def accumulate_subpixels(offset_x, offset_y):
nonlocal result
x = np.arange(width, dtype='float64') + offset_x
y = np.arange(height, dtype='float64') + offset_y
x, y = np.meshgrid(x, y)
x = (2 * x - width) * z
y = (2 * y - height) * z
x, y = x*c + y*s, y*c - x*s
x += center_x
y += center_y
x_buf = ffi.cast("double*", x.ctypes.data)
y_buf = ffi.cast("double*", y.ctypes.data)
lib.mandelbrot_generic(x_buf, y_buf, width*height, numerator, denominator, max_iter, inside_cutoff, outside_offset, clip_outside, np.real(julia_c), np.imag(julia_c), julia)
inside = x
outside = y
subpixel_image = color_map(inside, outside, inside_cutoff)
lock.acquire()
result += subpixel_image
lock.release()
def basic_eval(q, a, b, c, max_iter, shape=None):
if shape is None:
for z in (q, a, b, c):
if hasattr(z, 'shape'):
if shape is None:
shape = z.shape
if shape == ():
shape = z.shape
# Upshape and make unique
z = np.zeros(shape)
q = q + z
a = a + z
b = b + z
c = c + z
result = z
q_buf = ffi.cast("double*", q.ctypes.data)
a_buf = ffi.cast("double*", a.ctypes.data)
b_buf = ffi.cast("double*", b.ctypes.data)
c_buf = ffi.cast("double*", c.ctypes.data)
result_buf = ffi.cast("double*", result.ctypes.data)
lib.smooth_julia(q_buf, a_buf, b_buf, c_buf, result_buf, max_iter,
result.size)
return result
def pow_quaternion_inplace(x, y, z, exponent):
x_buf = ffi.cast("double*", x.ctypes.data)
y_buf = ffi.cast("double*", y.ctypes.data)
z_buf = ffi.cast("double*", z.ctypes.data)
lib.pow_quaternion(
x_buf, y_buf, z_buf,
exponent, x.size
)
return x, y, z
def buddhabulb_exposure(width, height, depth, center_x, center_y, center_z, zoom, rotation_theta, rotation_phi, rotation_gamma, exponent_theta, exponent_phi, exponent_r, num_samples, min_iter, max_iter, generator, num_threads=16, bailout=16, chunk_size=8192, julia=None):
num_color_channels = 3
result = np.zeros((depth, height, width), dtype="uint64")
result_buf = ffi.cast("unsigned long long*", result.ctypes.data)
num_samples = int(round(num_samples / num_threads))
ct, st = np.cos(rotation_theta), np.sin(rotation_theta)
cp, sp = np.cos(rotation_phi), np.sin(rotation_phi)
cg, sg = np.cos(rotation_gamma), np.sin(rotation_gamma)
dx = np.identity(3, dtype="double")
dx = np.matmul(dx, [[ct, 0, st], [0, 1, 0], [-st, 0, ct]])
dx = np.matmul(dx, [[cp, sp, 0], [-sp, cp, 0], [0, 0, 1]])
dx = np.matmul(dx, [[1, 0, 0], [0, cg, sg], [0, -sg, cg]])
dx[0] *= 2**zoom * height
dx[1] *= 2**zoom * height
dx[2] *= 2**zoom * depth
dx_buf = ffi.cast("double*", dx.ctypes.data)
offset = np.matmul(dx, [center_x, center_y, center_z])
x0 = width*0.5 - offset[0]
y0 = height*0.5 - offset[1]
z0 = depth*0.5 - offset[2]
def accumulate_samples():
remaining = num_samples
while remaining:
chunk = min(remaining, chunk_size)
x_samples, y_samples, z_samples = generator(chunk)
x_samples_buf = ffi.cast("double*", x_samples.ctypes.data)
y_samples_buf = ffi.cast("double*", y_samples.ctypes.data)
z_samples_buf = ffi.cast("double*", z_samples.ctypes.data)
if julia is not None:
cx_samples = 0*x_samples + julia[0]
cy_samples = 0*y_samples + julia[1]
cz_samples = 0*z_samples + julia[2]
else:
cx_samples = x_samples
cy_samples = y_samples
cz_samples = z_samples
cx_samples_buf = ffi.cast("double*", cx_samples.ctypes.data)
cy_samples_buf = ffi.cast("double*", cy_samples.ctypes.data)
cz_samples_buf = ffi.cast("double*", cz_samples.ctypes.data)
