def second_derivative(h_surf, u=0, v=0):
p1 = gp_Pnt()
pu, pv = gp_Vec(), gp_Vec()
puu, pvv = gp_Vec(), gp_Vec()
puv = gp_Vec()
prop = GeomLProp_SLProps(h_surf, u, v, 1, 1)
GeomLProp_SurfaceTool.D2(h_surf, u, v, p1, pu, pv, puu, pvv, puv)
e0 = pu.Crossed(pv)
pu.Normalize()
pv.Normalize()
e0.Normalize()
puu.Normalize()
pvv.Normalize()
puv.Normalize()
print(p1)
print("pu", pu)
print("pv", pv)
print("e0", e0)
print("puu", puu)
print("pvv", pvv)
print("puv", puv)
first_form = np.array([[pu.Dot(pu), pu.Dot(pv)], [pv.Dot(pu), pv.Dot(pv)]])
secnd_form = np.array([[e0.Dot(puu), e0.Dot(puv)],
[e0.Dot(puv), e0.Dot(pvv)]])
print(first_form)
print(secnd_form)
print(prop.GaussianCurvature())
print(prop.MeanCurvature())
d1, d2 = gp_Dir(), gp_Dir()
prop.CurvatureDirections(d1, d2)
a1 = gp_Ax3()
v1 = dir_to_vec(d1)
v2 = dir_to_vec(d2)
if pu.IsParallel(v1, 1 / 1000):
c1 = prop.MaxCurvature()
c2 = prop.MinCurvature()
print(v1.Dot(pu), v1.Dot(pv))
print(v2.Dot(pu), v2.Dot(pv))
else:
c1 = prop.MinCurvature()
c2 = prop.MaxCurvature()
print(v1.Dot(pu), v1.Dot(pv))
print(v2.Dot(pu), v2.Dot(pv))
print(c1, 1 / c1)
print(c2, 1 / c2)
px = np.linspace(-1, 1, 100) * 100
p1_y = px**2 / c1
p2_y = px**2 / c1
curv1 = curv_spl(px, p1_y)
curv2 = curv_spl(px, p2_y)
def reflect(p0, v0, face):
h_surf = BRep_Tool.Surface(face)
ray = Geom_Line(gp_Lin(p0, vec_to_dir(v0)))
uvw = GeomAPI_IntCS(ray.GetHandle(), h_surf).Parameters(1)
u, v, w = uvw
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(h_surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy)
vx.Normalize()
vy.Normalize()
vz.Normalize()
v1 = v0.Mirrored(gp_Ax2(p1, vec_to_dir(vz)))
return p1, v1
def radius_at_uv(face, u, v):
'''
returns the mean radius at a u,v coordinate
@param face: surface input
@param u,v: u,v coordinate
'''
h_srf = BRep_Tool().Surface(face)
uv_domain = GeomLProp_SurfaceTool().Bounds(h_srf)
curvature = GeomLProp_SLProps(h_srf, u, v, 1, 1e-6)
try:
_crv_min = 1. / curvature.MinCurvature()
except ZeroDivisionError:
_crv_min = 0.
try:
_crv_max = 1. / curvature.MaxCurvature()
except ZeroDivisionError:
_crv_max = 0.
return abs((_crv_min + _crv_max) / 2.)
