From 3d743714d169d028bd94032b74b54c715d993432 Mon Sep 17 00:00:00 2001
From: Nick Gasson <nick@nickg.me.uk>
Date: Sat, 13 Jun 2009 19:26:22 +0100
Subject: [PATCH] Approximate the length of a Bezier curve

---
 include/BezierCurve.hpp | 27 +++++++++++++++++++++++++--
 src/Points.cpp          |  2 +-
 2 files changed, 26 insertions(+), 3 deletions(-)

diff --git a/include/BezierCurve.hpp b/include/BezierCurve.hpp
index c46e57f..004f48f 100644
--- a/include/BezierCurve.hpp
+++ b/include/BezierCurve.hpp
@@ -25,6 +25,30 @@
 template <typename T>
 struct BezierCurve {
    Vector<T> p[4];
+   T length;  // A very rough approximation to the length
+
+   BezierCurve(Vector<T> p1, Vector<T> p2, Vector<T> p3, Vector<T> p4)
+   {
+      p[0] = p1;
+      p[1] = p2;
+      p[2] = p3;
+      p[3] = p4;
+      
+      // Approximate the length
+      Vector<T> cur = operator()(0.0), prev;
+
+      length = 0.0;
+      
+      const T step = 0.01;
+      for (T t = 0.1; t <= 1.0; t += step) {
+         prev = cur;
+         cur = operator()(t);
+
+         const Vector<T> diff = cur - prev;
+         
+         length += sqrt(diff.x*diff.x + diff.y*diff.y + diff.z*diff.z);
+      }
+   }
 
    Vector<T> operator()(T t) const
    {
@@ -79,8 +103,7 @@ template <typename T>
 BezierCurve<T> makeBezierCurve(Vector<T> p1, Vector<T> p2,
                                Vector<T> p3, Vector<T> p4)
 {
-   BezierCurve<T> b = { { p1, p2, p3, p4 } };
-   return b;
+   return BezierCurve<T>(p1, p2, p3, p4);
 }
 
 #endif
diff --git a/src/Points.cpp b/src/Points.cpp
index a328585..6b9bda1 100644
--- a/src/Points.cpp
+++ b/src/Points.cpp
@@ -116,7 +116,7 @@ void Points::render() const
 double Points::segmentLength(const track::TravelToken& aToken) const
 {
    if (aToken.position == displacedEndpoint())
-      return 4.0;   // No idea how to calculate the /actual/ value
+      return myCurve.length;
    else
       return 3.0;
 }
-- 
2.39.2