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poisson.py
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poisson.py
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from __future__ import division
import numpy as np
import math
import scipy.spatial.distance
from mpl_toolkits.mplot3d import Axes3D
def random_point_disk(num_points = 1):
alpha = np.random.random(num_points) * math.pi * 2.0
radius = np.sqrt(np.random.random(num_points))
x = np.cos(alpha) * radius
y = np.sin(alpha) * radius
return np.dstack((x,y))[0]
def random_point_sphere(num_points = 1):
theta = np.random.random(num_points) * math.pi * 2.0
phi = np.arccos(2.0 * np.random.random(num_points) - 1.0)
radius = pow(np.random.random(num_points), 1.0 / 3.0)
x = np.cos(theta) * np.sin(phi) * radius
y = np.sin(theta) * np.sin(phi) * radius
z = np.cos(phi) * radius
return np.dstack((x,y,z))[0]
def random_point_line(num_points = 1):
x = np.random.random(num_points)
return np.reshape(x, (num_points,1))
def random_point_square(num_points = 1):
x = np.random.random(num_points)
y = np.random.random(num_points)
return np.dstack((x,y))[0]
def random_point_box(num_points = 1):
x = np.random.random(num_points)
y = np.random.random(num_points)
z = np.random.random(num_points)
return np.dstack((x,y,z))[0]
# if we only compare it doesn't matter if it's squared
def min_dist_squared(points, point):
diff = points - np.array([point])
return np.min(np.einsum('ij,ij->i',diff,diff))
class PoissonGenerator:
def __init__(self, num_dim, disk, repeatPattern, first_point_zero):
self.first_point_zero = first_point_zero
self.disk = disk
self.num_dim = num_dim
self.repeatPattern = repeatPattern and disk == False
self.num_perms = (3 ** self.num_dim) if self.repeatPattern else 1
if num_dim == 3:
self.zero_point = [0,0,0]
if disk == True:
self.random_point = random_point_sphere
else:
self.random_point = random_point_box
elif num_dim == 2:
self.zero_point = [0,0]
if disk == True:
self.random_point = random_point_disk
else:
self.random_point = random_point_square
else:
self.zero_point = [0]
self.random_point = random_point_line
def first_point(self):
if self.first_point_zero == True:
return np.array(self.zero_point)
return self.random_point(1)[0]
def find_next_point(self, current_points, iterations_per_point):
best_dist = 0
best_point = []
random_points = self.random_point(iterations_per_point)
for new_point in random_points:
dist = min_dist_squared(current_points, new_point)
if dist > best_dist:
best_dist = dist
best_point = new_point
return best_point
def permute_point(self, point):
out_array = np.array(point,ndmin = 2)
if not self.repeatPattern:
return out_array
if self.num_dim == 3:
for z in range(-1,2):
for y in range(-1,2):
for x in range(-1,2):
if y != 0 or x != 0 or z != 0:
perm_point = point+[x,y,z]
out_array = np.append(out_array, np.array(perm_point,ndmin = 2), axis = 0 )
elif self.num_dim == 2:
for y in range(-1,2):
for x in range(-1,2):
if y != 0 or x != 0:
perm_point = point+[x,y]
out_array = np.append(out_array, np.array(perm_point,ndmin = 2), axis = 0 )
else:
for x in range(-1,2):
if x != 0:
perm_point = point+[x]
out_array = np.append(out_array, np.array(perm_point,ndmin = 2), axis = 0 )
return out_array
def find_point_set(self, num_points, num_iter, iterations_per_point, rotations, progress_notification = None):
best_point_set = []
best_dist_avg = 0
self.rotations = 1
if self.disk and self.num_dim == 2:
rotations = max(rotations, 1)
self.rotations = rotations
for i in range(num_iter):
if progress_notification != None:
progress_notification(i / num_iter)
points = self.permute_point(self.first_point())
for i in range(num_points-1):
next_point = self.find_next_point(points, iterations_per_point)
points = np.append(points, self.permute_point(next_point), axis = 0)
current_set_dist = 0
if rotations > 1:
points_permuted = np.copy(points)
for rotation in range(1, rotations):
rot_angle = rotation * math.pi * 2.0 / rotations
s, c = math.sin(rot_angle), math.cos(rot_angle)
rot_matrix = np.matrix([[c, -s], [s, c]])
points_permuted = np.append(points_permuted, np.array(np.dot(points, rot_matrix)), axis = 0)
current_set_dist = np.min(scipy.spatial.distance.pdist(points_permuted))
else:
current_set_dist = np.min(scipy.spatial.distance.pdist(points))
if current_set_dist > best_dist_avg:
best_dist_avg = current_set_dist
best_point_set = points
return best_point_set[::self.num_perms,:]
def cache_sort(self, points, sorting_buckets):
if sorting_buckets < 1:
return points
if self.num_dim == 3:
