# This file is part of pymadcad, distributed under license LGPL v3
''' This modules provide tools for accessing data using its space location (not for final user).
The complexity and therefore the cost of those operations are most of the time close to the hashmap complexity O(1). It means data is found in time independently of the actual size of the mesh or whatever storage it is.
'''
from .mathutils import *
from . import core
from . import mesh
from functools import reduce
from math import floor, ceil, sqrt, inf
[docs]class PositionMap:
''' Holds objects associated with their location.
Every object can be bound to multiple locations, and each location can hold multiple objects.
`cellsize` defines the box size for location hashing (the smaller it is, the bigger the memory footprint will be for non-point primitives)
Attributes defined here:
:cellsize: the boxing parameter (DON'T CHANGE IT IF NON-EMPTY)
:dict: the hashmap from box to objects lists
'''
__slots__ = 'cellsize', 'dict', 'options'
def __init__(self, cellsize, iterable=None):
self.options = {}
self.cellsize = cellsize
self.dict = {}
if iterable: self.update(iterable)
def keysfor(self, space):
''' Rasterize the primitive, yielding the successive position keys
currently allowed primitives are
:points: vec3
:segments: (vec3,vec3)
:triangles: (vec3,vec3,vec3)
'''
cell = self.cellsize
# point
if isinstance(space, vec3):
yield tuple(i64vec3(glm.floor(space/cell)))
# segment
elif isinstance(space, tuple) and len(space) == 2:
# permutation of coordinates to get the direction the closer to Z
n = glm.abs(space[1]-space[0])
if max(n) < NUMPREC*max((max(p) for p in space)): return
if n[1] >= n[0] and n[1] >= n[2]: order,reorder = (2,0,1),(1,2,0)
elif n[0] >= n[1] and n[0] >= n[2]: order,reorder = (1,2,0),(2,0,1)
else: order,reorder = (0,1,2),(0,1,2)
space = [ vec3(p[order[0]], p[order[1]], p[order[2]]) for p in space]
# prepare variables
cell2 = cell/2
v = space[1]-space[0]
dy = v[1]/v[2]
dx = v[0]/v[2]
o = space[0]
fy = lambda z: o[1] + dy*(z-o[2])
fx = lambda z: o[0] + dx*(z-o[2])
# z selection
if v[2] > 0: zmin,zmax = space[0][2], space[1][2]
else: zmin,zmax = space[1][2], space[0][2]
zmin -= zmin%cell
for i in range(max(1,ceil((zmax-zmin)/cell))):
z = zmin + cell*i + cell2
# y selection
if dy > 0: ymin,ymax = fy(z-cell2), fy(z+cell2)
else: ymin,ymax = fy(z+cell2), fy(z-cell2)
ymin -= ymin%cell
for j in range(max(1,ceil((ymax-ymin)/cell))):
y = ymin + j*cell + cell2
# x selection
if dx > 0: xmin,xmax = fx(z-cell2), fx(z+cell2)
else: xmin,xmax = fx(z+cell2), fx(z-cell2)
xmin -= xmin%cell
for k in range(max(1,ceil((xmax-xmin)/cell))):
x = xmin + k*cell + cell2
p = (x,y,z)
yield tuple([floor(p[i]/cell) for i in reorder])
# triangle
elif isinstance(space, tuple) and len(space) == 3:
# permutation of coordinates to get the normal the closer to Z
n = glm.abs(cross(space[1]-space[0], space[2]-space[0]))
if max(n) < NUMPREC*max((max(p) for p in space)): return
if n[1] >= n[0] and n[1] >= n[2]: order,reorder = (2,0,1),(1,2,0)
elif n[0] >= n[1] and n[0] >= n[2]: order,reorder = (1,2,0),(2,0,1)
else: order,reorder = (0,1,2),(0,1,2)
space = [ vec3(p[order[0]], p[order[1]], p[order[2]]) for p in space]
# prepare variables
v = [space[i-1]-space[i] for i in range(3)]
n = cross(v[0],v[1])
dx = -n[0]/n[2]
dy = -n[1]/n[2]
o = space[0]
fz = lambda x,y: o[2] + dx*(x-o[0]) + dy*(y-o[1])
cell2 = cell/2
pmin = reduce(glm.min, space)
pmax = reduce(glm.max, space)
