def computeMagnitude(point, sphereCenter):
magnitudeSquared = c3d.magnitudeSquared(point)
magnitude = math.sqrt(magnitudeSquared)
direction = c3d.multiplyByScalar(point, 1 / magnitude)
magnitudeSquared = max(1.0, magnitudeSquared)
magnitude = max(1.0, magnitude)
cosAlpha = np.dot(direction, sphereCenter)
sinAlpha = c3d.magnitude(np.cross(direction, sphereCenter))
cosBeta = 1.0 / magnitude
sinBeta = math.sqrt(magnitudeSquared - 1.0) * cosBeta
return 1.0 / (cosAlpha * cosBeta - sinAlpha * sinBeta)
def fromPoints(points, boundingSphere):
if len(points) < 1:
raise Exception('Your list of points must contain at least 2 points')
# Bring coordinates to ellipsoid scaled coordinates
scaleDown = lambda coord: [coord[0] * rX, coord[1] * rY, coord[2] * rZ]
scaledPoints = map(scaleDown, points)
scaledSphereCenter = scaleDown(boundingSphere.center)
magnitude = lambda coord: computeMagnitude(coord, scaledSphereCenter)
magnitudes = map(magnitude, scaledPoints)
return c3d.multiplyByScalar(scaledSphereCenter, max(magnitudes))
def fromPoints(self, points):
if len(points) < 1:
raise Exception('Your list of points must contain at least 2 points')
nbPositions = len(points)
for i in xrange(0, nbPositions):
point = points[i]
# Store the points containing the smallest and largest component
# Used for the naive approach
if point[0] < self.minPointX[0]:
self.minPointX = point
if point[1] < self.minPointY[1]:
self.minPointY = point
if point[2] < self.minPointZ[2]:
self.minPointZ = point
if point[0] > self.maxPointX[0]:
self.maxPointX = point
if point[1] > self.maxPointY[1]:
self.maxPointY = point
if point[2] > self.maxPointZ[2]:
self.maxPointZ = point
# Squared distance between each component min and max
xSpan = c3d.magnitudeSquared(c3d.subtract(self.maxPointX, self.minPointX))
ySpan = c3d.magnitudeSquared(c3d.subtract(self.maxPointY, self.minPointY))
zSpan = c3d.magnitudeSquared(c3d.subtract(self.maxPointZ, self.minPointZ))
diameter1 = self.minPointX
diameter2 = self.maxPointX
maxSpan = xSpan
if ySpan > maxSpan:
maxSpan = ySpan
diameter1 = self.minPointY
diameter2 = self.maxPointY
if zSpan > maxSpan:
maxSpan = zSpan
diameter1 = self.minPointZ
diameter2 = self.maxPointZ
ritterCenter = [
(diameter1[0] + diameter2[0]) * 0.5,
(diameter1[1] + diameter2[1]) * 0.5,
(diameter1[2] + diameter2[2]) * 0.5
]
radiusSquared = c3d.magnitudeSquared(c3d.subtract(diameter2, ritterCenter))
ritterRadius = math.sqrt(radiusSquared)
# Initial center and radius (naive) get min and max box
minBoxPt = [self.minPointX[0], self.minPointY[1], self.minPointZ[2]]
maxBoxPt = [self.maxPointX[0], self.maxPointY[1], self.maxPointZ[2]]
naiveCenter = c3d.multiplyByScalar(c3d.add(minBoxPt, maxBoxPt), 0.5)
naiveRadius = 0.0
for i in xrange(0, nbPositions):
currentP = points[i]
# Find the furthest point from the naive center to calculate the naive radius.
r = c3d.magnitude(c3d.subtract(currentP, naiveCenter))
if r > naiveRadius:
