From a5753d7953982234317ade005097987069cf0e1c Mon Sep 17 00:00:00 2001
From: Adrian Mariano <avm4@cornell.edu>
Date: Sat, 13 Jun 2020 22:35:22 -0400
Subject: [PATCH] Added non-uniform sampling to deriv and uniform option to
 path_tangents, and path_segment_lengths.

---
 math.scad  | 28 ++++++++++++++++++++++++++++
 paths.scad | 45 +++++++++++++++++++++++++++++++++++++++++----
 2 files changed, 69 insertions(+), 4 deletions(-)

diff --git a/math.scad b/math.scad
index 10938ab..5ec3209 100644
--- a/math.scad
+++ b/math.scad
@@ -899,7 +899,13 @@ function count_true(l, nmax=undef, i=0, cnt=0) =
 //   data[len(data)-1].  This function uses a symetric derivative approximation
 //   for internal points, f'(t) = (f(t+h)-f(t-h))/2h.  For the endpoints (when closed=false) the algorithm
 //   uses a two point method if sufficient points are available: f'(t) = (3*(f(t+h)-f(t)) - (f(t+2*h)-f(t+h)))/2h.
+// 
+//   If `h` is a vector then it is assumed to be nonuniform, with h[i] giving the sampling distance
+//   between data[i+1] and data[i], and the data values will be linearly resampled at each corner
+//   to produce a uniform spacing for the derivative estimate.  At the endpoints a single point method
+//   is used: f'(t) = (f(t+h)-f(t))/h.  
 function deriv(data, h=1, closed=false) =
+    is_vector(h) ? _deriv_nonuniform(data, h, closed=closed) :
     let( L = len(data) )
     closed? [
         for(i=[0:1:L-1])
@@ -919,6 +925,28 @@ function deriv(data, h=1, closed=false) =
     ];
 
 
+function _dnu_calc(f1,fc,f2,h1,h2) =
+    let(
+        f1 = h2<h1 ? lerp(fc,f1,h2/h1) : f1 , 
+        f2 = h1<h2 ? lerp(fc,f2,h1/h2) : f2
+    )
+    (f2-f1) / 2 / min([h1,h2]);
+
+
+function _deriv_nonuniform(data, h, closed) =
+    assert(len(h) == len(data)-(closed?0:1),str("Vector valued h must be length ",len(data)-(closed?0:1)))
+    let(
+      L = len(data)
+    )
+    closed? [for(i=[0:1:L-1])
+    	        _dnu_calc(data[(L+i-1)%L], data[i], data[(i+1)%L], select(h,i-1), h[i]) ]
+    : [
+        (data[1]-data[0])/h[0],
+        for(i=[1:1:L-2]) _dnu_calc(data[i-1],data[i],data[i+1], h[i-1],h[i]),
+        (data[L-1]-data[L-2])/h[L-2]                            
+      ];
+
+
 // Function: deriv2()
 // Usage: deriv2(data, [h], [closed])
 // Description:
diff --git a/paths.scad b/paths.scad
index ad8b732..654a427 100644
--- a/paths.scad
+++ b/paths.scad
@@ -149,6 +149,21 @@ function path_length(path,closed=false) =
     sum([for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i])])+(closed?norm(path[len(path)-1]-path[0]):0);
 
 
+// Function: path_segment_lengths()
+// Usage:
+//   path_segment_lengths(path,[closed])
+// Description:
+//   Returns list of the length of each segment in a path
+// Arguments:
+//   path = path to measure
+//   closed = true if the path is closed.  Default: false
+function path_segment_lengths(path, closed=false) =
+    [
+      for (i=[0:1:len(path)-2]) norm(path[i+1]-path[i]),
+      if (closed) norm(path[0]-path[len(path)-1])
+     ]; 
+
+
 // Function: path_pos_from_start()
 // Usage:
 //   pos = path_pos_from_start(path,length,[closed]);
@@ -280,13 +295,35 @@ function path_closest_point(path, pt) =
 
 
 // Function: path_tangents()
-// Usage: path_tangents(path, [closed])
+// Usage: path_tangents(path, [closed], [uniform])
 // Description:
 //   Compute the tangent vector to the input path.  The derivative approximation is described in deriv().
-//   The returns vectors will be normalized to length 1.
-function path_tangents(path, closed=false) =
+//   The returns vectors will be normalized to length 1.  If any derivatives are zero then
+//   the function fails with an error.  If you set `uniform` to false then the sampling is
+//   assumed to be non-uniform and the derivative is computed with adjustments to produce corrected
+//   values.
+// Arguments:
+//   path = path to find the tagent vectors for
+//   closed = set to true of the path is closed.  Default: false
+//   uniform = set to false to correct for non-uniform sampling.  Default: true
+// Example: A shape with non-uniform sampling gives distorted derivatives that may be undesirable
+//   rect = square([10,3]);
+//   tangents = path_tangents(rect,closed=true);
+//   stroke(rect,closed=true, width=0.1);
+//   color("purple")
+//       for(i=[0:len(tangents)-1])
+//           stroke([rect[i]-tangents[i], rect[i]+tangents[i]],width=.1, endcap2="arrow2");
+// Example: A shape with non-uniform sampling gives distorted derivatives that may be undesirable
+//   rect = square([10,3]);
+//   tangents = path_tangents(rect,closed=true,uniform=false);
+//   stroke(rect,closed=true, width=0.1);
+//   color("purple")
+//       for(i=[0:len(tangents)-1])
+//           stroke([rect[i]-tangents[i], rect[i]+tangents[i]],width=.1, endcap2="arrow2");
+function path_tangents(path, closed=false, uniform=true) =
     assert(is_path(path))
-    [for(t=deriv(path,closed=closed)) unit(t)];
+    !uniform ? [for(t=deriv(path,closed=closed, h=path_segment_lengths(path,closed))) unit(t)]
+             : [for(t=deriv(path,closed=closed)) unit(t)];
 
 
 // Function: path_normals()