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)
class Torus (plotocc):
def __init__(self):
super().__init__()
self.axs = gp_Ax3()
self.radi = [500, 200]
self.rxyz = [1.0, 1.1, 1.1]
mat = gp_Mat(
self.rxyz[0], 0, 0,
0, self.rxyz[1], 0,
0, 0, self.rxyz[2]
)
gtrf = gp_GTrsf(mat, gp_XYZ(0, 0, 0))
self.t = Geom_ToroidalSurface(self.axs, *self.radi)
self.face = BRepBuilderAPI_MakeFace(self.t, 1e-6).Face()
self.face = BRepBuilderAPI_GTransform(self.face, gtrf).Shape()
self.surf = BRep_Tool.Surface(self.face)
self.prop = GeomLProp_SLProps(self.surf, 0.0, 0.0, 1, 1.0)
self.export_stp(self.face)
print(self.t.UPeriod())
def get_prof(self, uv=[0, 0]):
u, v = uv
u1, v1 = 2 * np.pi * u, 2 * np.pi * v
p, vu, vv = gp_Pnt(), gp_Vec(), gp_Vec()
self.surf.D1(u1, v1, p, vu, vv)
self.prop.SetParameters(u1, v1)
vx = vu.Normalized()
vy = vv.Normalized()
vz = vx.Crossed(vy)
print(u, v)
print(p)
print(vx)
print(vy)
print(vz)
print(self.prop.GaussianCurvature())
print(self.prop.MaxCurvature())
print(self.prop.MinCurvature())
print(self.prop.MeanCurvature())
self.display.DisplayShape(p)
self.display.DisplayVector(vz.Scaled(20), p)
return p, vu, vv, vz
def ShowTorus(self):
self.display.DisplayShape(self.face, transparency=0.7)
self.show_axs_pln(scale=100)
self.show()
def curvature_at(self, u, v):
"""Compute the curvature at a point on the surface.
Parameters
----------
u : float
v : float
Returns
-------
:class:`~compas.geometry.Vector`
"""
props = GeomLProp_SLProps(self.occ_surface, u, v, 2, 1e-6)
gaussian = props.GaussianCurvature()
mean = props.MeanCurvature()
point = props.Value()
normal = props.Normal()
return gaussian, mean, Point.from_occ(point), Vector.from_occ(normal)