def map_bounds(self, X=None, Y=None, Z=None):
""" @brief Calculates remapped bounds
@returns Array of remapped bounds
@param X New X function or None
@param Y New Y function or None
@param Z New Z function or None
@details Note that X, Y, and Z should be the inverse
of a coordinate mapping to properly transform bounds.
"""
if self.dx is not None: x = Interval(self.xmin, self.xmax)
else: x = Interval(float('nan'))
if self.dy is not None: y = Interval(self.ymin, self.ymax)
else: y = Interval(float('nan'))
if self.dz is not None: z = Interval(self.zmin, self.zmax)
else: z = Interval(float('nan'))
if self.dx is not None: a = Interval(self.xmin, self.xmax)
else: a = Interval(float('nan'))
if self.dy is not None: b = Interval(self.ymin, self.ymax)
else: b = Interval(float('nan'))
if self.dz is not None: c = Interval(self.zmin, self.zmax)
else: c = Interval(float('nan'))
if X:
X_p = libfab.make_packed(X.ptr)
a = libfab.eval_i(X_p, x, y, z)
libfab.free_packed(X_p)
if Y:
Y_p = libfab.make_packed(Y.ptr)
b = libfab.eval_i(Y_p, x, y, z)
libfab.free_packed(Y_p)
if Z:
Z_p = libfab.make_packed(Z.ptr)
c = libfab.eval_i(Z_p, x, y, z)
libfab.free_packed(Z_p)
bounds = []
for i in [a,b,c]:
if math.isnan(i.lower) or math.isnan(i.upper):
bounds += [None, None]
else:
bounds += [i.lower, i.upper]
return bounds
def map_bounds(self, X=None, Y=None, Z=None):
""" @brief Calculates remapped bounds
@returns Array of remapped bounds
@param X New X function or None
@param Y New Y function or None
@param Z New Z function or None
@details Note that X, Y, and Z should be the inverse
of a coordinate mapping to properly transform bounds.
"""
if self.dx is not None: x = Interval(self.xmin, self.xmax)
else: x = Interval(float('nan'))
if self.dy is not None: y = Interval(self.ymin, self.ymax)
else: y = Interval(float('nan'))
if self.dz is not None: z = Interval(self.zmin, self.zmax)
else: z = Interval(float('nan'))
if self.dx is not None: a = Interval(self.xmin, self.xmax)
else: a = Interval(float('nan'))
if self.dy is not None: b = Interval(self.ymin, self.ymax)
else: b = Interval(float('nan'))
if self.dz is not None: c = Interval(self.zmin, self.zmax)
else: c = Interval(float('nan'))
if X:
X_p = libfab.make_packed(X.ptr)
a = libfab.eval_i(X_p, x, y, z)
libfab.free_packed(X_p)
if Y:
Y_p = libfab.make_packed(Y.ptr)
b = libfab.eval_i(Y_p, x, y, z)
libfab.free_packed(Y_p)
if Z:
Z_p = libfab.make_packed(Z.ptr)
c = libfab.eval_i(Z_p, x, y, z)
libfab.free_packed(Z_p)
bounds = []
for i in [a, b, c]:
if math.isnan(i.lower) or math.isnan(i.upper):
bounds += [None, None]
else:
bounds += [i.lower, i.upper]
return bounds
def asdf(self, region=None, resolution=None, mm_per_unit=None,
merge_leafs=True, interrupt=None):
""" @brief Constructs an ASDF from a math tree.
@details Runs in up to eight threads.
@param region Evaluation region (if None, taken from expression bounds)
@param resolution Render resolution in voxels/unit
@param mm_per_unit Real-world scale
@param merge_leafs Boolean determining whether leaf cells are combined
@param interrupt threading.Event that aborts rendering if set
@returns ASDF data structure
"""
if region is None:
if not self.bounded:
raise Exception('Unknown render region!')
elif resolution is None:
raise Exception('Region or resolution must be provided!')
