def place_labs(spheres): """This function takes in a dictionary of spheres from calculateSpheres.py and iterates through it to determine the best label placement The outer loop iterates through all the spheres in the dictionary The inner loop takes each sphere and iterates through all the other spheres to determine if the closest point between the two spheres overlaps if there is an overlap, the vector between the closest point and the center of the sphere in question gets inverted and added to a list of vectors when the inner loop is completed, the outer loop adds together all of the vectors in that list and determines the point from the center of the sphere in the direction and at the magnitude of the collective vector (this point is the far point). The midway point between the far point and the center is used for the sphere placement param spheres: all of the spheres that we need to determine label placement for type spheres: dictionary returns: the same dictionary with a point added to each element containing the point to center the label at return type: dictionary with a float value added to each position """ #add the vector componenets for spheres generated in the earlier code to an array for sphere in spheres: centerL = spheres[sphere][0] radiusL = spheres[sphere][1] vectors_to_consider = []# initializes the list of vectors for each sphere #if a possible label position is w/in the sphere and also at the optimal distance #invert the vector and add it to a distionary of potential vectors for the label for otherSphere in spheres: if otherSphere is not sphere: centerO = spheres[otherSphere][0] radiusO = spheres[otherSphere][1] point = point_closest(centerL, centerO, radiusO) if point_inside_of_sphere(point, centerL, radiusL): #make the vectors point from the label position to the center of the sphere vector_to_centerL = (centerL[0] - point[0], centerL[1] - point[1], centerL[2] - point[2]) inverted_vector_to_centerL = invert_vector_mag(vector_to_centerL) vectors_to_consider.append(inverted_vector_to_centerL) #initialize a vector that will be used to add together the magnitudes of the inverted vectors mega_vector = (0,0,0) #assign values to mega_vector and use the magnitude generated from the addition to obtain a far bound for vector in vectors_to_consider: mega_vector = (vector[0] + mega_vector[0], vector[1] + mega_vector[1], vector[2] + mega_vector[2]) far_point = (centerL[0] + mega_vector[0], centerL[1] + mega_vector[1], centerL[2] + mega_vector[2]) #if the distance between the center of the sphere and the far point from mega vector is less #than the sphere raidus, calculate a midpoint if distance(centerL, far_point) > radiusL: mag_mega_vector = distance((0,0,0), mega_vector) u_mega_vector = (mega_vector[0]/mag_mega_vector, mega_vector[1]/mag_mega_vector, mega_vector[2]/mag_mega_vector) far_point = ((u_mega_vector[0]*radiusL), (u_mega_vector[0]*radiusL), (u_mega_vector[2]*radiusL)) far_point = ((far_point[0] + centerL[0]), (far_point[1] + centerL[1]), (far_point[2] + centerL[2])) #midpoint b/w point and center midpoint = (((centerL[0] + far_point[0])/2), ((centerL[1] + far_point[1])/2), ((centerL[2] + far_point[2])/2)) spheres[sphere] = (spheres[sphere][0], spheres[sphere][1], midpoint) return spheres
def place_labs(spheres):
#add the vector componenets for spheres generated in the earlier code to an array
for sphere in spheres:
centerL = spheres[sphere][0]
radiusL = spheres[sphere][1]
vectors_to_consider = []
#if a possible label position is w/in the sphere and also at the optimal distance
#invert the vector and add it to a distionary of potential vectors for the label
for otherSphere in spheres:
if otherSphere is not sphere:
centerO = spheres[otherSphere][0]
radiusO = spheres[otherSphere][1]
point = point_closest(centerL, centerO, radiusO)
if point_inside_of_sphere(point, centerL, radiusL):
#make the vectors point from the label position to the center of the sphere
vector_to_centerL = (centerL[0] - point[0],
centerL[1] - point[1],
centerL[2] - point[2])
inverted_vector_to_centerL = invert_vector_mag(
vector_to_centerL)
vectors_to_consider.append(inverted_vector_to_centerL)
#initialize a vector that will be used to add together the magnitudes of the inverted vectors
mega_vector = (0, 0, 0)
#assign values to mega_vector and use the magnitude generated from the addition to obtain a far bound
for vector in vectors_to_consider:
mega_vector = (vector[0] + mega_vector[0],
vector[1] + mega_vector[1],
vector[2] + mega_vector[2])
far_point = (centerL[0] + mega_vector[0], centerL[1] + mega_vector[1],
centerL[2] + mega_vector[2])