xmin,xmax = pmin[0],pmax[0]
pmin -= pmin%cell
pmax += cell - pmax%cell
# x selection
xmin -= xmin%cell
for i in range(max(1,ceil((xmax-xmin)/cell))):
x = xmin + cell*i + cell2
# y selection
cand = []
for i in range(3):
# NOTE: cet interval ajoute parfois des cases inutiles apres les sommets
if (space[i-1][0]-x+cell2)*(space[i][0]-x-cell2) <= 0 or (space[i-1][0]-x-cell2)*(space[i][0]-x+cell2) <= 0:
d = v[i][1]/(v[i][0] if v[i][0] else inf)
cand.append( space[i][1] + d * (x-cell2-space[i][0]) )
cand.append( space[i][1] + d * (x+cell2-space[i][0]) )
ymin,ymax = max(pmin[1],min(cand)), min(pmax[1],max(cand))
ymin -= ymin%cell
for j in range(max(1,ceil((ymax-ymin)/cell))):
y = ymin + cell*j + cell2
# z selection
cand = []
cand.append( fz(x-cell2, y-cell2) )
cand.append( fz(x+cell2, y-cell2) )
cand.append( fz(x-cell2, y+cell2) )
cand.append( fz(x+cell2, y+cell2) )
zmin,zmax = max(pmin[2],min(cand)), min(pmax[2],max(cand))
zmin -= zmin%cell
for k in range(max(1,ceil((zmax-zmin)/cell))):
z = zmin + cell*k + cell2
# remove box from corners that goes out of the area
p = (x,y,z)
if pmin[0]<p[0] and pmin[1]<p[1] and pmin[2]<p[2] and p[0]<pmax[0] and p[1]<pmax[1] and p[2]<pmax[2]:
yield tuple([floor(p[i]/cell) for i in reorder])
else:
raise TypeError("PositionMap only supports keys of type: points, segments, triangles")
[docs] def keysfor(self, space):
''' Rasterize the primitive, yielding the successive position keys
currently allowed primitives are
:points: vec3
:segments: (vec3,vec3)
:triangles: (vec3,vec3,vec3)
'''
# point
if isinstance(space, vec3):
return tuple(i64vec3(glm.floor(space/cell))),
# segment
elif isinstance(space, tuple) and len(space) == 2:
return core.rasterize_segment(space, self.cellsize)
# triangle
elif isinstance(space, tuple) and len(space) == 3:
return core.rasterize_triangle(space, self.cellsize)
else:
raise TypeError("PositionMap only supports keys of type: points, segments, triangles")
[docs] def update(self, other):
''' Add the elements from an other PositionMap or from an iterable '''
if isinstance(other, PositionMap):
assert self.cellsize == other.cellsize
for k,v in other.dict.items():
if k in self.dict: self.dict[k].extend(v)
else: self.dict[k] = v
elif hasattr(other, '__iter__'):
for space,obj in other:
self.add(space,obj)
else:
raise TypeError("update requires a PositionMap or an iterable of couples (space, obj)")
[docs] def add(self, space, obj):
''' Add an object associated with a primitive '''
for k in self.keysfor(space):
if k not in self.dict: self.dict[k] = [obj]
else: self.dict[k].append(obj)
[docs] def get(self, space):
''' Get the objects associated with the given primitive '''
for k in self.keysfor(space):
if k in self.dict:
yield from self.dict[k]
def __contains__(self, space):
return next(self.get(space), None) is not None
_display = (
[
vec3(0,0,0),
vec3(1,0,0),vec3(0,1,0),vec3(0,0,1),
vec3(0,1,1),vec3(1,0,1),vec3(1,1,0),
vec3(1,1,1)],
[
(0,1),(0,2),(0,3),
(1,6),(2,6),
(1,5),(3,5),
(2,4),(3,4),
(4,7),(5,7),(6,7),
],
)
[docs] def display(self, scene):
web = mesh.Web()
if 'color' in self.options: web.options['color'] = self.options['color']
base = vec3(self.cellsize)
for k in self.dict:
l = len(web.points)
web += mesh.Web([base*(p+k) for p in self._display[0]], self._display[1], groups=[k])
return web.display(scene)
[docs]def meshcellsize(mesh):
''' Returns a good cell size to index primitives of a mesh with a PositionMap
See implementation.
