import math
import numpy as np
from time import time
import os
from webgui_jupyter_widgets import BaseWebGuiScene, encodeData, WebGuiDocuWidget
import webgui_jupyter_widgets.widget as wg
class WebGLScene(BaseWebGuiScene):
def __init__(self, mesh, clipping, on_init):
from IPython.display import display, Javascript
import threading
self.mesh = mesh
self.clipping = clipping
self.on_init = on_init
def GetData(self, set_minmax=True):
import json
# d = BuildRenderData(self.mesh, self.cf, self.order, draw_surf=self.draw_surf, draw_vol=self.draw_vol, deformation=self.deformation, region=self.region)
d = self.mesh._webgui_data()
bp = d['Bezier_trig_points']
for i in range(len(bp)):
bp[i] = encodeData(np.array(bp[i], dtype=np.float32))
ep = d['edges']
for i in range(len(ep)):
ep[i] = encodeData(np.array(ep[i], dtype=np.float32))
if self.clipping is not None:
d['clipping'] = True
if isinstance(self.clipping, dict):
allowed_args = ("x", "y", "z", "dist", "function", "pnt", "vec")
if "vec" in self.clipping:
vec = self.clipping["vec"]
self.clipping["x"] = vec[0]
self.clipping["y"] = vec[1]
self.clipping["z"] = vec[2]
if "pnt" in self.clipping:
d['mesh_center'] = list(self.clipping["pnt"])
for name, val in self.clipping.items():
if not (name in allowed_args):
raise Exception('Only {} allowed as arguments for clipping!'.format(", ".join(allowed_args)))
d['clipping_' + name] = val
if self.on_init:
d['on_init'] = self.on_init
return d
bezier_trig_trafos = { } # cache trafos for different orders
def BuildRenderData(mesh, func, order=2, draw_surf=True, draw_vol=True, deformation=None, region=True):
d = {}
d['ngsolve_version'] = "Netgen"
d['mesh_dim'] = 3 # mesh.dim TODO
d['order2d'] = 1
d['order3d'] = 0
d['draw_vol'] = False
d['draw_surf'] = True
d['funcdim'] = 1
func2 = None
if func and func.is_complex:
d['is_complex'] = True
func1 = func[0].real
func2 = ngs.CoefficientFunction( (func[0].imag, 0.0) )
elif func and func.dim>1:
func1 = func[0]
func2 = ngs.CoefficientFunction( tuple(func[i] if i<func.dim else 0.0 for i in range(1,3)) ) # max 3-dimensional functions
d['funcdim'] = func.dim
elif func:
func1 = func
d['funcdim'] = 1
else:
# no function at all -> we are just drawing a mesh, eval mesh element index instead
mats = mesh.GetMaterials()
bnds = mesh.GetBoundaries()
nmats = len(mesh.GetMaterials())
nbnds = len(mesh.GetBoundaries())
n = max(nmats, nbnds)
func1 = ngs.CoefficientFunction(list(range(n)))
n_regions = [0, 0, nmats, nbnds]
d['mesh_regions_2d'] = n_regions[mesh.dim]
d['mesh_regions_3d'] = nmats if mesh.dim==3 else 0
d['funcdim'] = 0
func1 = ngs.CoefficientFunction( (ngs.x, ngs.y, ngs.z, func1 ) )
func0 = ngs.CoefficientFunction( (ngs.x, ngs.y, ngs.z, 0.0 ) )
if deformation is not None:
func1 += ngs.CoefficientFunction((deformation, 0.0))
func0 += ngs.CoefficientFunction((deformation, 0.0))
d['show_wireframe'] = False
d['show_mesh'] = True
if order2d>0:
og = order2d
d['show_wireframe'] = True
d['show_mesh'] = True
timer2.Start()
timer3Bvals.Start()
# transform point-values to Bernsteinbasis
def Binomial(n,i): return math.factorial(n) / math.factorial(i) / math.factorial(n-i)
def Bernstein(x, i, n): return Binomial(n,i) * x**i*(1-x)**(n-i)
Bvals = ngs.Matrix(og+1,og+1)
for i in range(og+1):
for j in range(og+1):
Bvals[i,j] = Bernstein(i/og, j, og)
iBvals = Bvals.I
timer3Bvals.Stop()
# print (Bvals)
# print (iBvals)
Bezier_points = []
ipts = [(i/og,0) for i in range(og+1)] + [(0, i/og) for i in range(og+1)] + [(i/og,1.0-i/og) for i in range(og+1)]