def reflect_axs2(beam, surf, axs=gp_Ax3(), indx=1):
p0, v0 = beam.Location(), dir_to_vec(beam.Direction())
h_surf = BRep_Tool.Surface(surf)
ray = Geom_Line(gp_Lin(p0, vec_to_dir(v0)))
if GeomAPI_IntCS(ray, h_surf).NbPoints() == 0:
return beam, beam, None
elif GeomAPI_IntCS(ray, h_surf).NbPoints() == 1:
return beam, beam, None
GeomAPI_IntCS(ray, h_surf).IsDone()
u, v, w = GeomAPI_IntCS(ray, h_surf).Parameters(indx)
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(h_surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy)
vx.Normalize()
vy.Normalize()
vz.Normalize()
v1 = v0.Mirrored(gp_Ax2(p1, vec_to_dir(vz), vec_to_dir(vx)))
norm_ax = gp_Ax3(p1, vec_to_dir(vz), vec_to_dir(vx))
beam_ax = gp_Ax3(p1, vec_to_dir(v1), beam.XDirection().Reversed())
return beam_ax, norm_ax, 1
def reflect(beam, face, axs=gp_Ax3()):
p0, v0 = beam.Location(), dir_to_vec(beam.Direction())
h_surf = BRep_Tool.Surface(face)
ray = Geom_Line(gp_Lin(p0, vec_to_dir(v0)))
if GeomAPI_IntCS(ray, h_surf).NbPoints() == 0:
print("Out of Surface", axs.Location())
pln = make_plane(axs.Location(), dir_to_vec(axs.Direction()), 500,
-500, 500, -500)
h_surf = BRep_Tool.Surface(pln)
GeomAPI_IntCS(ray, h_surf).IsDone()
uvw = GeomAPI_IntCS(ray, h_surf).Parameters(1)
u, v, w = uvw
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(h_surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy)
vx.Normalize()
vy.Normalize()
vz.Normalize()
v1 = v0.Mirrored(gp_Ax2(p1, vec_to_dir(vz), vec_to_dir(vx)))
return gp_Ax3(p1, vec_to_dir(v1), beam.XDirection().Reversed())
def Reflect(self, beam=gp_Ax3(), surf=make_plane()):
h_surf = BRep_Tool.Surface(surf)
ray = Geom_Line(beam.Location(), beam.Direction())
if GeomAPI_IntCS(ray, h_surf).NbPoints() == 0:
beam_v1 = beam
else:
GeomAPI_IntCS(ray, h_surf).IsDone()
uvw = GeomAPI_IntCS(ray, h_surf).Parameters(1)
u, v, w = uvw
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(h_surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy)
vx.Normalize()
vy.Normalize()
vz.Normalize()
norm = gp_Ax3(p1, vec_to_dir(vz), vec_to_dir(vx))
beam_v0 = beam
beam_v0.SetLocation(p1)
beam_v1 = beam_v0.Mirrored(norm.Ax2())
beam_v1.XReverse()
return beam_v1
def check_ground(self):
if len(self.pts) != 1:
ray = spl_2pnt(self.pts[-2], self.pts[-1])
vec = gp_Vec(self.pts[-2], self.pts[-1])
self.p_trce.Perform(ray, self.h_surf)
if self.p_trce.NbPoints() != 0 and vec.Z() < 0:
print()
uvw = self.p_trce.Parameters(1)
u, v, w = uvw
p0, v0 = gp_Pnt(), gp_Vec()
GeomLProp_CurveTool.D1(ray, w, p0, v0)
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(self.h_surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy)
self.pts[-1] = p0
print(self.r.t, w, p0)
print(v0)
print(gp_Vec(self.pts[-2], self.pts[-1]))
norm = gp_Ax3(p1, vec_to_dir(vz), vec_to_dir(vx))
v1 = v0
v1.Mirror(norm.Ax2())
self.r.set_initial_value(self.gen_condition(p0, v1),
self.r.t + self.dt)
def reflect_b2(self, num=1):
h_surf = BRep_Tool.Surface(self.b2)
ray = Geom_Line(self.beam.Axis())
self.RayTrace.Perform(ray, h_surf)
if self.RayTrace.NbPoints() == 0:
beam = self.beam
else:
self.num += 1
uvw = self.RayTrace.Parameters(num)
u, v, w = uvw
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(h_surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy).Reversed()
norm = gp_Ax3(p1, vec_to_dir(vz), vec_to_dir(vx))
self.show_axs_pln(norm, scale=10)
beam = self.beam
beam.SetLocation(p1)
beam.SetDirection(beam.Direction().Reversed())
beam.Mirror(norm.Axis())
print(self.num, self.b2, p1)