lib.buddhabulb(x_samples_buf, y_samples_buf, z_samples_buf, cx_samples_buf, cy_samples_buf, cz_samples_buf, chunk, result_buf, width, height, depth, x0, y0, z0, dx_buf, exponent_theta, exponent_phi, exponent_r, max_iter, min_iter, bailout)
remaining -= chunk
ts = []
for _ in range(num_threads):
ts.append(Thread(target=accumulate_samples))
ts[-1].start()
for t in ts:
t.join()
return result
def accumulate_subpixels(offset_x, offset_y):
nonlocal result
inside_arr = np.empty(height * width, dtype='int64')
outside_arr = np.empty(height * width, dtype='float64')
inside_buf = ffi.cast("long long*", inside_arr.ctypes.data)
outside_buf = ffi.cast("double*", outside_arr.ctypes.data)
lib.mandelbrot(inside_buf, outside_buf, width, height, offset_x, offset_y, x, y, zoom, int(exponent - 0.5), max_iter, inside_cutoff, clip_outside)
subpixel_image = color_map(inside_arr.reshape(height, width), outside_arr.reshape(height, width), inside_cutoff)
lock.acquire()
result += subpixel_image
lock.release()
def accumulate_samples():
remaining = num_samples
while remaining:
chunk = min(remaining, chunk_size)
samples = generator(chunk)
samples_buf = ffi.cast("double*", samples.ctypes.data)
if julia:
cs = samples*0j + julia_c
else:
cs = samples
cs_buf = ffi.cast("double*", cs.ctypes.data)
seed = np.random.randint(0, 1<<32);
lib.buddhabrot(samples_buf, cs_buf, chunk, result_buf, width, height, x0, y0, dx00, dx01, dx10, dx11, numerator, denominator, max_iter, min_iter, bailout, seed)
remaining -= chunk
def biaxial_julia(x, y, z, c0x, c0y, c1y, c1z, exponent0, exponent1, max_iter, shape=None):
refs, bufs = bufferize(x, y, z, c0x, c0y, c1y, c1z)
result = np.zeros(refs[0].shape)
result_buf = ffi.cast("double*", result.ctypes.data)
args = bufs + [result_buf, exponent0, exponent1, max_iter, result.size]
lib.biaxial_julia(*args)
return result
def mandelbulb(x, y, z, cx, cy, cz, exponent_theta, exponent_phi, exponent_r, max_iter, shape=None):
if shape is None:
for w in (x, y, z, cx, cy, cz):
if hasattr(w, 'shape'):
if shape is None:
shape = w.shape
if shape == ():
shape = w.shape
# Upshape and make unique
w = np.zeros(shape)
x = x + w
y = y + w
z = z + w
cx = cx + w
cy = cy + w
cz = cz + w
result = w
x_buf = ffi.cast("double*", x.ctypes.data)
y_buf = ffi.cast("double*", y.ctypes.data)
z_buf = ffi.cast("double*", z.ctypes.data)
cx_buf = ffi.cast("double*", cx.ctypes.data)
cy_buf = ffi.cast("double*", cy.ctypes.data)
cz_buf = ffi.cast("double*", cz.ctypes.data)
result_buf = ffi.cast("double*", result.ctypes.data)
lib.smooth_mandelbulb(
x_buf, y_buf, z_buf,
cx_buf, cy_buf, cz_buf,
result_buf, exponent_theta, exponent_phi, exponent_r, max_iter,
result.size
)
return result
def accumulate_subpixels(offset_x, offset_y):
nonlocal result
x = np.arange(width, dtype='float64') + offset_x
y = np.arange(height, dtype='float64') + offset_y
x = x_scale * (2 * x - width) * zoom / height
y = (2 * y - height) * zoom / height
x, y = np.meshgrid(x, y)
qw = center.w + x * cos(theta) + u_max * sin(theta)
qx = center.x + u_max * cos(theta) - x * sin(theta)
qy = center.y + y * cos(phi) + v_max * sin(phi)
qz = center.z + v_max * cos(phi) - y * sin(phi)
uw = sin(theta) * u_delta
ux = cos(theta) * u_delta
uy = 0
uz = 0
vw = 0
vx = 0
vy = sin(phi) * v_delta
vz = cos(phi) * v_delta
area = qw + 0
red = qx + 0
green = qy + 0
blue = qz + 0
qw_buf = ffi.cast("double*", area.ctypes.data)
qx_buf = ffi.cast("double*", red.ctypes.data)
qy_buf = ffi.cast("double*", green.ctypes.data)
qz_buf = ffi.cast("double*", blue.ctypes.data)
