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Adds curvature interpolation #2

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Adds curvature interpolation #2

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55 changes: 55 additions & 0 deletions lib/expline/spline.ex
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Original file line number Diff line number Diff line change
Expand Up @@ -324,6 +324,61 @@ defmodule Expline.Spline do
end
end

@doc """
Interpolate a curvature from the spline.

## Examples

iex> with {:ok, spline} <- Expline.Spline.from_points([{0.0, 0.0}, {1.0, 1.0}, {2.0, 2.0}]),
...> do: Expline.Spline.interpolate_curvature(spline, 0.5)
{:ok, 1.0}
"""
@spec interpolate_curvature(t(), independent_value()) :: {:ok, curvature()}
| {:error, interpolation_error()}
| {:error, :corrupt_spline}
def interpolate_curvature(%__MODULE__{} = spline, x) when is_float(x) do
with :error <- Map.fetch(spline.derivatives, x) do
case :ordsets.filter(fn ({x1, x2}) -> x1 < x and x < x2 end, spline.ranges) do
[{_x1, _x2} = range] ->
do_interpolate_curvature(spline, range, x)
[] ->
extrapolate_curvature(spline, x)
_ranges ->
{:error, :corrupt_spline}
end
end
end

@spec do_interpolate_curvature(t(), range(), independent_value()) :: {:ok, dependent_value()}
defp do_interpolate_curvature(%__MODULE__{} = spline, {x1, x2}, x) do
y1 = Map.get(spline.points, x1)
y2 = Map.get(spline.points, x2)

k1 = Map.get(spline.derivatives, x1)
k2 = Map.get(spline.derivatives, x2)

# Described by equations (1), (2), (3), and (4) on
# https://en.wikipedia.org/wiki/Spline_interpolation
t = (x - x1) / (x2 - x1)
a = k1 * (x2 - x1) - (y2 - y1)
b = -k2 * (x2 - x1) + (y2 - y1)

dy = ((y2 - y1) + (1 - 2 * t) * (a * (1 - t) + b * t) + t * (1 - t) * (b - a)) / (x2 - x1)
{:ok, dy}
end

@spec extrapolate_curvature(t(), independent_value()) :: {:ok, dependent_value()}
| {:error, :corrupt_extrema}
defp extrapolate_curvature(spline, x) do
cond do
spline.min > x ->
{:ok, Map.get(spline.derivatives, spline.min)}
spline.max < x ->
{:ok, Map.get(spline.derivatives, spline.max)}
true -> {:error, :corrupt_extrema}
end
end

@spec make_derivatives(%{ required(independent_value()) => dependent_value() }) :: %{ required(independent_value()) => curvature() }
defp make_derivatives(points) do
n = map_size(points) - 1
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