def nearLocateMesh(xyo, IKLE, MESHX, MESHY, tree=None):
"""
Requires the scipy.spatial and the matplotlib.tri packages to be loaded.
- Will use already computed tree or re-create it if necessary.
- Will use already computed neighbourhood or re-create it if necessary.
This function return the element number for the triangle including xyo=(xo,yo)
or -1 if the (xo,yo) is outside the mesh
Return: the element, the barycentric weights, and the tree and the neighbourhood if computed
"""
# ~~> Create the KDTree of the iso-barycentres
if tree == None:
isoxy = np.column_stack((np.sum(MESHX[IKLE], axis=1) / 3.0,
np.sum(MESHY[IKLE], axis=1) / 3.0))
tree = cKDTree(isoxy)
# ~~> Find the indices corresponding to the nearest elements to the points
inear = -1
for d, i in zip(*tree.query(xyo, 8)):
ax, bx, cx = MESHX[IKLE[i]]
ay, by, cy = MESHY[IKLE[i]]
w = isInsideTriangle(xyo, (ax, ay), (bx, by), (cx, cy), nomatter=True)
if w != []: return i, w, tree
if inear < 0:
inear = i
dnear = d
if dnear > d:
inear = i
dnear = d
# ~~> Find the indices and weights corresponding to the element containing the point
ax, bx, cx = MESHX[IKLE[inear]]
ay, by, cy = MESHY[IKLE[inear]]
return inear, isInsideTriangle(xyo, (ax, ay), (bx, by), (cx, cy),
nomatter=False), tree
def nearLocateMesh(xyo,IKLE,MESHX,MESHY,tree=None):
"""
Requires the scipy.spatial and the matplotlib.tri packages to be loaded.
- Will use already computed tree or re-create it if necessary.
- Will use already computed neighbourhood or re-create it if necessary.
This function return the element number for the triangle including xyo=(xo,yo)
or -1 if the (xo,yo) is outside the mesh
Return: the element, the barycentric weights, and the tree and the neighbourhood if computed
"""
# ~~> Create the KDTree of the iso-barycentres
if tree == None:
isoxy = np.column_stack((np.sum(MESHX[IKLE],axis=1)/3.0,np.sum(MESHY[IKLE],axis=1)/3.0))
tree = cKDTree(isoxy)
# ~~> Find the indices corresponding to the nearest elements to the points
inear = -1
for d,i in zip(*tree.query(xyo,8)):
ax,bx,cx = MESHX[IKLE[i]]
ay,by,cy = MESHY[IKLE[i]]
w = isInsideTriangle( xyo,(ax,ay),(bx,by),(cx,cy),nomatter=True )
if w != []: return i,w,tree
if inear < 0:
inear = i
dnear = d
if dnear > d:
inear = i
dnear = d
# ~~> Find the indices and weights corresponding to the element containing the point
ax,bx,cx = MESHX[IKLE[inear]]
ay,by,cy = MESHY[IKLE[inear]]
return inear,isInsideTriangle( xyo,(ax,ay),(bx,by),(cx,cy),nomatter=False ),tree
def traceRay2XY(IKLE,MESHX,MESHY,neighbours,ei,xyi,en,xyn):
"""
This assumes that you cannot go back on your ray.
"""
# ~~> latest addition to the ray
ax,bx,cx = MESHX[IKLE[en]]
ay,by,cy = MESHY[IKLE[en]]
bi = getBarycentricWeights( xyi,(ax,ay),(bx,by),(cx,cy) )
pnt = {'n':1, 'xy':[xyi], 'e':[en], 'b':[bi],
'd':[np.power(xyi[0]-xyn[0],2) + np.power(xyi[1]-xyn[1],2)]}
# ~~> convergence on distance to target xyn
accuracy = np.power(10.0, -5+np.floor(np.log10(abs(ax+bx+cx+ay+by+cy))))
if pnt['d'][0] < accuracy: return True,pnt
# ~~> get the ray through to the farthest neighbouring edges
ks = []; ds = []
for k in [0,1,2]:
xyj = getSegmentIntersection( (MESHX[IKLE[en][k]],MESHY[IKLE[en][k]]),(MESHX[IKLE[en][(k+1)%3]],MESHY[IKLE[en][(k+1)%3]]),xyi,xyn )
if xyj == []: continue # there are no intersection with that edges
ej = neighbours[en][k]
if ej == ei: continue # you should not back track on your ray