self.pts.append(p1)
# self.beam.XReverse()
# self.beam.Mirror(norm.Ax2())
return beam
def reflect_beam(self, beam0=gp_Ax3(), tr=0):
v0 = dir_to_vec(beam0.Direction())
v1 = dir_to_vec(beam0.XDirection())
surf = BRep_Tool.Surface(self.surf)
ray = Geom_Line(beam0.Axis())
uvw = GeomAPI_IntCS(ray, surf).Parameters(1)
u, v, w = uvw
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(surf, u, v, p1, vx, vy)
vz = vx.Crossed(vy)
if vz.Dot(v0) > 0:
vz.Reverse()
vx.Normalize()
vy.Normalize()
vz.Normalize()
self.beam = gp_Ax3(p1, vec_to_dir(v0.Reversed()),
vec_to_dir(v1.Reversed()))
self.norm = gp_Ax3(p1, vec_to_dir(vz), vec_to_dir(vx))
if tr == 0:
self.beam.Mirror(self.norm.Ax2())
if self.beam.Direction().Dot(self.norm.Direction()) < 0:
self.beam.ZReverse()
elif tr == 1:
self.beam.ZReverse()
def __init__(self):
plotocc.__init__(self)
self.compound = TopoDS_Compound()
self.builder = BRep_Builder()
self.builder.MakeCompound(self.compound)
self.beam = gp_Ax3()
self.beam.SetLocation(gp_Pnt(0.5, 0.5, 0.0))
self.beam.SetDirection(gp_Dir(0.0, 0.5, 1.0))
self.beam_line = line_from_axs(self.beam, length=20)
self.builder.Add(self.compound, self.beam_line)
ax = gp_Ax3(gp_Pnt(0, 0, 10), gp_Dir(0, 0, -1))
px = np.linspace(-1, 1, 10) * 10
py = np.linspace(-1, 1, 10) * 10
mesh = np.meshgrid(px, py)
surf = mesh[0]**2 / 100 + mesh[1]**2 / 150
self.surf = spl_face(*mesh, surf, ax)
self.surf_bound = self.make_PolySurf(radi=5, axs=ax)
self.beam_glin = Geom_Line(self.beam.Location(), self.beam.Direction())
self.ics = GeomAPI_IntCS(self.beam_glin, BRep_Tool.Surface(self.surf))
print(self.ics.NbPoints())
# print(self.ics.Point(1))
self.ics = GeomAPI_IntCS(self.beam_glin,
BRep_Tool.Surface(self.surf_bound))
print(self.ics.NbPoints())
#self.display.DisplayShape(self.surf, transparency=0.7)
self.display.DisplayShape(self.surf_bound, transparency=0.7)
self.plns = TopoDS_Shell()
self.builder.MakeShell(self.plns)
for ix in np.linspace(0, 1, 5):
for iy in np.linspace(0, 1, 5):
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(BRep_Tool.Surface(self.surf), ix, iy,
p1, vx, vy)
vz = vx.Crossed(vy)
axs = gp_Ax3(p1, vec_to_dir(vz), vec_to_dir(vx))
pln = self.make_PolyPlane(axs=axs, radi=2.5, shft=15.0)
print(pln)
self.builder.Add(self.compound, make_vertex(p1))
self.builder.Add(self.plns, pln)
self.builder.Add(self.compound, self.plns)
for face in Topo(self.plns).faces():
self.ics.Perform(self.beam_glin, BRep_Tool.Surface(face))
uvw = self.ics.Parameters(1)
u, v, w = uvw
p1, vx, vy = gp_Pnt(), gp_Vec(), gp_Vec()
GeomLProp_SurfaceTool.D1(BRep_Tool.Surface(face), u, v, p1, vx, vy)
vz = vx.Crossed(vy)
if u > 0 and v > 0:
print(u, v)
print(p1)
print(self.ics.Point(1))
self.display.DisplayShape(p1)
self.display.DisplayShape(face, color="BLUE")
else:
print(u, v)
p1 = gp_Pnt(-20, -20, -50)
pts, crv = spl_curv_pts([p0, p1])
pln = make_plane(vec_normal=gp_Vec(0, 1, 1))
h_surf = BRep_Tool.Surface(pln)
api = GeomAPI_IntCS(crv, h_surf)
print(api.IsDone())
print(api.NbSegments())
uvw = api.Parameters(1)
u, v, w = uvw
pnt_crv = gp_Pnt()
pnt_1st = gp_Pnt()
pnt_2nd = gp_Pnt()
pnt_srf = gp_Pnt()
GeomLProp_CurveTool.Value(crv, w, pnt_crv)
GeomLProp_CurveTool.Value(crv, 0, pnt_1st)
GeomLProp_CurveTool.Value(crv, 1, pnt_2nd)
GeomLProp_SurfaceTool.Value(h_surf, u, v, pnt_srf)
print(uvw)
print(pnt_crv)
print(pnt_1st)
print(pnt_2nd)
print(pnt_srf)
pnt_crv = gp_Pnt()
vec_crv = gp_Vec()
GeomLProp_CurveTool.D1(crv, w, pnt_crv, vec_crv)
print(pnt_crv)
print(vec_crv)
print(gp_Vec(p0, p1))
