Monty.Frameworks.Utils.SpatialArithmetics.TangentFrame (ExTbpMonty.Core v0.1.0)

An orthonormal (u, v, n) frame riding on a surface.

Mirrors tbp/monty/frameworks/utils/spatial_arithmetics.py::TangentFrame. n is the surface normal, u a tangent direction, v completes the right-handed set. As the sensor moves over a curved surface, transport/2 turns the frame by exactly the rotation that keeps it in the new tangent plane — parallel transport, which is what lets Monty "unroll" a curved surface into a flat one.

A surface normal names a plane but not a basis within it, so the initial u is picked by crossing an arbitrary axis with the normal. That choice is invisible to Monty, which only ever asks for relative directions.

Summary

Types

t()

vector()

Functions

basis_u(tangent_frame)

The horizontal tangent direction.

basis_v(tangent_frame)

The vertical tangent direction.

new(surface_normal)

The frame whose normal is surface_normal.

normal(tangent_frame)

The surface normal this frame rides on.

transport(tangent_frame, new_normal)

The frame at new_normal, with its basis carried over by the rotation between the two normals.

Types

t()

@type t() :: %Monty.Frameworks.Utils.SpatialArithmetics.TangentFrame{
  basis_u: vector(),
  basis_v: vector(),
  normal: vector()
}

vector()

@type vector() :: [float()]

Functions

basis_u(tangent_frame)

@spec basis_u(t()) :: vector()

The horizontal tangent direction.

basis_v(tangent_frame)

@spec basis_v(t()) :: vector()

The vertical tangent direction.

new(surface_normal)

@spec new(vector()) :: t()

The frame whose normal is surface_normal.

When surface_normal is (anti)parallel to the arbitrary axis, crossing them would give zero, so a second axis is used instead.

normal(tangent_frame)

@spec normal(t()) :: vector()

The surface normal this frame rides on.

transport(tangent_frame, new_normal)

@spec transport(t(), vector()) :: t()

The frame at new_normal, with its basis carried over by the rotation between the two normals.

Normals that already agree need no rotation, and u is left alone. Otherwise u is turned about the axis shared by both tangent planes — the axis perpendicular to both normals — so it stays in the plane as the plane tilts.

The result is re-orthonormalised against new_normal: a thousand transports over a curved surface would otherwise accumulate enough floating point drift for u to leave the tangent plane.