def _pointsOnEllipse(c, smaa, smia, ang, n):
"""Generates points lying on the ellipse with center c,
semi-major/semi-minor axis lengths smaa/smia, and major axis
angle (E of N) ang.
"""
points = []
c = g.cartesianUnitVector(c)
north, east = g.northEast(c)
sa = math.sin(math.radians(ang))
ca = math.cos(math.radians(ang))
smaa = math.radians(smaa * g.DEG_PER_ARCSEC)
smia = math.radians(smia * g.DEG_PER_ARCSEC)
aoff = random.uniform(0.0, 2.0 * math.pi)
for i in xrange(n):
a = aoff + 2.0 * i * math.pi / n
x = smaa * math.cos(a)
y = smia * math.sin(a)
# rotate x, y by a
nc = ca * x - sa * y
ec = sa * x + ca * y
cc = math.sqrt(abs(1.0 - nc * nc - ec * ec))
points.append(
g.normalize((cc * c[0] + nc * north[0] + ec * east[0],
cc * c[1] + nc * north[1] + ec * east[1],
cc * c[2] + nc * north[2] + ec * east[2])))
return points
def _pointsOnEllipse(c, smaa, smia, ang, n):
"""Generates points lying on the ellipse with center c,
semi-major/semi-minor axis lengths smaa/smia, and major axis
angle (E of N) ang.
"""
points = []
c = g.cartesianUnitVector(c)
north, east = g.northEast(c)
sa = math.sin(math.radians(ang))
ca = math.cos(math.radians(ang))
smaa = math.radians(smaa * g.DEG_PER_ARCSEC)
smia = math.radians(smia * g.DEG_PER_ARCSEC)
aoff = random.uniform(0.0, 2.0 * math.pi)
for i in xrange(n):
a = aoff + 2.0 * i * math.pi / n
x = smaa * math.cos(a)
y = smia * math.sin(a)
# rotate x, y by a
nc = ca * x - sa * y
ec = sa * x + ca * y
cc = math.sqrt(abs(1.0 - nc * nc - ec * ec))
points.append(g.normalize((cc * c[0] + nc * north[0] + ec * east[0],
cc * c[1] + nc * north[1] + ec * east[1],
cc * c[2] + nc * north[2] + ec * east[2])))
return points
def testSpatialPredicates(self):
# ellipse-point
for cen in ((0.0, 0.0), (45.0, 45.0), (135.0, -45.0), (0.0, 90.0)):
smaa = random.uniform(30, 20000)
smia = random.uniform(1, smaa)
a = random.uniform(0.0, 360.0)
e = g.SphericalEllipse(cen, smaa, smia, a)
self.assertTrue(e.contains(cen))
self.assertTrue(e.contains(g.cartesianUnitVector(cen)))
self.assertTrue(e.intersects(cen))
self.assertTrue(e.intersects(g.cartesianUnitVector(cen)))
points = _pointsOnCircle(
cen,
e.getInnerCircle().getRadius() - g.ANGLE_EPSILON, 100)
for p in points:
self.assertTrue(e.contains(p))
points = _pointsOnCircle(
cen,
e.getBoundingCircle().getRadius() + g.ANGLE_EPSILON, 100)
for p in points:
self.assertFalse(e.intersects(p))
points = _pointsOnEllipse(
cen, smaa - g.ANGLE_EPSILON * g.ARCSEC_PER_DEG,
smia - g.ANGLE_EPSILON * g.ARCSEC_PER_DEG, a, 100)
for p in points:
self.assertTrue(e.contains(p))
points = _pointsOnEllipse(
cen, smaa + g.ANGLE_EPSILON * g.ARCSEC_PER_DEG,
smia + g.ANGLE_EPSILON * g.ARCSEC_PER_DEG, a, 100)
for p in points:
self.assertFalse(e.contains(p))
# ellipse-circle
cen = (0.0, 0.0)
e = g.SphericalEllipse(cen, 7200.0, 3600.0, 90.0)
c = g.SphericalCircle(cen,
e.getInnerCircle().getRadius() - g.ANGLE_EPSILON)
self.assertTrue(e.intersects(c))
self.assertTrue(c.intersects(e))
self.assertTrue(e.contains(c))
self.assertFalse(c.contains(e))
# ellipse-box
b = g.SphericalBox((-0.5, -0.5), (0.5, 0.5))
self.assertTrue(e.intersects(b))
self.assertTrue(e.contains(b))
b = g.SphericalBox((0.5, -0.5), (359.5, 0.5))
