def __init__(self, element, _pen_x, _pen_y, rX, rY, xRotation, largeArc, sweep, _end_x, _end_y ):
"""
3 coordinate systems
circular coordinates - in this coordinate system, the elipse is circular and unrotated
elements coordinates - circular coordinates * elipse transformation (x*rX and y*Ry, then rotate to generate the elipse)
global coordinates - elements coordinates * upper element transformations
"""
assert not ( _pen_x == _end_x and _pen_y == _end_y )
assert rX <> 0
assert rY <> 0
self._pen_x = _pen_x
self._pen_y = _pen_y
self._end_x = _end_x
self._end_y = _end_y
self.scaling = element.scaling2() #scaling between element and global coordinates
self.rX = rX #in elements coordinates
self.rY = rY #in elements coordinates
self.xRotation = xRotation
self.largeArc = largeArc
self.sweep = sweep
#finding center in circular coordinates
# X = T_ellipse dot Y
# where T_ellipse = [[c -s],[s, c]] dot [[ rX 0],[0 rY]], X is element coordinates, and Y is circular coordinates
##import FreeCAD
##FreeCAD.Console.PrintMessage( 'Xrotation %f\n' % (self.xRotation))
c = cos( xRotation*pi/180)
s = sin( xRotation*pi/180)
T_ellipse = dot( array([[c,-s] ,[s,c]]), array([[ rX, 0], [0, rY] ]))
self.T_ellipse = T_ellipse
#FreeCAD.Console.PrintMessage( 'T %s\n' % (T))
x1,y1 = numpy.linalg.solve(T_ellipse, [_pen_x, _pen_y])
x2,y2 = numpy.linalg.solve(T_ellipse, [_end_x, _end_y])
c_x_Y, c_y_Y = findCircularArcCentrePoint( 1, x1, y1, x2, y2, largeArc==1, sweep==1 )
self.center_circular = array([c_x_Y, c_y_Y])
#now determining dtheta in circular coordinates
#a,b = 1,1
c = ( ( x2-x1 )**2 + ( y2-y1 )**2 ) ** 0.5
dtheta = arccos2( ( 1 + 1 - c**2 ) / ( 2 ) ) #cos rule
#print(x2,x1,y2,y1,c)
#print(dtheta)
if not dtheta >= 0:
raise SvgParseError, "dtheta not >= 0, dtheta %e. locals %s" % (dtheta, locals())
if largeArc:
dtheta = 2*pi - dtheta
if not sweep: # If sweep-flag is '1', then the arc will be drawn in a "positive-angle" direction
dtheta = -dtheta
self.dtheta = dtheta
self.theta_start = atan2( y1 - c_y_Y, x1 - c_x_Y)
self.T_element, self.c_element = element.Transforms()
#print(self.valueAt(0), element.applyTransforms(_pen_x, _pen_y))
#print(self.valueAt(1), element.applyTransforms(_end_x, _end_y))
self.startPoint = self.valueAt(0)
self.endPoint = self.valueAt(1)
self.center = self.applyTransforms( self.center_circular )
self.circular = rX == rY
if self.circular:
self.r = rX
def t_of_position( self, pos ):
pos_element = numpy.linalg.solve( self.T_element, pos - self.c_element )
A = numpy.linalg.solve(self.T_ellipse, pos_element)
B = self.center_circular
C = B + array([cos(self.theta_start), sin(self.theta_start)])
AB = (A - B) / norm(A-B)
BC = C - B
theta = arccos2(dot(AB,BC))
D = array([ A[0] - B[0], A[1] - B[1], 0.0 ])
E = array([ A[0] - C[0], A[1] - C[1], 0.0 ])
F = cross(D,E)
if F[2] < 0:
theta = -theta
#print(theta, self.dtheta, theta / self.dtheta )
return theta / self.dtheta
def t_of_position(self, pos):
pos_element = numpy.linalg.solve(self.T_element, pos - self.c_element)
A = numpy.linalg.solve(self.T_ellipse, pos_element)
B = self.center_circular
C = B + array([cos(self.theta_start), sin(self.theta_start)])
AB = (A - B) / norm(A - B)
BC = C - B
theta = arccos2(dot(AB, BC))
D = array([A[0] - B[0], A[1] - B[1], 0.0])
E = array([A[0] - C[0], A[1] - C[1], 0.0])
F = cross(D, E)
if F[2] < 0:
theta = -theta
#print(theta, self.dtheta, theta / self.dtheta )
return theta / self.dtheta
def __init__(self, element, _pen_x, _pen_y, rX, rY, xRotation, largeArc,
sweep, _end_x, _end_y):
"""
3 coordinate systems
circular coordinates - in this coordinate system, the elipse is circular and unrotated
elements coordinates - circular coordinates * elipse transformation (x*rX and y*Ry, then rotate to generate the elipse)
global coordinates - elements coordinates * upper element transformations
"""
assert not (_pen_x == _end_x and _pen_y == _end_y)
assert rX <> 0
assert rY <> 0
self._pen_x = _pen_x
self._pen_y = _pen_y
self._end_x = _end_x
self._end_y = _end_y
self.scaling = element.scaling2(
) #scaling between element and global coordinates
self.rX = rX #in elements coordinates
self.rY = rY #in elements coordinates
self.xRotation = xRotation
self.largeArc = largeArc
self.sweep = sweep
#finding center in circular coordinates
# X = T_ellipse dot Y
# where T_ellipse = [[c -s],[s, c]] dot [[ rX 0],[0 rY]], X is element coordinates, and Y is circular coordinates
##import FreeCAD
##FreeCAD.Console.PrintMessage( 'Xrotation %f\n' % (self.xRotation))
c = cos(xRotation * pi / 180)
s = sin(xRotation * pi / 180)
T_ellipse = dot(array([[c, -s], [s, c]]), array([[rX, 0], [0, rY]]))
self.T_ellipse = T_ellipse
#FreeCAD.Console.PrintMessage( 'T %s\n' % (T))
x1, y1 = numpy.linalg.solve(T_ellipse, [_pen_x, _pen_y])
x2, y2 = numpy.linalg.solve(T_ellipse, [_end_x, _end_y])
c_x_Y, c_y_Y = findCircularArcCentrePoint(1, x1, y1, x2, y2,
largeArc == 1, sweep == 1)
self.center_circular = array([c_x_Y, c_y_Y])
#now determining dtheta in circular coordinates
#a,b = 1,1
c = ((x2 - x1)**2 + (y2 - y1)**2)**0.5
dtheta = arccos2((1 + 1 - c**2) / (2)) #cos rule
#print(x2,x1,y2,y1,c)
#print(dtheta)
if not dtheta >= 0:
raise SvgParseError, "dtheta not >= 0, dtheta %e. locals %s" % (
dtheta, locals())
if largeArc:
dtheta = 2 * pi - dtheta
if not sweep: # If sweep-flag is '1', then the arc will be drawn in a "positive-angle" direction
dtheta = -dtheta
self.dtheta = dtheta
self.theta_start = arctan2(y1 - c_y_Y, x1 - c_x_Y)
self.T_element, self.c_element = element.Transforms()
#print(self.valueAt(0), element.applyTransforms(_pen_x, _pen_y))
#print(self.valueAt(1), element.applyTransforms(_end_x, _end_y))
self.startPoint = self.valueAt(0)
self.endPoint = self.valueAt(1)
self.center = self.applyTransforms(self.center_circular)
self.circular = rX == rY
if self.circular:
self.r = rX