xyj = xyj[0]
dij = np.power(xyi[0]-xyj[0],2) + np.power(xyi[1]-xyj[1],2)
ks.append(k)
ds.append(dij)
if ds != []:
k = ks[np.argmax(ds)]
ej = neighbours[en][k]
xyj = getSegmentIntersection( (MESHX[IKLE[en][k]],MESHY[IKLE[en][k]]),(MESHX[IKLE[en][(k+1)%3]],MESHY[IKLE[en][(k+1)%3]]),xyi,xyn )[0]
djn = np.power(xyn[0]-xyj[0],2) + np.power(xyn[1]-xyj[1],2)
# ~~> Possible recursive call
if True or djn > accuracy: # /!\ this may be a problem
if ej < 0:
# you have reach the end of the line
bj = getBarycentricWeights( xyj,(ax,ay),(bx,by),(cx,cy) )
pnt['n'] += 1; pnt['xy'].insert(0,xyj); pnt['e'].insert(0,en); pnt['b'].insert(0,bj); pnt['d'].insert(0,djn)
return djn<accuracy,pnt
else:
found,ray = traceRay2XY(IKLE,MESHX,MESHY,neighbours,en,xyj,ej,xyn)
ray['n'] += 1; ray['xy'].append(xyi); ray['e'].append(en); ray['b'].append(bi); ray['d'].append(dij)
return found,ray
# ~~> convergence on having found the appropriate triangle
bn = isInsideTriangle( xyn,(ax,ay),(bx,by),(cx,cy) )
if bn != []:
pnt['n'] += 1; pnt['xy'].insert(0,xyn); pnt['e'].insert(0,en); pnt['b'].insert(0,bn); pnt['d'].insert(0,0.0)
return True,pnt
# ~~> you should not be here !
return False,pnt
def traceRay2XY(IKLE, MESHX, MESHY, neighbours, ei, xyi, en, xyn):
"""
This assumes that you cannot go back on your ray.
"""
# ~~> latest addition to the ray
ax, bx, cx = MESHX[IKLE[en]]
ay, by, cy = MESHY[IKLE[en]]
bi = getBarycentricWeights(xyi, (ax, ay), (bx, by), (cx, cy))
pnt = {
'n': 1,
'xy': [xyi],
'e': [en],
'b': [bi],
'd': [np.power(xyi[0] - xyn[0], 2) + np.power(xyi[1] - xyn[1], 2)]
}
# ~~> convergence on distance to target xyn
accuracy = np.power(
10.0, -5 + np.floor(np.log10(abs(ax + bx + cx + ay + by + cy))))
if pnt['d'][0] < accuracy: return True, pnt
# ~~> get the ray through to the farthest neighbouring edges
ks = []
ds = []
for k in [0, 1, 2]:
xyj = getSegmentIntersection(
(MESHX[IKLE[en][k]], MESHY[IKLE[en][k]]),
(MESHX[IKLE[en][(k + 1) % 3]], MESHY[IKLE[en][(k + 1) % 3]]), xyi,
xyn)
if xyj == []: continue # there are no intersection with that edges
ej = neighbours[en][k]
if ej == ei: continue # you should not back track on your ray
xyj = xyj[0]
dij = np.power(xyi[0] - xyj[0], 2) + np.power(xyi[1] - xyj[1], 2)
ks.append(k)
ds.append(dij)
if ds != []:
k = ks[np.argmax(ds)]
ej = neighbours[en][k]
xyj = getSegmentIntersection(
(MESHX[IKLE[en][k]], MESHY[IKLE[en][k]]),
(MESHX[IKLE[en][(k + 1) % 3]], MESHY[IKLE[en][(k + 1) % 3]]), xyi,
xyn)[0]
djn = np.power(xyn[0] - xyj[0], 2) + np.power(xyn[1] - xyj[1], 2)
# ~~> Possible recursive call
if True or djn > accuracy: # /!\ this may be a problem
if ej < 0:
# you have reach the end of the line
bj = getBarycentricWeights(xyj, (ax, ay), (bx, by), (cx, cy))
pnt['n'] += 1
pnt['xy'].insert(0, xyj)
pnt['e'].insert(0, en)
pnt['b'].insert(0, bj)
pnt['d'].insert(0, djn)
return djn < accuracy, pnt
else:
found, ray = traceRay2XY(IKLE, MESHX, MESHY, neighbours, en,
xyj, ej, xyn)
ray['n'] += 1
ray['xy'].append(xyi)
ray['e'].append(en)
ray['b'].append(bi)
ray['d'].append(dij)
return found, ray
# ~~> convergence on having found the appropriate triangle
bn = isInsideTriangle(xyn, (ax, ay), (bx, by), (cx, cy))
if bn != []:
pnt['n'] += 1
pnt['xy'].insert(0, xyn)
pnt['e'].insert(0, en)
pnt['b'].insert(0, bn)
pnt['d'].insert(0, 0.0)
return True, pnt
# ~~> you should not be here !
return False, pnt