From b527134b31f6d1e2b3cc4ca77f4e1205efbec546 Mon Sep 17 00:00:00 2001
From: JasonChmn <jason.chemin@hotmail.fr>
Date: Fri, 19 Apr 2019 11:03:21 +0200
Subject: [PATCH] Modification in doc of files in curves folder v2
---
include/curves/bezier_curve.h | 14 ++++++++++++--
1 file changed, 12 insertions(+), 2 deletions(-)
diff --git a/include/curves/bezier_curve.h b/include/curves/bezier_curve.h
index 50d45bf..036423c 100644
--- a/include/curves/bezier_curve.h
+++ b/include/curves/bezier_curve.h
@@ -205,6 +205,7 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
/// \param order : order of derivative.
/// \param t : time when to evaluate the curve.
/// \return \f$\frac{d^Nx(t)}{dt^N}\f$, point corresponding on derivative curve of order N at time t.
+ ///
virtual point_t derivate(const time_t t, const std::size_t order) const
{
bezier_curve_t deriv =compute_derivate(order);
@@ -212,8 +213,10 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
}
/// \brief Evaluate all Bernstein polynomes for a certain degree.
+ /// A bezier curve with N control points is represented by : \f$x(t) = \sum_{i=0}^{N} B_i^N(t) P_i\f$
+ /// with \f$ B_i^N(t) = \binom{N}{i}t^i (1-t)^{N-i} \f$.<br/>
/// Warning: the horner scheme is about 100 times faster than this method.
- /// This method will probably be removed in the future.
+ /// This method will probably be removed in the future as the computation of bernstein polynomial is very costly.
/// \param t : unNormalized time
/// \return \f$x(t)\f$, point corresponding on curve at time t.
///
@@ -228,7 +231,14 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
return res*mult_T_;
}
- /// \brief Evaluate all Bernstein polynomes for a certain degree using horner's scheme.
+ /// \brief Evaluate all Bernstein polynomes for a certain degree using Horner's scheme.
+ /// For a polynom of degree N expressed by : \f$x(t) = a_0 + a_1t + a_2t^2 + ... + a_nt^n\f$
+ /// where \f$number of additions = N\f$ / f$number of multiplication = N!\f$
+ /// Using Horner's method, the polynom is transformed into :
+ /// \f$x(t) = a_0 + t(a_1 + t(a_2+t(...))\f$
+ /// where number of additions = N / number of multiplication = N.
+ /// A bezier curve with N control points is expressed as : \f$x(t) = \sum_{i=0}^{N} B_i^N(t) P_i\f$
+ /// We can apply the Horner's scheme : \f$ x(t) = (1-t)^N(\sum_{i=0}^{N} \binom{N}{i} \frac{1-t}{t}^i P_i) \f$
/// \param t : unNormalized time
/// \return \f$x(t)\f$, point corresponding on curve at time t.
///
--
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