lib.julia(qw_buf, qx_buf, qy_buf, qz_buf, width * height, uw, ux, uy,
uz, u_samples, vw, vx, vy, vz, v_samples, a.w, a.x, a.y, a.z,
b.w, b.x, b.y, b.z, c.w, c.x, c.y, c.z, max_iter,
pseudo_mandelbrot, coloring, bg_luminance, attenuation)
subpixel_image = color_map(area, red, green, blue)
lock.acquire()
result += subpixel_image
lock.release()
def pow3d(x, y, z, exponent_theta, exponent_phi, exponent_r, shape=None):
if shape is None:
for w in (x, y, z):
if hasattr(w, 'shape'):
if shape is None:
shape = w.shape
if shape == ():
shape = w.shape
# Upshape and make unique
w = np.zeros(shape)
x = x + w
y = y + w
z = z + w
x_buf = ffi.cast("double*", x.ctypes.data)
y_buf = ffi.cast("double*", y.ctypes.data)
z_buf = ffi.cast("double*", z.ctypes.data)
lib.pow3d(
x_buf, y_buf, z_buf,
exponent_theta, exponent_phi, exponent_r,
x.size
)
return x, y, z
def bufferize(*args, shape=None):
if shape is None:
for w in args:
if hasattr(w, 'shape'):
if shape is None:
shape = w.shape
if shape == ():
shape = w.shape
# Upshape and make unique
w = np.zeros(shape)
refs = []
results = []
for z in args:
z = z + w
z_buffer = ffi.cast("double*", z.ctypes.data)
refs.append(z)
results.append(z_buffer)
return refs, results
def buddhabrot_exposure(width, height, center_x, center_y, zoom, rotation, numerator, denominator, num_samples, min_iter, max_iter, generator, num_threads=16, bailout=16, chunk_size=8192, julia_c=1j, julia=False):
num_color_channels = 3
result = np.zeros((height, width), dtype="uint64")
result_buf = ffi.cast("unsigned long long*", result.ctypes.data)
num_samples = int(round(num_samples / num_threads))
c, s = np.cos(rotation), np.sin(rotation)
z = 2**zoom * height
dx00 = z*c
dx11 = z*c
dx01 = z*s
dx10 = -z*s
x0 = width*0.5 - dx00 * center_x - dx01 * center_y
y0 = height*0.5 - dx10 * center_x - dx11 * center_y
def accumulate_samples():
remaining = num_samples
while remaining:
chunk = min(remaining, chunk_size)
samples = generator(chunk)
samples_buf = ffi.cast("double*", samples.ctypes.data)
if julia:
cs = samples*0j + julia_c
else:
cs = samples
cs_buf = ffi.cast("double*", cs.ctypes.data)
seed = np.random.randint(0, 1<<32);
lib.buddhabrot(samples_buf, cs_buf, chunk, result_buf, width, height, x0, y0, dx00, dx01, dx10, dx11, numerator, denominator, max_iter, min_iter, bailout, seed)
remaining -= chunk
ts = []
for _ in range(num_threads):
ts.append(Thread(target=accumulate_samples))
ts[-1].start()
for t in ts:
t.join()
return result
def accumulate_samples():
remaining = num_samples
while remaining:
chunk = min(remaining, chunk_size)
x_samples, y_samples, z_samples = generator(chunk)
x_samples_buf = ffi.cast("double*", x_samples.ctypes.data)
y_samples_buf = ffi.cast("double*", y_samples.ctypes.data)
z_samples_buf = ffi.cast("double*", z_samples.ctypes.data)
if julia is not None:
cx_samples = 0*x_samples + julia[0]
cy_samples = 0*y_samples + julia[1]
cz_samples = 0*z_samples + julia[2]
else:
cx_samples = x_samples
cy_samples = y_samples
cz_samples = z_samples
cx_samples_buf = ffi.cast("double*", cx_samples.ctypes.data)
cy_samples_buf = ffi.cast("double*", cy_samples.ctypes.data)
cz_samples_buf = ffi.cast("double*", cz_samples.ctypes.data)
lib.buddhabulb(x_samples_buf, y_samples_buf, z_samples_buf, cx_samples_buf, cy_samples_buf, cz_samples_buf, chunk, result_buf, width, height, depth, x0, y0, z0, dx_buf, exponent_theta, exponent_phi, exponent_r, max_iter, min_iter, bailout)
remaining -= chunk