region = Region(
(self.xmin, self.ymin, self.zmin if self.zmin else 0),
(self.xmax, self.ymax, self.zmax if self.zmax else 0),
resolution
)
if interrupt is None: interrupt = threading.Event()
# Shared flag to interrupt rendering
halt = ctypes.c_int(0)
# Split the region into up to 8 sections
split = region.octsect(all=True)
subregions = [split[i] for i in range(8) if split[i] is not None]
ids = [i for i in range(8) if split[i] is not None]
threads = len(subregions)
clones = [self.clone() for i in range(threads)]
packed = [libfab.make_packed(c.ptr) for c in clones]
# Generate a root for the tree
asdf = ASDF(libfab.asdf_root(packed[0], region), color=self.color)
# Multithread the solver process
q = Queue.Queue()
args = zip(packed, ids, subregions, [q]*threads)
# Helper function to construct a single branch
def construct_branch(ptree, id, region, queue):
asdf = libfab.build_asdf(ptree, region, merge_leafs, halt)
queue.put((id, asdf))
# Run the constructor in parallel to make the branches
multithread(construct_branch, args, interrupt, halt)
for p in packed: libfab.free_packed(p)
# Attach the branches to the root
for s in subregions:
try: id, branch = q.get_nowait()
except Queue.Empty: break
else: asdf.ptr.contents.branches[id] = branch
libfab.get_d_from_children(asdf.ptr)
libfab.simplify(asdf.ptr, merge_leafs)
# Set a scale on the ASDF if one was provided
if mm_per_unit is not None: asdf.rescale(mm_per_unit)
return asdf
def asdf(self,
region=None,
resolution=None,
mm_per_unit=None,
merge_leafs=True,
interrupt=None):
""" @brief Constructs an ASDF from a math tree.
@details Runs in up to eight threads.
@param region Evaluation region (if None, taken from expression bounds)
@param resolution Render resolution in voxels/unit
@param mm_per_unit Real-world scale
@param merge_leafs Boolean determining whether leaf cells are combined
@param interrupt threading.Event that aborts rendering if set
@returns ASDF data structure
"""
if region is None:
if not self.bounded:
raise Exception('Unknown render region!')
elif resolution is None:
raise Exception('Region or resolution must be provided!')
region = Region(
(self.xmin, self.ymin, self.zmin if self.zmin else 0),
(self.xmax, self.ymax, self.zmax if self.zmax else 0),
resolution)
if interrupt is None: interrupt = threading.Event()
# Shared flag to interrupt rendering
halt = ctypes.c_int(0)
# Split the region into up to 8 sections
split = region.octsect(all=True)
subregions = [split[i] for i in range(8) if split[i] is not None]
ids = [i for i in range(8) if split[i] is not None]
threads = len(subregions)
clones = [self.clone() for i in range(threads)]
packed = [libfab.make_packed(c.ptr) for c in clones]
# Generate a root for the tree
asdf = ASDF(libfab.asdf_root(packed[0], region), color=self.color)
asdf.lock.acquire()
# Multithread the solver process
q = Queue.Queue()
args = zip(packed, ids, subregions, [q] * threads)
# Helper function to construct a single branch
def construct_branch(ptree, id, region, queue):
asdf = libfab.build_asdf(ptree, region, merge_leafs, halt)
queue.put((id, asdf))
# Run the constructor in parallel to make the branches
multithread(construct_branch, args, interrupt, halt)
for p in packed:
libfab.free_packed(p)
# Attach the branches to the root
for s in subregions:
try:
id, branch = q.get_nowait()
except Queue.Empty:
break
else:
# Make sure we didn't get a NULL pointer back
# (which could occur if the halt flag was raised)
try:
branch.contents
except ValueError:
asdf.lock.release()
return None
asdf.ptr.contents.branches[id] = branch
libfab.get_d_from_children(asdf.ptr)
libfab.simplify(asdf.ptr, merge_leafs)
asdf.lock.release()
# Set a scale on the ASDF if one was provided
if mm_per_unit is not None: asdf.rescale(mm_per_unit)
return asdf
class MathTree(object):
""" @class MathTree
@brief Represents a distance metric math expression.