#if the distance between the center of the sphere and the far point from mega vector is less
#than the sphere raidus, calculate a midpoint
if distance(centerL, far_point) > radiusL:
mag_mega_vector = distance((0, 0, 0), mega_vector)
u_mega_vector = (mega_vector[0] / mag_mega_vector,
mega_vector[1] / mag_mega_vector,
mega_vector[2] / mag_mega_vector)
far_point = ((u_mega_vector[0] * radiusL),
(u_mega_vector[0] * radiusL),
(u_mega_vector[2] * radiusL))
far_point = ((far_point[0] + centerL[0]),
(far_point[1] + centerL[1]),
(far_point[2] + centerL[2]))
#midpoint b/w point and center
midpoint = (((centerL[0] + far_point[0]) / 2),
((centerL[1] + far_point[1]) / 2),
((centerL[2] + far_point[2]) / 2))
spheres[sphere] = (spheres[sphere][0], spheres[sphere][1], midpoint)
return spheres
def point_closest(center1, center2, radius2): """This determines closest point between the sphere we are looking at for overlap and the sphere we are labeling It creates a vector between the two centers (pointing toward the center of the sphere we are trying to label) and and then moves from the center of the potentially overlapping sphere the distance of that sphere's radius because that would be the farthest point towards the sphere of interest that the potentially overlapping sphere could overlap param center1: the center of the sphere being labeled type center1: 3d tuple param center2: center of the sphere that is potentially overlapping type center2 : 3d tuple param radius2: radius of the potentially overlapping sphere type radius2: float returns: the point in the 2nd sphere (sphere we ar testing for overlap) that is closest to the center of the sphere we are labeling rtype: 3d tuple """ vector = (center1[0]-center2[0], center1[1] - center2[1], center1[2] - center2[2])# vector between the two sphere centers magVector = distance(center1, center2)#determines the magnitude of the vector if magVector == 0: magVector = 0.01 uVector = (vector[0]/magVector, vector[1]/magVector, vector[2]/magVector)# determines the direction of the vector #looks at the center of the potentially overlapping sphere goes the distance of the radius in the direction of the center of the #sphere in question return (center2[0]+(radius2*uVector[0]), center2[1]+(radius2*uVector[1]), center2[2] + radius2*uVector[2])
def invert_vector_mag(vector):
mag_vector = distance((0, 0, 0), vector)
if mag_vector == 0:
vector = ((vector[0] / 0.01), (vector[1] / 0.01), (vector[2] / 0.01))
else:
vector = ((vector[0] / mag_vector), (vector[1] / mag_vector),
(vector[2] / mag_vector))
return vector
def point_closest(center1, center2, radius2):
vector = (center1[0] - center2[0], center1[1] - center2[1],
center1[2] - center2[2])
magVector = distance(center1, center2)
if magVector == 0:
magVector = 0.01
uVector = (vector[0] / magVector, vector[1] / magVector,
vector[2] / magVector)
return (center2[0] + (radius2 * uVector[0]),
center2[1] + (radius2 * uVector[1]),
center2[2] + radius2 * uVector[2])
def point_inside_of_sphere(point, center, radius):
""" This method determines whether a point is contained within a sphere
This is used to determine if a point is contained within our sphere of interest when determining overlapping points
param point: point of interest determined by the point closest function
type point: 3d tuple
param center: center of the sphere being looked at
type center: 3d tuple
param radius: radius of the sphere in question as determined by the calculateSphere.py algorithm
type radius: float
returns : True if the point is contained within the sphere otherwise false
rtype: Boolean
"""
#distance function used is imported from the calculateSpheres.py class
if distance(point, center) < radius:
return True
else:
return False
def invert_vector_mag(vector): """This function inverts the vector that points from the closest overlapping point to the center of the sphere It is used so that when the final vector is made to place the label it will be as far away from overlapping spheres as possible Inverts using magnitude Potential Error: when one of the vector values is 0. Handled by adding an small value to any vector value that was 0 param vector: vector that points from the closest overlapping point to the center of the sphere type vector: 3d tuple returns: the inverted version of the original vector rtype: 3d tuple """ mag_vector = distance((0,0,0), vector) if mag_vector == 0: vector = ((vector[0]/0.01), (vector[1]/0.01), (vector[2]/0.01)) else: vector = ((vector[0]/mag_vector), (vector[1]/mag_vector), (vector[2]/mag_vector)) return vector
def point_inside_of_sphere(point, center, radius):
if distance(point, center) < radius:
return True
else:
return False