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further fixes to ellipse bounding box

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jan 2017-08-29 16:55:06 -07:00
parent 85e2c662cc
commit 3d89cd42a0
1 changed files with 20 additions and 3 deletions
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23
masque/shapes/arc.py
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@ -206,6 +206,18 @@ class Arc(Shape):
return [poly]
def get_bounds(self) -> numpy.ndarray:
'''
Equation for rotated ellipse is
x = x0 + a * cos(t) * cos(rot) - b * sin(t) * sin(phi)
y = y0 + a * cos(t) * sin(rot) + b * sin(t) * cos(rot)
where t is our parameter.
Differentiating and solving for 0 slope wrt. t, we find
tan(t) = -+ b/a cot(phi)
where -+ is for x, y cases, so that's where the extrema are.
If the extrema are innaccessible due to arc constraints, check the arc endpoints instead.
'''
mins = []
maxs = []
for sgn in (+1, -1):
@ -235,13 +247,18 @@ class Arc(Shape):
ynt = (ypt - pi) % (2 * pi) + a0_offset
# Points along coordinate axes
xr = numpy.sqrt((rx * cos_r) ** 2 + (ry * sin_r) ** 2)
yr = numpy.sqrt((rx * sin_r) ** 2 + (ry * cos_r) ** 2)
xs = rx * sin_r
yc = ry * cos_r
sin_ax = yc / (yc * yc + xs * xs)
cos_ax = xs / (yc * yc + xs * xs)
xr = rx * cos_r * cos_ax - ry * sin_r * sin_ax
yr = ry * sin_r * cos_ax + ry * cos_r * sin_ax
# Arc endpoints
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
if a0 < xpt < a1:
xp = xr