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Use polar angle for ellipse bounds

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jan 2017-08-29 15:51:00 -07:00
parent fdd18ca7d8
commit 8256a540dc
1 changed files with 27 additions and 12 deletions
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39
masque/shapes/arc.py
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@ -74,7 +74,7 @@ class Arc(Shape):
def angles(self) -> vector2: def angles(self) -> vector2:
""" """
Return the start and stop angles [a_start, a_stop]. Return the start and stop angles [a_start, a_stop].
Angles are measured from x-axis after rotation, and are stored mod 2*pi Angles are measured from x-axis after rotation
:return: [a_start, a_stop] :return: [a_start, a_stop]
""" """
@ -168,7 +168,12 @@ class Arc(Shape):
' (default was also overridden)') ' (default was also overridden)')
r0, r1 = self.radii r0, r1 = self.radii
a0, a1 = self.angles
# Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
a0, a1 = (numpy.arctan2(r0*numpy.sin(a), r1*numpy.cos(a)) for a in self.angles)
sign = numpy.sign(self.angles[1] - self.angles[0])
if sign != numpy.sign(a1 - a0):
a1 += sign * 2 * pi
# Approximate perimeter # Approximate perimeter
# Ramanujan, S., "Modular Equations and Approximations to ," # Ramanujan, S., "Modular Equations and Approximations to ,"
@ -201,8 +206,6 @@ class Arc(Shape):
return [poly] return [poly]
def get_bounds(self) -> numpy.ndarray: def get_bounds(self) -> numpy.ndarray:
a = self.angles - 0.5 * pi
mins = [] mins = []
maxs = [] maxs = []
for sgn in (+1, -1): for sgn in (+1, -1):
@ -210,33 +213,45 @@ class Arc(Shape):
rx = self.radius_x + wh rx = self.radius_x + wh
ry = self.radius_y + wh ry = self.radius_y + wh
# Create paremeter 'a' for parametrized ellipse
a0, a1 = (numpy.arctan2(rx*numpy.sin(a), ry*numpy.cos(a)) for a in self.angles)
sign = numpy.sign(self.angles[1] - self.angles[0])
if sign != numpy.sign(a1 - a0):
a1 += sign * 2 * pi
a = numpy.array((a0, a1))
a0_offset = a0 - (a0 % (2 * pi))
sin_r = numpy.sin(self.rotation) sin_r = numpy.sin(self.rotation)
cos_r = numpy.cos(self.rotation) cos_r = numpy.cos(self.rotation)
tan_r = numpy.tan(self.rotation) tan_r = numpy.tan(self.rotation)
sin_a = numpy.sin(a) sin_a = numpy.sin(a)
cos_a = numpy.cos(a) cos_a = numpy.cos(a)
xpt = numpy.arctan(-ry / rx * tan_r) # Cutoff angles
ypt = numpy.arctan(+ry / rx / tan_r) xpt = (-self.rotation) % (2 * pi) + a0_offset
xnt = numpy.arcsin(numpy.sin(xpt - pi)) ypt = self.rotation % (2 * pi) + a0_offset
ynt = numpy.arcsin(numpy.sin(ypt - pi)) xnt = (xpt - pi) % (2 * pi) + a0_offset
ynt = (ypt - pi) % (2 * pi) + a0_offset
# Points along coordinate axes
xr = numpy.sqrt((rx * cos_r) ** 2 + (ry * sin_r) ** 2) xr = numpy.sqrt((rx * cos_r) ** 2 + (ry * sin_r) ** 2)
yr = numpy.sqrt((rx * sin_r) ** 2 + (ry * cos_r) ** 2) yr = numpy.sqrt((rx * sin_r) ** 2 + (ry * cos_r) ** 2)
# Arc endpoints
xn, xp = sorted(rx * cos_r * cos_a - ry * sin_r * sin_a) xn, xp = sorted(rx * cos_r * cos_a - ry * sin_r * sin_a)
yn, yp = sorted(rx * sin_r * cos_a - ry * cos_r * sin_a) yn, yp = sorted(rx * sin_r * cos_a - ry * cos_r * sin_a)
if min(a) < xpt < max(a): if a0 < xpt < a1:
xp = xr xp = xr
if min(a) < xnt < max(a): if a0 < xnt < a1:
xn = -xr xn = -xr
if min(a) < ypt < max(a): if a0 < ypt < a1:
yp = yr yp = yr
if min(a) < ynt < max(a): if a0 < ynt < a1:
yn = -yr yn = -yr
mins.append([xn, yn]) mins.append([xn, yn])