angleDifference -= 2.0 * math.pi
global globalSideAngle
sides = int(math.ceil(abs(angleDifference) / globalSideAngle))
sideAngle = angleDifference / float(sides)
arcComplexes = []
center = complex(
centerTransformed.real * radius.real,
centerTransformed.imag * radius.imag) * xAxisRotationComplex
for side in xrange(1, sides):
unitPolar = euclidean.getWiddershinsUnitPolar(beginAngle +
float(side) * sideAngle)
circumferential = complex(
unitPolar.real * radius.real,
unitPolar.imag * radius.imag) * beginMinusCenterTransformedLength
point = center + circumferential * xAxisRotationComplex
arcComplexes.append(point)
arcComplexes.append(end)
return arcComplexes