self.assertTrue(e.intersects(b))
self.assertFalse(e.contains(b))
def testCartesianUnitVector(self):
v = g.cartesianUnitVector((1.0, 0.0, 0.0))
self.assertEqual(v[0], 1.0)
self.assertEqual(v[1], 0.0)
self.assertEqual(v[2], 0.0)
v = g.cartesianUnitVector((1.0, 1.0, 1.0))
self.assertAlmostEqual(v[0], 0.577350269189626)
self.assertAlmostEqual(v[1], 0.577350269189626)
self.assertAlmostEqual(v[2], 0.577350269189626)
v = g.cartesianUnitVector((45.0, 35.2643896827547))
self.assertAlmostEqual(v[0], 0.577350269189626)
self.assertAlmostEqual(v[1], 0.577350269189626)
self.assertAlmostEqual(v[2], 0.577350269189626)
v = g.cartesianUnitVector((180.0, 0.0))
self.assertAlmostEqual(v[0], -1.0)
self.assertAlmostEqual(v[1], 0.0)
self.assertAlmostEqual(v[2], 0.0)
def testCartesianUnitVector(self):
v = g.cartesianUnitVector((1.0, 0.0, 0.0))
self.assertEqual(v[0], 1.0)
self.assertEqual(v[1], 0.0)
self.assertEqual(v[2], 0.0)
v = g.cartesianUnitVector((1.0, 1.0, 1.0))
self.assertAlmostEqual(v[0], 0.577350269189626)
self.assertAlmostEqual(v[1], 0.577350269189626)
self.assertAlmostEqual(v[2], 0.577350269189626)
v = g.cartesianUnitVector((45.0, 35.2643896827547))
self.assertAlmostEqual(v[0], 0.577350269189626)
self.assertAlmostEqual(v[1], 0.577350269189626)
self.assertAlmostEqual(v[2], 0.577350269189626)
v = g.cartesianUnitVector((180.0, 0.0))
self.assertAlmostEqual(v[0], -1.0)
self.assertAlmostEqual(v[1], 0.0)
self.assertAlmostEqual(v[2], 0.0)
def testSpatialPredicates(self):
# ellipse-point
for cen in ((0.0, 0.0), (45.0, 45.0), (135.0, -45.0), (0.0, 90.0)):
smaa = random.uniform(30, 20000)
smia = random.uniform(1, smaa)
a = random.uniform(0.0, 360.0)
e = g.SphericalEllipse(cen, smaa, smia, a)
self.assertTrue(e.contains(cen))
self.assertTrue(e.contains(g.cartesianUnitVector(cen)))
self.assertTrue(e.intersects(cen))
self.assertTrue(e.intersects(g.cartesianUnitVector(cen)))
points = _pointsOnCircle(
cen, e.getInnerCircle().getRadius() - g.ANGLE_EPSILON, 100)
for p in points:
self.assertTrue(e.contains(p))
points = _pointsOnCircle(
cen, e.getBoundingCircle().getRadius() + g.ANGLE_EPSILON, 100)
for p in points:
self.assertFalse(e.intersects(p))
points = _pointsOnEllipse(
cen, smaa - g.ANGLE_EPSILON * g.ARCSEC_PER_DEG,
smia - g.ANGLE_EPSILON * g.ARCSEC_PER_DEG, a, 100)
for p in points:
self.assertTrue(e.contains(p))
points = _pointsOnEllipse(
cen, smaa + g.ANGLE_EPSILON * g.ARCSEC_PER_DEG,
smia + g.ANGLE_EPSILON * g.ARCSEC_PER_DEG, a, 100)
for p in points:
self.assertFalse(e.contains(p))
# ellipse-circle
cen = (0.0, 0.0)
e = g.SphericalEllipse(cen, 7200.0, 3600.0, 90.0)
c = g.SphericalCircle(
cen, e.getInnerCircle().getRadius() - g.ANGLE_EPSILON)
self.assertTrue(e.intersects(c))
self.assertTrue(c.intersects(e))
self.assertTrue(e.contains(c))
self.assertFalse(c.contains(e))
# ellipse-box
b = g.SphericalBox((-0.5, -0.5), (0.5, 0.5))
self.assertTrue(e.intersects(b))
self.assertTrue(e.contains(b))
b = g.SphericalBox((0.5, -0.5), (359.5, 0.5))
self.assertTrue(e.intersects(b))
self.assertFalse(e.contains(b))
def _pointsOnCircle(c, r, n, clockwise=False):
"""Generates an n-gon lying on the circle with center c and
radius r. Vertices are equi-spaced.
