def _XYZ(self, uv):
# https://math.stackexchange.com/questions/461547/whats-the-equation-of-helix-surface
theta, t = uv
f = self.curve._f
N = self.curve._N
B = self.curve._B
r = self.radius
XYZ = jnp.array(
f(t)) + r * N(t) * jnp.cos(theta) + r * B(t) * jnp.sin(theta)
return XYZ
def _X(self, uv):
return jnp.cosh(uv[1]) * jnp.cos(uv[0])
def _Y(self, uv):
return (self.a + (self.b * jnp.cos(uv[1]))) * jnp.sin(uv[0])
def _Y(self, uv):
return (self.R + self.r * jnp.cos(uv[1])) * jnp.sin(uv[0])
def _Z(self, uv):
u, v = uv
return self.c * jnp.cos(v)
def _X(self, uv):
u, v = uv
return self.a * jnp.cos(u) * jnp.sin(v)
def _Z(self, uv):
w, B = uv
a, b, c = self.abc
top = (a**2 * jnp.sin(w)**2) + (b**2 * jnp.cos(w)**2) - c**2
return c * jnp.sin(B) * (jnp.sqrt(top) / jnp.sqrt(a**2 - c**2))
def _Y(self, uv):
w, B = uv
a, b, c = self.abc
return b * jnp.cos(B) * jnp.sin(w)
def _X(self, uv):
w, B = uv
a, b, c = self.abc
top = a**2 - (b**2 * jnp.sin(B)**2) - (c**2 * jnp.cos(B)**2)
return a * jnp.cos(w) * (jnp.sqrt(top) / jnp.sqrt(a**2 - c**2))
def _Z(self, uv):
return self.r * jnp.cos(uv[1])
def _X(self, uv):
return self.r * jnp.cos(uv[0]) * jnp.sin(uv[1])
def polar2cart(self, rt):
r, theta = rt
return [r * jnp.cos(theta), r * jnp.sin(theta)]
def _X(self, uv):
u, v = uv
return self.curve._x(v) * jnp.cos(u)
def _Y(self, t):
return jnp.cos(t) - 2 * jnp.cos(2 * t)
def _y(self, t):
return self.a * (jnp.cos(t) + jnp.log(jnp.tan(t / 2.0)))
def _Y(self, t):
return self.R * jnp.cos(t)