@details
Arithmetic operators are overloaded to extend the tree with
either distance metric arithmetic or shape logical expressions,
depending on the value of the instance variable 'shape'
"""
def __init__(self, math, shape=False, color=None):
""" @brief MathTree constructor
@param math Math string (in prefix notation)
@param shape Boolean modifying arithmetic operators
@param color Color tuple or None
"""
## @var math
# Math string (in sparse prefix syntax)
if type(math) in [int, float]:
self.math = 'f' + str(math)
else:
self.math = math
## @var shape
# Boolean modify the behavior of arithmetic operators
self.shape = shape
## @var color
# Assigned color, or None
self.color = color
self._str = None
self._ptr = None
## @var bounds
# X, Y, Z bounds (or None)
self.bounds = [None] * 6
self.lock = threading.Lock()
@threadsafe
def __del__(self):
""" @brief MathTree destructor """
if self._ptr is not None and libfab is not None:
libfab.free_tree(self.ptr)
@property
def ptr(self):
""" @brief Parses self.math and returns a pointer to a MathTree structure
"""
if self._ptr is None:
self._ptr = libfab.parse(self.math)
return self._ptr
############################################################################
@property
def dx(self):
try:
return self.xmax - self.xmin
except TypeError:
return None
@property
def dy(self):
try:
return self.ymax - self.ymin
except TypeError:
return None
@property
def dz(self):
try:
return self.zmax - self.zmin
except TypeError:
return None
@property
def bounds(self):
return [
self.xmin, self.xmax, self.ymin, self.ymax, self.zmin, self.zmax
]
@bounds.setter
def bounds(self, value):
for b in ['xmin', 'xmax', 'ymin', 'ymax', 'zmin', 'zmax']:
setattr(self, b, value.pop(0))
@property
def xmin(self):
return self._xmin
@xmin.setter
def xmin(self, value):
if value is None: self._xmin = None
else:
try:
self._xmin = float(value)
except:
raise ValueError('xmin must be a float')
@property
def xmax(self):
return self._xmax
@xmax.setter
def xmax(self, value):
if value is None: self._xmax = None
else:
try:
self._xmax = float(value)
except:
raise ValueError('xmax must be a float')
@property
def ymin(self):
return self._ymin
@ymin.setter
def ymin(self, value):
if value is None: self._ymin = None
else:
try:
self._ymin = float(value)
except:
raise ValueError('ymin must be a float')
@property
def ymax(self):
return self._ymax
@ymax.setter
def ymax(self, value):
if value is None: self._ymax = None
else:
try:
self._ymax = float(value)
except:
raise ValueError('ymax must be a float')
@property
def zmin(self):
return self._zmin
@zmin.setter
def zmin(self, value):
if value is None: self._zmin = None
else:
try:
self._zmin = float(value)
except:
raise ValueError('zmin must be a float')
@property
def zmax(self):
return self._zmax
@zmax.setter
def zmax(self, value):
if value is None: self._zmax = None
else:
try:
self._zmax = float(value)
except:
raise ValueError('zmax must be a float')
@property
def bounded(self):
return all(d is not None for d in [self.dx, self.dy, self.dz])
############################################################################
@property
def color(self):
return self._color
@color.setter
def color(self, rgb):
named = {
'red': (255, 0, 0),
'blue': (0, 0, 255),
'green': (0, 255, 0),
'white': (255, 255, 255),
'grey': (128, 128, 128),
'black': (0, 0, 0),
'yellow': (255, 255, 0),
'cyan': (0, 255, 255),
'magenta': (255, 0, 255),
'teal': (0, 255, 255),
'pink': (255, 0, 255),
'brown': (145, 82, 45),
'tan': (125, 90, 60),
'navy': (0, 0, 128)
}
if type(rgb) is str and rgb in named:
self._color = named[rgb]
elif type(rgb) in [tuple, list] and len(rgb) == 3:
self._color = tuple(rgb)
elif rgb is None:
self._color = rgb
else:
raise ValueError(
'Invalid color (must be integer 3-value tuple or keyword)')
############################################################################
@staticmethod
def wrap(value):
''' Converts a value to a MathTree.