"""
c = g.cartesianUnitVector(c)
north, east = g.northEast(c)
points = []
sr = math.sin(math.radians(r))
cr = math.cos(math.radians(r))
aoff = random.uniform(0.0, 2.0 * math.pi)
for i in xrange(n):
a = 2.0 * i * math.pi / n
if not clockwise:
a = -a
sa = math.sin(a + aoff)
ca = math.cos(a + aoff)
p = (ca * north[0] + sa * east[0], ca * north[1] + sa * east[1],
ca * north[2] + sa * east[2])
points.append(
g.normalize((cr * c[0] + sr * p[0], cr * c[1] + sr * p[1],
cr * c[2] + sr * p[2])))
return points
def _pointsOnPeriodicHypotrochoid(c, R, r, d, n):
assert isinstance(r, int) and isinstance(R, int)
assert R > r
assert (2 * r) % (R - r) == 0
points = []
c = g.cartesianUnitVector(c)
north, east = g.northEast(c)
scale = 1.0 / (R - r + d + 1)
period = (2 * r) / (R - r)
if period % 2 != 0:
period *= 2
for i in xrange(n):
theta = i * period * math.pi / n
x = (R - r) * math.cos(theta) + d * math.cos((R - r) * theta / r)
y = (R - r) * math.sin(theta) - d * math.sin((R - r) * theta / r)
x *= scale
y *= scale
z = math.sqrt(1.0 - x * x - y * y)
points.append(g.normalize((z * c[0] + x * north[0] + y * east[0],
z * c[1] + x * north[1] + y * east[1],
z * c[2] + x * north[2] + y * east[2])))
return points
def _pointsOnPeriodicHypotrochoid(c, R, r, d, n):
assert isinstance(r, int) and isinstance(R, int)
assert R > r
assert (2 * r) % (R - r) == 0
points = []
c = geom.cartesianUnitVector(c)
north, east = geom.northEast(c)
scale = 1.0 / (R - r + d + 1)
period = (2 * r) / (R - r)
if period % 2 != 0:
period *= 2
for i in range(n):
theta = i * period * math.pi / n
x = (R - r) * math.cos(theta) + d * math.cos((R - r) * theta / r)
y = (R - r) * math.sin(theta) - d * math.sin((R - r) * theta / r)
x *= scale
y *= scale
z = math.sqrt(1.0 - x * x - y * y)
points.append(geom.normalize((z * c[0] + x * north[0] + y * east[0],
z * c[1] + x * north[1] + y * east[1],
z * c[2] + x * north[2] + y * east[2])))
return points
def _pointsOnCircle(c, r, n, clockwise=False):
"""Generates an n-gon lying on the circle with center c and
radius r. Vertices are equi-spaced.
