def curvature(self, seg, u):
'''Returns Frenet curvature of spline at parameter u'''
# https://en.wikipedia.org/wiki/Frenet-Serret_formulas
vel = self.velocity(seg, u)
return Vector3.cross(vel, self.acceleration(
seg, u)).length() / (vel.length())**3
def get(self, t, scale):
t = float(scale * t)
x_basis = self.p1 - self.p0
y_basis = x_basis.length() * Vector3.cross(x_basis, Vector3.k()).normalize()
basis = Mat2x2.fromvectors(
x_basis,
y_basis
)
transformed_v0 = (basis * self.v0).normalize()
transformed_v1 = (basis * self.v1).normalize()
slope_0 = transformed_v0.y / transformed_v0.x
slope_1 = transformed_v1.y / transformed_v1.x
spline = Vector3(
t,
(self.H2(t) * slope_0) + (self.H3(t) * slope_1)
)
# f.write("{},{}\n".format(
# spline.x, spline.y
# ))
spline_der = Vector3(
scale,
(self.d_H2(t, scale) * slope_0) + (self.d_H3(t, scale) * slope_1)
)
return ((basis * spline) + self.p0, (basis * spline_der))