None values are left alone,
Strings are assumed to be valid math strings and wrapped
Floats / ints are converted'''
if isinstance(value, MathTree):
return value
elif value is None:
return value
elif type(value) is str:
return MathTree(value)
elif type(value) is not float:
try:
value = float(value)
except (ValueError, TypeError):
raise TypeError('Wrong type for MathTree arithmetic (%s)' %
type(value))
return MathTree.Constant(value)
@classmethod
@forcetree
def min(cls, A, B):
return cls('i' + A.math + B.math)
@classmethod
@forcetree
def max(cls, A, B):
return cls('a' + A.math + B.math)
@classmethod
@forcetree
def pow(cls, A, B):
return cls('p' + A.math + B.math)
@classmethod
@forcetree
def sqrt(cls, A):
return cls('r' + A.math)
@classmethod
@forcetree
def abs(cls, A):
return cls('b' + A.math)
@classmethod
@forcetree
def square(cls, A):
return cls('q' + A.math)
@classmethod
@forcetree
def sin(cls, A):
return cls('s' + A.math)
@classmethod
@forcetree
def cos(cls, A):
return cls('c' + A.math)
@classmethod
@forcetree
def tan(cls, A):
return cls('t' + A.math)
@classmethod
@forcetree
def asin(cls, A):
return cls('S' + A.math)
@classmethod
@forcetree
def acos(cls, A):
return cls('C' + A.math)
@classmethod
@forcetree
def atan(cls, A):
return cls('T' + A.math)
#########################
# MathTree Arithmetic #
#########################
# If shape is set, then + and - perform logical combination;
# otherwise, they perform arithmeic.
@matching
@forcetree
def __add__(self, rhs):
if self.shape or (rhs and rhs.shape):
if rhs is None: return self.clone()
t = MathTree('i' + self.math + rhs.math, True)
if self.dx is not None and rhs.dx is not None:
t.xmin = min(self.xmin, rhs.xmin)
t.xmax = max(self.xmax, rhs.xmax)
if self.dx is not None and rhs.dy is not None:
t.ymin = min(self.ymin, rhs.ymin)
t.ymax = max(self.ymax, rhs.ymax)
if self.dz is not None and rhs.dz is not None:
t.zmin = min(self.zmin, rhs.zmin)
t.zmax = max(self.zmax, rhs.zmax)
return t
else:
return MathTree('+' + self.math + rhs.math)
@matching
@forcetree
def __radd__(self, lhs):
if lhs is None: return self.clone()
if self.shape or (lhs and lhs.shape):
t = MathTree('i' + lhs.math + self.math)
if self.dx is not None and lhs.dx is not None:
t.xmin = min(self.xmin, lhs.xmin)
t.xmax = max(self.xmax, lhs.xmax)
if self.dy is not None and lhs.dy is not None:
t.ymin = min(self.ymin, lhs.ymin)
t.ymax = max(self.ymax, lhs.ymax)
if self.dz is not None and lhs.dz is not None:
t.zmin = min(self.zmin, lhs.zmin)
t.zmax = max(self.zmax, lhs.zmax)
return t
else:
return MathTree('+' + lhs.math + self.math)
@matching
@forcetree
def __sub__(self, rhs):
if self.shape or (rhs and rhs.shape):
if rhs is None: return self.clone()
t = MathTree('a' + self.math + 'n' + rhs.math, True)
for i in ['xmin', 'xmax', 'ymin', 'ymax', 'zmin', 'zmax']:
setattr(t, i, getattr(self, i))
return t
else:
return MathTree('-' + self.math + rhs.math)
@matching
@forcetree
def __rsub__(self, lhs):
if self.shape or (lhs and lhs.shape):
if lhs is None: return MathTree('n' + self.math)
t = MathTree('a' + lhs.math + 'n' + self.math, True)
for i in ['xmin', 'xmax', 'ymin', 'ymax', 'zmin', 'zmax']:
setattr(t, i, getattr(lhs, i))
return t
else:
return MathTree('-' + lhs.math + self.math)
@matching
@forcetree
def __and__(self, rhs):
if self.shape or rhs.shape:
t = MathTree('a' + self.math + rhs.math, True)
if self.dx is not None and rhs.dx is not None:
t.xmin = max(self.xmin, rhs.xmin)
t.xmax = min(self.xmax, rhs.xmax)
if self.dy is not None and rhs.dy is not None:
t.ymin = max(self.ymin, rhs.ymin)
t.ymax = min(self.ymax, rhs.ymax)
if self.dz is not None and rhs.dz is not None:
t.zmin = max(self.zmin, rhs.zmin)
t.zmax = min(self.zmax, rhs.zmax)
return t
else:
raise NotImplementedError(
'& operator is undefined for non-shape math expressions.')