"""
c = g.cartesianUnitVector(c)
north, east = g.northEast(c)
points = []
sr = math.sin(math.radians(r))
cr = math.cos(math.radians(r))
aoff = random.uniform(0.0, 2.0 * math.pi)
for i in xrange(n):
a = 2.0 * i * math.pi / n
if not clockwise:
a = -a
sa = math.sin(a + aoff)
ca = math.cos(a + aoff)
p = (ca * north[0] + sa * east[0],
ca * north[1] + sa * east[1],
ca * north[2] + sa * east[2])
points.append(g.normalize((cr * c[0] + sr * p[0],
cr * c[1] + sr * p[1],
cr * c[2] + sr * p[2])))
return points
def testEdge(self):
v1 = g.cartesianUnitVector(0.0, 45.0)
v2 = g.cartesianUnitVector(180.0, 45.0)
n = (0.0, -1.0, 0.0)
b = g.SphericalBox.edge(v1, v2, n)
self.assertEqual(b.getMin()[0], 0.0)
self.assertEqual(b.getMax()[0], 360.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertEqual(b.getMax()[1], 90.0)
v1 = g.cartesianUnitVector(0.0, 45.0)
v2 = g.cartesianUnitVector(0.0, 75.0)
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 0.0)
self.assertAlmostEqual(b.getMax()[0], 0.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertAlmostEqual(b.getMax()[1], 75.0)
v1 = g.cartesianUnitVector(-0.1 * g.ANGLE_EPSILON, 45.0)
v2 = g.cartesianUnitVector(180 + 0.1 * g.ANGLE_EPSILON, 45.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertEqual(b.getMin()[0], 0.0)
self.assertEqual(b.getMax()[0], 360.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertEqual(b.getMax()[1], 90.0)
v1 = g.cartesianUnitVector(-0.1 * g.ANGLE_EPSILON, 45.0)
v2 = g.cartesianUnitVector(0.1 * g.ANGLE_EPSILON, 75.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 360.0)
self.assertAlmostEqual(b.getMax()[0], 0.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertAlmostEqual(b.getMax()[1], 75.0)
v1 = g.cartesianUnitVector(1.0, 1.0)
v2 = g.cartesianUnitVector(2.0, 2.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 1.0)
self.assertAlmostEqual(b.getMax()[0], 2.0)
self.assertAlmostEqual(b.getMin()[1], 1.0)
self.assertAlmostEqual(b.getMax()[1], 2.0)
v1 = g.cartesianUnitVector(-1.0, 3.0)
v2 = g.cartesianUnitVector(2.0, -1.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 359.0)
self.assertAlmostEqual(b.getMax()[0], 2.0)
self.assertAlmostEqual(b.getMin()[1], -1.0)
self.assertAlmostEqual(b.getMax()[1], 3.0)
def testEdge(self):
v1 = g.cartesianUnitVector(0.0, 45.0)
v2 = g.cartesianUnitVector(180.0, 45.0)
n = (0.0, -1.0, 0.0)
b = g.SphericalBox.edge(v1, v2, n)
self.assertEqual(b.getMin()[0], 0.0)
self.assertEqual(b.getMax()[0], 360.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertEqual(b.getMax()[1], 90.0)
v1 = g.cartesianUnitVector(0.0, 45.0)
v2 = g.cartesianUnitVector(0.0, 75.0)
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 0.0)
self.assertAlmostEqual(b.getMax()[0], 0.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertAlmostEqual(b.getMax()[1], 75.0)
v1 = g.cartesianUnitVector(-0.1 * g.ANGLE_EPSILON, 45.0)
v2 = g.cartesianUnitVector(180 + 0.1 *g.ANGLE_EPSILON, 45.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertEqual(b.getMin()[0], 0.0)
self.assertEqual(b.getMax()[0], 360.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertEqual(b.getMax()[1], 90.0)
v1 = g.cartesianUnitVector(-0.1 * g.ANGLE_EPSILON, 45.0)
v2 = g.cartesianUnitVector(0.1 * g.ANGLE_EPSILON, 75.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 360.0)
self.assertAlmostEqual(b.getMax()[0], 0.0)
self.assertAlmostEqual(b.getMin()[1], 45.0)
self.assertAlmostEqual(b.getMax()[1], 75.0)
v1 = g.cartesianUnitVector(1.0, 1.0)
v2 = g.cartesianUnitVector(2.0, 2.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 1.0)
self.assertAlmostEqual(b.getMax()[0], 2.0)
self.assertAlmostEqual(b.getMin()[1], 1.0)
self.assertAlmostEqual(b.getMax()[1], 2.0)
v1 = g.cartesianUnitVector(-1.0, 3.0)
v2 = g.cartesianUnitVector(2.0, -1.0)
n = g.normalize(g.cross(v1, v2))
b = g.SphericalBox.edge(v1, v2, n)
self.assertAlmostEqual(b.getMin()[0], 359.0)
self.assertAlmostEqual(b.getMax()[0], 2.0)
self.assertAlmostEqual(b.getMin()[1], -1.0)
self.assertAlmostEqual(b.getMax()[1], 3.0)