points_discretized = np.floor(points * [sorting_buckets,-sorting_buckets, sorting_buckets])
indices_cache_space = np.array(points_discretized[:,2] * sorting_buckets * 4 + points_discretized[:,1] * sorting_buckets * 2 + points_discretized[:,0])
points = points[np.argsort(indices_cache_space)]
elif self.num_dim == 2:
points_discretized = np.floor(points * [sorting_buckets,-sorting_buckets])
indices_cache_space = np.array(points_discretized[:,1] * sorting_buckets * 2 + points_discretized[:,0])
points = points[np.argsort(indices_cache_space)]
else:
points_discretized = np.floor(points * [sorting_buckets])
indices_cache_space = np.array(points_discretized[:,0])
points = points[np.argsort(indices_cache_space)]
return points
def format_points_string(self, points):
types_hlsl = ["float", "float2", "float3"]
points_str_hlsl = "// hlsl array\n"
points_str_hlsl += "static const uint SAMPLE_NUM = " + str(points.size // self.num_dim) + ";\n"
points_str_hlsl += "static const " + types_hlsl[self.num_dim-1] + " POISSON_SAMPLES[SAMPLE_NUM] = \n{ \n"
points_str_cpp = "// C++ array\n"
points_str_cpp += "const int SAMPLE_NUM = " + str(points.size // self.num_dim) + ";\n"
points_str_cpp += "const float POISSON_SAMPLES[SAMPLE_NUM][" + str(self.num_dim) + "] = \n{ \n"
if self.num_dim == 3:
for p in points:
points_str_hlsl += "float3( " + str(p[0]) + "f, " + str(p[1]) + "f, " + str(p[2]) + "f ), \n"
points_str_cpp += str(p[0]) + "f, " + str(p[1]) + "f, " + str(p[2]) + "f, \n"
elif self.num_dim == 2:
for p in points:
points_str_hlsl += "float2( " + str(p[0]) + "f, " + str(p[1]) + "f ), \n"
points_str_cpp += str(p[0]) + "f, " + str(p[1]) + "f, \n"
else:
for p in points:
points_str_hlsl += str(p[0]) + "f, \n"
points_str_cpp += str(p[0]) + "f, \n"
points_str_hlsl += "};\n\n"
points_str_cpp += "};\n\n"
return points_str_hlsl + points_str_cpp
def generate_ui(self, fig, points, highlightFirst = 0):
num_points = points.size // self.num_dim
if self.num_dim == 3:
ax = fig.add_subplot(111, projection='3d')
if self.disk == True:
#less optimal, more readable
sphere_guide = [[0,0,0]]
num_guides = 30
for theta in np.linspace(0, 2.0 * math.pi, num_guides):
for phi in np.arccos(np.linspace(-1, 1.0, num_guides)):
x = np.cos(theta) * np.sin(phi)
y = np.sin(theta) * np.sin(phi)
z = np.cos(phi)
sphere_guide = np.append(sphere_guide, np.array([[x,y,z]],ndmin = 2), axis = 0)
ax.plot_wireframe(sphere_guide[1:,0], sphere_guide[1:,1], sphere_guide[1:,2])
ax.set_xlim(-1,1)
ax.set_ylim(-1,1)
ax.set_zlim(-1,1)
elif self.repeatPattern == True:
ax.scatter(points[:,0], points[:,1], points[:,2] + 1, c='b')
ax.scatter(points[:,0], points[:,1] + 1, points[:,2] + 1, c='b')
ax.scatter(points[:,0] + 1, points[:,1] + 1, points[:,2] + 1, c='b')
ax.scatter(points[:,0] + 1, points[:,1], points[:,2] + 1, c='b')
ax.scatter(points[:,0], points[:,1] + 1, points[:,2], c='b')
ax.scatter(points[:,0] + 1, points[:,1] + 1, points[:,2], c='b')
ax.scatter(points[:,0] + 1, points[:,1], points[:,2], c='b')
a = np.linspace(0, 2.0, 3)
b = np.linspace(0, 2.0, 3)
a, b = np.meshgrid(a,b)
ax.plot_wireframe(a, b, 1.0)
ax.plot_wireframe(a, 1.0, b)
ax.plot_wireframe(1.0, a, b)
ax.set_xlim(0,2)
ax.set_ylim(0,2)
ax.set_zlim(0,2)
else:
ax.set_xlim(0,1)
ax.set_ylim(0,1)
ax.set_zlim(0,1)
ax.scatter(points[highlightFirst:,0], points[highlightFirst:,1], points[highlightFirst:,2], c='g')
ax.scatter(points[:highlightFirst,0], points[:highlightFirst,1], points[:highlightFirst,2], c='r')
elif self.num_dim == 2:
ax = fig.add_subplot(111)
if self.disk == True:
param = np.linspace(0, 2.0 * math.pi, 1000)
x = np.cos(param)
y = np.sin(param)
ax.plot(x, y, 'b-')
elif self.repeatPattern == True:
ax.plot(points[:,0] + 1, points[:,1], 'bo')
ax.plot(points[:,0] + 1, points[:,1] + 1, 'bo')
ax.plot(points[:,0], points[:,1] + 1, 'bo')
if self.disk == False:
param = np.linspace(0, 2.0, 100)
ax.plot(param, [1] * 100, 'k')
ax.plot([1] * 100, param, 'k')
for rotation in range(1,self.rotations):
rot_angle = rotation * math.pi * 2.0 / self.rotations
s, c = math.sin(rot_angle), math.cos(rot_angle)
rot_matrix = np.matrix([[c, -s], [s, c]])
points_permuted = np.array(np.dot(points, rot_matrix))
ax.plot(points_permuted[:,0], points_permuted[:,1], 'bo')
ax.plot(points[:highlightFirst,0], points[:highlightFirst,1], 'go')
ax.plot(points[highlightFirst:,0], points[highlightFirst:,1], 'ro')
else:
ax = fig.add_subplot(111)
ax.plot(points[:highlightFirst,0], [0] * num_points, 'go')
ax.plot(points[highlightFirst:,0], [0] * num_points, 'ro')
if self.repeatPattern == True:
ax.plot(points[:,0] + 1, [0] * num_points, 'bo')