The torus 𝕋^d ≅ [-π,π)^d is modeled as an [AbstractPowerManifold](@extref ManifoldsBase.AbstractPowerManifold) of the (real-valued) Circle and uses ArrayPowerRepresentation.
Points on the torus are hence row vectors, x ∈ ℝ^{d}.
The following code can be used to make a three-dimensional torus 𝕋^3 and compute a tangent vector:
using Manifolds
M = Torus(3)
p = [0.5, 0.0, 0.0]
q = [0.0, 0.5, 1.0]
X = log(M, p, q)
Most functions are directly implemented for an [AbstractPowerManifold](@extref ManifoldsBase.AbstractPowerManifold) with ArrayPowerRepresentation except the following special cases:
Modules = [Manifolds]
Pages = ["manifolds/Torus.jl"]
Order = [:type, :function]
Two-dimensional torus embedded in ℝ^3.
Modules = [Manifolds]
Pages = ["manifolds/EmbeddedTorus.jl"]
Order = [:type, :function]