Clarify smootharclengthinterpolation

README.md

@@ -63,6 +63,7 @@ corresponding to `(u,t)` pairs.
   - `CubicHermiteSpline(du, u, t)` - A third order Hermite interpolation, which matches the values and first (`du`) order derivatives in the data points exactly.
   - `PCHIPInterpolation(u, t)` - a type of `CubicHermiteSpline` where the derivative values `du` are derived from the input data in such a way that the interpolation never overshoots the data.
   - `QuinticHermiteSpline(ddu, du, u, t)` - A fifth order Hermite interpolation, which matches the values and first (`du`) and second (`ddu`) order derivatives in the data points exactly.
+  - `SmoothArcLengthInterpolation(u)` create a continuously differentiable interpolation by arc length through the data, by approximating a non-arc length interpolation with line segments and circle segments. See the docs for more details.
 
 ## Extension Methods
 

docs/src/arclength_interpolation.md

@@ -4,7 +4,7 @@ Arc length interpolation is interpolation between points using a curve that is p
 
 ## Usage
 
-`DataInteprolations.jl` offers an arc length interpolation method that approximates an existing non arc length interpolation by circle and line segments. This can be done by providing an interpolation object (the shape interpolation):
+`DataInteprolations.jl` offers an arc length interpolation method that approximates an existing non arc length interpolation piecewise by circle and line segments. This can be done by providing an interpolation object (the shape interpolation):
 
 ```@example tutorial
 using DataInterpolations

docs/src/index.md

@@ -33,6 +33,7 @@ corresponding to `(u,t)` pairs.
   - `CubicHermiteSpline(du, u, t)` - A third order Hermite interpolation, which matches the values and first (`du`) order derivatives in the data points exactly.
   - `PCHIPInterpolation(u, t)` - a type of `CubicHermiteSpline` where the derivative values `du` are derived from the input data in such a way that the interpolation never overshoots the data.
   - `QuinticHermiteSpline(ddu, du, u, t)` - a fifth order Hermite interpolation, which matches the values and first (`du`) and second (`ddu`) order derivatives in the data points exactly.
+  - `SmoothArcLengthInterpolation(u)` create a continuously differentiable interpolation by arc length through the data, by approximating a non arc length interpolation with line segments and circle segments. See [here](#smooth-arc-length-interpolation) for more details.
 
 ## Extension Methods
 

src/interpolation_caches.jl

@@ -1393,6 +1393,8 @@ If you want to do this, construct the shape interpolation yourself and use the
     for the `SmoothArcLengthInterpolation` to be C¹ smooth, the `interpolation_type` must be C¹ smooth as well.
   - `m`: The number of points at which the shape interpolation is evaluated in each interval between time points.
     The `SmoothArcLengthInterpolation` converges to the shape interpolation (in shape) as m → ∞.
+  - `in_place`: Whether the value of the interpolation should be calculated in pre-allocated memory. This saves
+    allocations, but is not compatible with e.g. ForwardDiff. Defaults to `false`.
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
     are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
     `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
@@ -1443,6 +1445,8 @@ Approximate the `shape_itp` with a C¹ unit speed interpolation using line segme
 
   - `m`: The number of points at which the shape interpolation is evaluated in each interval between time points.
     The `SmoothArcLengthInterpolation` converges to the shape interpolation (in shape) as m → ∞.
+  - `in_place`: Whether the value of the interpolation should be calculated in pre-allocated memory. This saves
+    allocations, but is not compatible with e.g. ForwardDiff. Defaults to `false`.
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
     are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
     `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
@@ -1520,6 +1524,8 @@ segments and circle segments.
   - `shape_itp`: The interpolation that is being approximated, if one exists. Note that this
     interpolation is not being used; it is just passed along to keep track of where the shape
     of the `SmoothArcLengthInterpolation` originated.
+  - `in_place`: Whether the value of the interpolation should be calculated in pre-allocated memory. This saves
+    allocations, but is not compatible with e.g. ForwardDiff. Defaults to `false`.
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
     are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
     `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
@@ -1618,7 +1624,7 @@ function SmoothArcLengthInterpolation(
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.None,
         cache_parameters::Bool = false,
         assume_linear_t = 1e-2,
-        in_place::Bool = true)
+        in_place::Bool = false)
     N = size(u, 1)
     n_circle_arcs = size(u, 2) - 1
 

test/derivative_tests.jl

@@ -270,9 +270,9 @@ end
     u = [0.3 -1.5 3.1; -0.2 0.2 -1.5; 10.4 -37.2 -5.8]
     test_derivatives(
         SmoothArcLengthInterpolation, args = [u], kwargs = Pair[
-            :m => 5, :in_place => false],
+            :m => 5],
         name = "Smooth Arc Length Interpolation")
-    A = SmoothArcLengthInterpolation(u'; m = 25, in_place = false)
+    A = SmoothArcLengthInterpolation(u'; m = 25)
     @test all(t -> norm(derivative(A, t)) ≈ 1, range(0, A.t[end]; length = 100))
     @test all(
         t_ -> derivative(A, prevfloat(t_)) ≈ derivative(A, nextfloat(t_)), A.t[2:(end - 1)])