From 73fee04ec667c913e3da62ec2caa918b5b5f61bc Mon Sep 17 00:00:00 2001
From: JasonChmn <jason.chemin@hotmail.fr>
Date: Tue, 30 Apr 2019 11:05:34 +0200
Subject: [PATCH] Edit doc deCastelJau algorithm in bezier curve
---
include/curves/bezier_curve.h | 14 +++++++++++---
1 file changed, 11 insertions(+), 3 deletions(-)
diff --git a/include/curves/bezier_curve.h b/include/curves/bezier_curve.h
index 38ce0aa..8682c75 100644
--- a/include/curves/bezier_curve.h
+++ b/include/curves/bezier_curve.h
@@ -218,7 +218,7 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
/// Warning: the horner scheme is about 100 times faster than this method.<br>
/// This method will probably be removed in the future as the computation of bernstein polynomial is very costly.
/// \param t : time when to evaluate the curve.
- /// \return \f$x(t)\f$, point corresponding on curve at time t.
+ /// \return \f$x(t)\f$ point corresponding on curve at time t.
///
point_t evalBernstein(const Numeric t) const
{
@@ -241,7 +241,7 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
/// Using Horner's method, the polynom is transformed into : <br>
/// \f$x(t) = a_0 + t(a_1 + t(a_2+t(...))\f$ with N additions and multiplications.
/// \param t : time when to evaluate the curve.
- /// \return \f$x(t)\f$, point corresponding on curve at time t.
+ /// \return \f$x(t)\f$ point corresponding on curve at time t.
///
point_t evalHorner(const Numeric t) const
{
@@ -264,8 +264,11 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
const t_point_t& waypoints() const {return pts_;}
/// \brief Evaluate the curve value at time t using deCasteljau algorithm.
+ /// The algorithm will compute the \f$N-1\f$ centroids of parameters \f${t,1-t}\f$ of consecutive \f$N\f$ control points
+ /// of bezier curve, and perform it iteratively until getting one point in the list which will be the evaluation of bezier
+ /// curve at time \f$t\f$.
/// \param t : time when to evaluate the curve.
- /// \return \f$x(t)\f$, point corresponding on curve at time t.
+ /// \return \f$x(t)\f$ point corresponding on curve at time t.
///
point_t evalDeCasteljau(const Numeric t) const {
// normalize time :
@@ -277,11 +280,16 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
return pts[0]*mult_T_;
}
+
t_point_t deCasteljauReduction(const Numeric t) const{
return deCasteljauReduction(waypoints(),t/T_);
}
/// \brief Compute de Casteljau's reduction of the given list of points at time t.
+ /// For the list \f$pts\f$ of N points, compute a new list of points of size N-1 :<br>
+ /// \f$<br>( pts[0]*(1-t)+pts[1], pts[1]*(1-t)+pts[2], ..., pts[0]*(N-2)+pts[N-1] )\f$<br>
+ /// with t the time when to evaluate bezier curve.<br>\
+ /// The new list contains centroid of parameters \f${t,1-t}\f$ of consecutive points in the list.
/// \param pts : list of points.
/// \param u : NORMALIZED time when to evaluate the curve.
/// \return Reduced list of point (size of pts - 1).
--
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