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# Source: https://github.com/python/pyperformance
# License: MIT
# create chaosgame-like fractals
# Copyright (C) 2005 Carl Friedrich Bolz
import math
import random
class GVector(object):
def __init__(self, x=0, y=0, z=0):
self.x = x
self.y = y
self.z = z
def Mag(self):
return math.sqrt(self.x**2 + self.y**2 + self.z**2)
def dist(self, other):
return math.sqrt(
(self.x - other.x) ** 2 + (self.y - other.y) ** 2 + (self.z - other.z) ** 2
)
def __add__(self, other):
if not isinstance(other, GVector):
raise ValueError("Can't add GVector to " + str(type(other)))
v = GVector(self.x + other.x, self.y + other.y, self.z + other.z)
return v
def __sub__(self, other):
return self + other * -1
def __mul__(self, other):
v = GVector(self.x * other, self.y * other, self.z * other)
return v
__rmul__ = __mul__
def linear_combination(self, other, l1, l2=None):
if l2 is None:
l2 = 1 - l1
v = GVector(
self.x * l1 + other.x * l2, self.y * l1 + other.y * l2, self.z * l1 + other.z * l2
)
return v
def __str__(self):
return "<%f, %f, %f>" % (self.x, self.y, self.z)
def __repr__(self):
return "GVector(%f, %f, %f)" % (self.x, self.y, self.z)
class Spline(object):
"""Class for representing B-Splines and NURBS of arbitrary degree"""
def __init__(self, points, degree, knots):
"""Creates a Spline.
points is a list of GVector, degree is the degree of the Spline.
"""
if len(points) > len(knots) - degree + 1:
raise ValueError("too many control points")
elif len(points) < len(knots) - degree + 1:
raise ValueError("not enough control points")
last = knots[0]
for cur in knots[1:]:
if cur < last:
raise ValueError("knots not strictly increasing")
last = cur
self.knots = knots
self.points = points
self.degree = degree
def GetDomain(self):
"""Returns the domain of the B-Spline"""
return (self.knots[self.degree - 1], self.knots[len(self.knots) - self.degree])
def __call__(self, u):
"""Calculates a point of the B-Spline using de Boors Algorithm"""
dom = self.GetDomain()
if u < dom[0] or u > dom[1]:
raise ValueError("Function value not in domain")
if u == dom[0]:
return self.points[0]
if u == dom[1]:
return self.points[-1]
I = self.GetIndex(u)
d = [self.points[I - self.degree + 1 + ii] for ii in range(self.degree + 1)]
U = self.knots
for ik in range(1, self.degree + 1):
for ii in range(I - self.degree + ik + 1, I + 2):
ua = U[ii + self.degree - ik]
ub = U[ii - 1]
co1 = (ua - u) / (ua - ub)
co2 = (u - ub) / (ua - ub)
index = ii - I + self.degree - ik - 1
d[index] = d[index].linear_combination(d[index + 1], co1, co2)
return d[0]
def GetIndex(self, u):
dom = self.GetDomain()
for ii in range(self.degree - 1, len(self.knots) - self.degree):
if u >= self.knots[ii] and u < self.knots[ii + 1]:
I = ii
break
else:
I = dom[1] - 1
return I
def __len__(self):
return len(self.points)
def __repr__(self):
return "Spline(%r, %r, %r)" % (self.points, self.degree, self.knots)
def write_ppm(im, w, h, filename):
with open(filename, "wb") as f:
f.write(b"P6\n%i %i\n255\n" % (w, h))
for j in range(h):
for i in range(w):
val = im[j * w + i]
c = val * 255
f.write(b"%c%c%c" % (c, c, c))
class Chaosgame(object):
def __init__(self, splines, thickness, subdivs):
self.splines = splines
self.thickness = thickness
self.minx = min([p.x for spl in splines for p in spl.points])
self.miny = min([p.y for spl in splines for p in spl.points])
self.maxx = max([p.x for spl in splines for p in spl.points])
self.maxy = max([p.y for spl in splines for p in spl.points])
self.height = self.maxy - self.miny
self.width = self.maxx - self.minx
self.num_trafos = []