@matching
@forcetree
def __rand__(self, lhs):
if self.shape or lhs.shape:
t = MathTree('a' + lhs.math + self.math, True)
if self.dx is not None and lhs.dx is not None:
t.xmin = max(self.xmin, lhs.xmin)
t.xmax = min(self.xmax, lhs.xmax)
if self.dy is not None and lhs.dy is not None:
t.ymin = max(self.ymin, lhs.ymin)
t.ymax = min(self.ymax, lhs.ymax)
if self.dz is not None and lhs.dz is not None:
t.zmin = max(self.zmin, lhs.zmin)
t.zmax = min(self.zmax, lhs.zmax)
return t
else:
raise NotImplementedError(
'& operator is undefined for non-shape math expressions.')
@matching
@forcetree
def __or__(self, rhs):
if self.shape or rhs.shape:
t = MathTree('i' + self.math + rhs.math, True)
if self.dx is not None and rhs.dx is not None:
t.xmin = min(self.xmin, rhs.xmin)
t.xmax = max(self.xmax, rhs.xmax)
if self.dy is not None and rhs.dy is not None:
t.ymin = min(self.ymin, rhs.ymin)
t.ymax = max(self.ymax, rhs.ymax)
if self.dz is not None and rhs.dz is not None:
t.zmin = min(self.zmin, rhs.zmin)
t.zmax = max(self.zmax, rhs.zmax)
return t
else:
raise NotImplementedError(
'| operator is undefined for non-shape math expressions.')
@matching
@forcetree
def __ror__(self, lhs):
if self.shape or lhs.shape:
t = MathTree('i' + lhs.math + self.math, True)
if self.dx is not None and lhs.dx is not None:
t.xmin = min(self.xmin, lhs.xmin)
t.xmax = max(self.xmax, lhs.xmax)
if self.dy is not None and lhs.dy is not None:
t.ymin = min(self.ymin, lhs.ymin)
t.ymax = max(self.ymax, lhs.ymax)
if self.dz is not None and lhs.dz is not None:
t.zmin = min(self.zmin, lhs.zmin)
t.zmax = max(self.zmax, lhs.zmax)
return t
else:
raise NotImplementedError(
'| operator is undefined for non-shape math expressions.')
@forcetree
def __mul__(self, rhs):
return MathTree('*' + self.math + rhs.math)
@forcetree
def __rmul__(self, lhs):
return MathTree('*' + lhs.math + self.math)
@forcetree
def __div__(self, rhs):
return MathTree('/' + self.math + rhs.math)
@forcetree
def __rdiv__(self, lhs):
return MathTree('/' + lhs.math + self.math)
@forcetree
def __neg__(self):
return MathTree('n' + self.math, shape=self.shape)
###############################
## String and representation ##
###############################
def __str__(self):
if self._str is None:
self._str = self.make_str()
return self._str
def make_str(self, verbose=False):
""" @brief Converts the object into an infix-notation string
@details
Creates a OS pipe, instructs the object to print itself into the pipe, and reads the output in chunks of maximum size 1024.
"""
# Create a pipe to get the printout
read, write = os.pipe()
# Start the print function running in a separate thread
# (so that we can eat the output and avoid filling the pipe)
if verbose: printer = libfab.fdprint_tree_verbose
else: printer = libfab.fdprint_tree
t = threading.Thread(target=printer, args=(self.ptr, write))
t.daemon = True
t.start()
s = r = os.read(read, 1024)
while r:
r = os.read(read, 1024)
s += r
t.join()
os.close(read)
return s
def __repr__(self):
return "'%s' (tree at %s)" % (self, hex(self.ptr.value))
def verbose(self):
return self.make_str(verbose=True)
def save_dot(self, filename, arrays=False):
""" @brief Converts math expression to .dot graph description
"""
if arrays:
libfab.dot_arrays(self.ptr, filename)
else:
libfab.dot_tree(self.ptr, filename)
@property
def node_count(self):
return libfab.count_nodes(self.ptr)
#################################
## Tree manipulation functions ##
#################################
@forcetree
def map(self, X=None, Y=None, Z=None):
""" @brief Applies a map operator to a tree
@param X New X function or None
@param Y New Y function or None
@param Z New Z function or None
"""
return MathTree('m' + (X.math if X else ' ') + (Y.math if Y else ' ') +
(Z.math if Z else ' ') + self.math,
shape=self.shape,
color=self.color)
@forcetree
def map_bounds(self, X=None, Y=None, Z=None):
""" @brief Calculates remapped bounds
@returns Array of remapped bounds
@param X New X function or None
@param Y New Y function or None
@param Z New Z function or None
@details Note that X, Y, and Z should be the inverse
of a coordinate mapping to properly transform bounds.