naiveRadius = r
# Make adjustments to the Ritter Sphere to include all points.
oldCenterToPointSquared = c3d.magnitudeSquared(c3d.subtract(currentP, ritterCenter))
if oldCenterToPointSquared > radiusSquared:
oldCenterToPoint = math.sqrt(oldCenterToPointSquared)
ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5
# Calculate center of new Ritter sphere
oldToNew = oldCenterToPoint - ritterRadius
ritterCenter = [
(ritterRadius * ritterCenter[0] + oldToNew * currentP[0]) / oldCenterToPoint,
(ritterRadius * ritterCenter[1] + oldToNew * currentP[1]) / oldCenterToPoint,
(ritterRadius * ritterCenter[2] + oldToNew * currentP[2]) / oldCenterToPoint,
]
# Keep the naive sphere if smaller
if naiveRadius < ritterRadius:
self.radius = ritterRadius
self.center = ritterCenter
else:
self.radius = naiveRadius
self.center = naiveCenter
def fromPoints(self, points):
if len(points) < 1:
raise Exception(
'Your list of points must contain at least 2 points')
nbPositions = len(points)
for i in xrange(0, nbPositions):
point = points[i]
# Store the points containing the smallest and largest component
# Used for the naive approach
if point[0] < self.minPointX[0]:
self.minPointX = point
if point[1] < self.minPointY[1]:
self.minPointY = point
if point[2] < self.minPointZ[2]:
self.minPointZ = point
if point[0] > self.maxPointX[0]:
self.maxPointX = point
if point[1] > self.maxPointY[1]:
self.maxPointY = point
if point[2] > self.maxPointZ[2]:
self.maxPointZ = point
# Squared distance between each component min and max
xSpan = c3d.magnitudeSquared(
c3d.subtract(self.maxPointX, self.minPointX))
ySpan = c3d.magnitudeSquared(
c3d.subtract(self.maxPointY, self.minPointY))
zSpan = c3d.magnitudeSquared(
c3d.subtract(self.maxPointZ, self.minPointZ))
diameter1 = self.minPointX
diameter2 = self.maxPointX
maxSpan = xSpan
if ySpan > maxSpan:
maxSpan = ySpan
diameter1 = self.minPointY
diameter2 = self.maxPointY
if zSpan > maxSpan:
maxSpan = zSpan
diameter1 = self.minPointZ
diameter2 = self.maxPointZ
ritterCenter = [(diameter1[0] + diameter2[0]) * 0.5,
(diameter1[1] + diameter2[1]) * 0.5,
(diameter1[2] + diameter2[2]) * 0.5]
radiusSquared = c3d.magnitudeSquared(
c3d.subtract(diameter2, ritterCenter))
ritterRadius = math.sqrt(radiusSquared)
# Initial center and radius (naive) get min and max box
minBoxPt = [self.minPointX[0], self.minPointY[1], self.minPointZ[2]]
maxBoxPt = [self.maxPointX[0], self.maxPointY[1], self.maxPointZ[2]]
naiveCenter = c3d.multiplyByScalar(c3d.add(minBoxPt, maxBoxPt), 0.5)
naiveRadius = 0.0
for i in xrange(0, nbPositions):
currentP = points[i]
# Find the furthest point from the naive center to calculate the naive radius.
r = c3d.magnitude(c3d.subtract(currentP, naiveCenter))
if r > naiveRadius:
naiveRadius = r
# Make adjustments to the Ritter Sphere to include all points.
oldCenterToPointSquared = c3d.magnitudeSquared(
c3d.subtract(currentP, ritterCenter))
if oldCenterToPointSquared > radiusSquared:
oldCenterToPoint = math.sqrt(oldCenterToPointSquared)
ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5
# Calculate center of new Ritter sphere
oldToNew = oldCenterToPoint - ritterRadius
ritterCenter = [
(ritterRadius * ritterCenter[0] + oldToNew * currentP[0]) /
oldCenterToPoint,
(ritterRadius * ritterCenter[1] + oldToNew * currentP[1]) /
oldCenterToPoint,
(ritterRadius * ritterCenter[2] + oldToNew * currentP[2]) /
oldCenterToPoint
]
# Keep the naive sphere if smaller
if naiveRadius < ritterRadius:
self.radius = ritterRadius
self.center = ritterCenter
else:
self.radius = naiveRadius
self.center = naiveCenter