'''
# the number of key for triangles is propotionate to the surface
# points are placed on this surface, so sqrt(len(pts)) is a good hint for the point density on the surface
return length(mesh.box().width) / sqrt(len(mesh.points))
[docs]class PointSet:
''' Holds a list of points and hash them.
The points are holds using indices, that allows to get the point buffer at any time, or to retrieve only a point index.
`cellsize` defines the box size in which two points are considered to be the same
Methods are inspired from the builtin type set
Attributes defined here:
:points: the point buffer (READ-ONLY PURPOSE)
:cellsize: the boxing parameter (DON'T CHANGE IT IF NON-EMPTY). mendatory and is the distance at which you want to distinguish points
:dict: the hashmap from box to point indices
Build parameters:
:iterable: use it to build the set by inserting elements
:manage: pass a list for inplace use it, only indexing will be built
'''
__slots__ = 'points', 'cellsize', 'dict'
def __init__(self, cellsize, iterable=None, manage=None):
self.cellsize = cellsize
self.dict = {}
if manage is not None:
self.points = manage
for i in reversed(range(len(self.points))):
self.dict[self.keyfor(self.points[i])] = i
else:
self.points = typedlist(dtype=vec3)
if iterable: self.update(iterable)
[docs] def keyfor(self, pt):
''' Hash key for a point '''
return tuple(i64vec3(glm.floor(pt/self.cellsize)))
def keysfor(self, pt):
''' Iterable of positions at which an equivalent point can be '''
vox = pt/self.cellsize
k = i64vec3(glm.floor(vox-0.5+NUMPREC)), i64vec3(glm.floor(vox+0.5-NUMPREC))
return (
(k[0][0], k[0][1], k[0][2]),
(k[1][0], k[0][1], k[0][2]),
(k[0][0], k[1][1], k[0][2]),
(k[1][0], k[1][1], k[0][2]),
(k[0][0], k[0][1], k[1][2]),
(k[1][0], k[0][1], k[1][2]),
(k[0][0], k[1][1], k[1][2]),
(k[1][0], k[1][1], k[1][2]),
)
[docs] def update(self, iterable):
''' Add the points from an iterable '''
for pt in iterable: self.add(pt)
[docs] def difference_update(self, iterable):
''' Remove the points from an iterable '''
for pt in iterable: self.discard(pt)
[docs] def add(self, pt):
''' Add a point '''
for key in self.keysfor(pt):
if key in self.dict:
return self.dict[key]
self.dict[self.keyfor(pt)] = l = len(self.points)
self.points.append(pt)
return l
[docs] def remove(self, pt):
''' Remove a point '''
for key in self.keysfor(pt):
if key in self.dict:
del self.dict[key]
return
else: raise IndexError("position doesn't exist in set")
[docs] def discard(self, pt):
''' Remove the point at given location if any '''
for key in self.keysfor(pt):
if key in self.dict:
del self.dict[key]
def __contains__(self, pt):
for key in self.keysfor(pt):
if key in self.dict: return True
return False
[docs] def __getitem__(self, pt):
for key in self.keysfor(pt):
if key in self.dict: return self.dict[key]
raise IndexError("position doesn't exist in set")
__iadd__ = update
__isub__ = difference_update
[docs] def __add__(self, iterable):
s = PositionSet()
s.union(self.points)
s.union(iterable)
return s
[docs] def __sub__(self, iterable):
s = PositionSet()
s.union(self.points)
s.difference(iterable)
return s