maxlength = thickness * self.width / self.height
for spl in splines:
length = 0
curr = spl(0)
for i in range(1, subdivs + 1):
last = curr
t = 1 / subdivs * i
curr = spl(t)
length += curr.dist(last)
self.num_trafos.append(max(1, int(length / maxlength * 1.5)))
self.num_total = sum(self.num_trafos)
def get_random_trafo(self):
r = random.randrange(int(self.num_total) + 1)
l = 0
for i in range(len(self.num_trafos)):
if r >= l and r < l + self.num_trafos[i]:
return i, random.randrange(self.num_trafos[i])
l += self.num_trafos[i]
return len(self.num_trafos) - 1, random.randrange(self.num_trafos[-1])
def transform_point(self, point, trafo=None):
x = (point.x - self.minx) / self.width
y = (point.y - self.miny) / self.height
if trafo is None:
trafo = self.get_random_trafo()
start, end = self.splines[trafo[0]].GetDomain()
length = end - start
seg_length = length / self.num_trafos[trafo[0]]
t = start + seg_length * trafo[1] + seg_length * x
basepoint = self.splines[trafo[0]](t)
if t + 1 / 50000 > end:
neighbour = self.splines[trafo[0]](t - 1 / 50000)
derivative = neighbour - basepoint
else:
neighbour = self.splines[trafo[0]](t + 1 / 50000)
derivative = basepoint - neighbour
if derivative.Mag() != 0:
basepoint.x += derivative.y / derivative.Mag() * (y - 0.5) * self.thickness
basepoint.y += -derivative.x / derivative.Mag() * (y - 0.5) * self.thickness
else:
# can happen, especially with single precision float
pass
self.truncate(basepoint)
return basepoint
def truncate(self, point):
if point.x >= self.maxx:
point.x = self.maxx
if point.y >= self.maxy:
point.y = self.maxy
if point.x < self.minx:
point.x = self.minx
if point.y < self.miny:
point.y = self.miny
def create_image_chaos(self, w, h, iterations, rng_seed):
# Always use the same sequence of random numbers
# to get reproductible benchmark
random.seed(rng_seed)
im = bytearray(w * h)
point = GVector((self.maxx + self.minx) / 2, (self.maxy + self.miny) / 2, 0)
for _ in range(iterations):
point = self.transform_point(point)
x = (point.x - self.minx) / self.width * w
y = (point.y - self.miny) / self.height * h
x = int(x)
y = int(y)
if x == w:
x -= 1
if y == h:
y -= 1
im[(h - y - 1) * w + x] = 1
return im
###########################################################################
# Benchmark interface
if not hasattr(random, "randrange"):
print("SKIP")
raise SystemExit
bm_params = {
(100, 50): (0.25, 100, 50, 50, 50, 1234),
(1000, 1000): (0.25, 200, 400, 400, 1000, 1234),
(5000, 1000): (0.25, 400, 500, 500, 7000, 1234),
}
def bm_setup(params):
splines = [
Spline(
[
GVector(1.597, 3.304, 0.0),
GVector(1.576, 4.123, 0.0),
GVector(1.313, 5.288, 0.0),
GVector(1.619, 5.330, 0.0),
GVector(2.890, 5.503, 0.0),
GVector(2.373, 4.382, 0.0),
GVector(1.662, 4.360, 0.0),
],
3,
[0, 0, 0, 1, 1, 1, 2, 2, 2],
),
Spline(
[
GVector(2.805, 4.017, 0.0),
GVector(2.551, 3.525, 0.0),
GVector(1.979, 2.620, 0.0),
GVector(1.979, 2.620, 0.0),
],
3,
[0, 0, 0, 1, 1, 1],
),
Spline(
[
GVector(2.002, 4.011, 0.0),
GVector(2.335, 3.313, 0.0),
GVector(2.367, 3.233, 0.0),
GVector(2.367, 3.233, 0.0),
],
3,
[0, 0, 0, 1, 1, 1],
),
]
chaos = Chaosgame(splines, params[0], params[1])
image = None
def run():
nonlocal image
_, _, width, height, iter, rng_seed = params
image = chaos.create_image_chaos(width, height, iter, rng_seed)
def result():
norm = params[4]
# Images are not the same when floating point behaviour is different,
# so return percentage of pixels that are set (rounded to int).
# write_ppm(image, params[2], params[3], 'out-.ppm')
pix = int(100 * sum(image) / len(image))
return norm, pix
return run, result