"""
if self.dx is not None: x = Interval(self.xmin, self.xmax)
else: x = Interval(float('nan'))
if self.dy is not None: y = Interval(self.ymin, self.ymax)
else: y = Interval(float('nan'))
if self.dz is not None: z = Interval(self.zmin, self.zmax)
else: z = Interval(float('nan'))
if self.dx is not None: a = Interval(self.xmin, self.xmax)
else: a = Interval(float('nan'))
if self.dy is not None: b = Interval(self.ymin, self.ymax)
else: b = Interval(float('nan'))
if self.dz is not None: c = Interval(self.zmin, self.zmax)
else: c = Interval(float('nan'))
if X:
X_p = libfab.make_packed(X.ptr)
a = libfab.eval_i(X_p, x, y, z)
libfab.free_packed(X_p)
if Y:
Y_p = libfab.make_packed(Y.ptr)
b = libfab.eval_i(Y_p, x, y, z)
libfab.free_packed(Y_p)
if Z:
Z_p = libfab.make_packed(Z.ptr)
c = libfab.eval_i(Z_p, x, y, z)
libfab.free_packed(Z_p)
bounds = []
for i in [a, b, c]:
if math.isnan(i.lower) or math.isnan(i.upper):
bounds += [None, None]
else:
bounds += [i.lower, i.upper]
return bounds
@threadsafe
def clone(self):
m = MathTree(self.math, shape=self.shape, color=self.color)
m.bounds = [b for b in self.bounds]
if self._ptr is not None:
m._ptr = libfab.clone_tree(self._ptr)
return m
#################################
# Rendering functions #
#################################
def render(self,
region=None,
resolution=None,
mm_per_unit=None,
threads=8,
interrupt=None):
""" @brief Renders a math tree into an Image
@param region Evaluation region (if None, taken from expression bounds)
@param resolution Render resolution in voxels/unit
@param mm_per_unit Real-world scale
@param threads Number of threads to use
@param interrupt threading.Event that aborts rendering if set
@returns Image data structure
"""
if region is None:
if self.dx is None or self.dy is None:
raise Exception('Unknown render region!')
elif resolution is None:
raise Exception('Region or resolution must be provided!')
region = Region(
(self.xmin, self.ymin, self.zmin if self.zmin else 0),
(self.xmax, self.ymax, self.zmax if self.zmax else 0),
resolution)
try:
float(mm_per_unit)
except ValueError, TypeError:
raise ValueError('mm_per_unit must be a number')
if interrupt is None: interrupt = threading.Event()
halt = ctypes.c_int(0) # flag to abort render
image = Image(
region.ni,
region.nj,
channels=1,
depth=16,
)
# Divide the task to share among multiple threads
clones = [self.clone() for i in range(threads)]
packed = [libfab.make_packed(c.ptr) for c in clones]
subregions = region.split_xy(threads)
# Solve each region in a separate thread
args = zip(packed, subregions, [image.pixels] * threads,
[halt] * threads)
multithread(libfab.render16, args, interrupt, halt)
for p in packed:
libfab.free_packed(p)
image.xmin = region.X[0] * mm_per_unit
image.xmax = region.X[region.ni] * mm_per_unit
image.ymin = region.Y[0] * mm_per_unit
image.ymax = region.Y[region.nj] * mm_per_unit
image.zmin = region.Z[0] * mm_per_unit
image.zmax = region.Z[region.nk] * mm_per_unit
return image