ir_trig = ngs.IntegrationRule(ipts, [0,]*len(ipts))
ipts = [(i/og,0) for i in range(og+1)] + [(0, i/og) for i in range(og+1)] + [(i/og,1.0) for i in range(og+1)] + [(1.0, i/og) for i in range(og+1)]
ir_quad = ngs.IntegrationRule(ipts, [0,]*len(ipts))
vb = [ngs.VOL, ngs.BND][mesh.dim-2]
if region and region.VB() == vb:
vb = region
cf = func1 if draw_surf else func0
timer2map.Start()
pts = mesh.MapToAllElements({ngs.ET.TRIG: ir_trig, ngs.ET.QUAD: ir_quad}, vb)
timer2map.Stop()
pmat = cf(pts)
timermult.Start()
pmat = pmat.reshape(-1, og+1, 4)
if False:
BezierPnts = np.tensordot(iBvals.NumPy(), pmat, axes=(1,1))
else:
BezierPnts = np.zeros( (og+1, pmat.shape[0], 4) )
for i in range(4):
ngsmat = ngs.Matrix(pmat[:,:,i].transpose())
BezierPnts[:,:,i] = iBvals * ngsmat
timermult.Stop()
timer2list.Start()
for i in range(og+1):
Bezier_points.append(encodeData(BezierPnts[i], dtype=np.float32))
timer2list.Stop()
d['Bezier_points'] = Bezier_points
ipts = [(i/og,0) for i in range(og+1)]
ir_seg = ngs.IntegrationRule(ipts, [0,]*len(ipts))
vb = [ngs.VOL, ngs.BND, ngs.BBND][mesh.dim-1]
if region and region.VB() == vb:
vb = region
pts = mesh.MapToAllElements(ir_seg, vb)
pmat = func0(pts)
pmat = pmat.reshape(-1, og+1, 4)
edge_data = np.tensordot(iBvals.NumPy(), pmat, axes=(1,1))
edges = []
for i in range(og+1):
edges.append(encodeData(edge_data[i], dtype=np.float32))
d['edges'] = edges
ndtrig = int((og+1)*(og+2)/2)
if og in bezier_trig_trafos.keys():
iBvals_trig = bezier_trig_trafos[og]
else:
def BernsteinTrig(x, y, i, j, n):
return math.factorial(n)/math.factorial(i)/math.factorial(j)/math.factorial(n-i-j) \
* x**i*y**j*(1-x-y)**(n-i-j)
Bvals = ngs.Matrix(ndtrig, ndtrig)
ii = 0
for ix in range(og+1):
for iy in range(og+1-ix):
jj = 0
for jx in range(og+1):
for jy in range(og+1-jx):
Bvals[ii,jj] = BernsteinTrig(ix/og, iy/og, jx, jy, og)
jj += 1
ii += 1
iBvals_trig = Bvals.I
bezier_trig_trafos[og] = iBvals_trig
# Bezier_points = [ [] for i in range(ndtrig) ]
Bezier_points = []
ipts = [(i/og,j/og) for j in range(og+1) for i in range(og+1-j)]
ir_trig = ngs.IntegrationRule(ipts, [0,]*len(ipts))
ipts = ([(i/og,j/og) for j in range(og+1) for i in range(og+1-j)] +
[(1-i/og,1-j/og) for j in range(og+1) for i in range(og+1-j)])
ir_quad = ngs.IntegrationRule(ipts, [0,]*len(ipts))
vb = [ngs.VOL, ngs.BND][mesh.dim-2]
if region and region.VB() == vb:
vb = region
pts = mesh.MapToAllElements({ngs.ET.TRIG: ir_trig, ngs.ET.QUAD: ir_quad}, vb)
pmat = ngs.CoefficientFunction( func1 if draw_surf else func0 ) (pts)
funcmin = np.min(pmat[:,3])
funcmax = np.max(pmat[:,3])
pmin = np.min(pmat[:,0:3], axis=0)
pmax = np.max(pmat[:,0:3], axis=0)
mesh_center = 0.5*(pmin+pmax)
mesh_radius = np.linalg.norm(pmax-pmin)/2
pmat = pmat.reshape(-1, len(ir_trig), 4)
BezierPnts = np.tensordot(iBvals_trig.NumPy(), pmat, axes=(1,1))
for i in range(ndtrig):
Bezier_points.append(encodeData(BezierPnts[i], dtype=np.float32))
d['Bezier_trig_points'] = Bezier_points
d['mesh_center'] = list(mesh_center)
d['mesh_radius'] = mesh_radius
if func:
d['funcmin'] = funcmin
d['funcmax'] = funcmax
return d
def Draw(shape, clipping=None, js_code=None, filename=""):
# todo: also handle occ geometry, list of shapes, etc.
scene = WebGLScene(shape, clipping=clipping, on_init=js_code)
if wg._IN_IPYTHON:
if wg._IN_GOOGLE_COLAB:
from IPython.display import display, HTML
html = scene.GenerateHTML()
display(HTML(html))
else:
# render scene using widgets.DOMWidget
scene.Draw()
return scene
else:
if filename:
scene.GenerateHTML(filename=filename)
return scene