From 3db722da4c470d2d98edeadf4b0173fc49be0424 Mon Sep 17 00:00:00 2001
From: JasonChmn <jason.chemin@hotmail.fr>
Date: Tue, 30 Apr 2019 10:35:50 +0200
Subject: [PATCH] Edit doc on bernstein and bezier
---
include/curves/bernstein.h | 7 +++++-
include/curves/bezier_curve.h | 44 +++++++++++++++++------------------
2 files changed, 28 insertions(+), 23 deletions(-)
diff --git a/include/curves/bernstein.h b/include/curves/bernstein.h
index 86eb3ab..5066f83 100644
--- a/include/curves/bernstein.h
+++ b/include/curves/bernstein.h
@@ -21,6 +21,8 @@
namespace curves
{
/// \brief Computes factorial of a number.
+/// \param n : an unsigned integer.
+/// \return \f$n!\f$
///
inline unsigned int fact(const unsigned int n)
{
@@ -30,7 +32,10 @@ inline unsigned int fact(const unsigned int n)
return res;
}
-/// \brief Computes a binomal coefficient.
+/// \brief Computes a binomial coefficient.
+/// \param n : an unsigned integer.
+/// \param k : an unsigned integer.
+/// \return \f$\binom{n}{k}f$
///
inline unsigned int bin(const unsigned int n, const unsigned int k)
{
diff --git a/include/curves/bezier_curve.h b/include/curves/bezier_curve.h
index f6ad560..38ce0aa 100644
--- a/include/curves/bezier_curve.h
+++ b/include/curves/bezier_curve.h
@@ -45,8 +45,8 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
/// \brief Constructor.
/// Given the first and last point of a control points set, automatically create the bezier curve.
- /// \param PointsBegin : an iterator pointing to the first element of a control point container.
- /// \param PointsEnd : an iterator pointing to the last element of a control point container.
+ /// \param PointsBegin : an iterator pointing to the first element of a control points container.
+ /// \param PointsEnd : an iterator pointing to the last element of a control points container.
///
template<typename In>
bezier_curve(In PointsBegin, In PointsEnd)
@@ -148,7 +148,7 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
public:
/// \brief Evaluation of the bezier curve at time t.
/// \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.
virtual point_t operator()(const time_t t) const
{
if(Safe &! (0 <= t && t <= T_))
@@ -161,9 +161,9 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
}
/// \brief Compute the derivative curve at order N.
- /// Computes the derivative at order N, \f$\frac{d^Nx(t)}{dt^N}\f$ of bezier curve of parametric equation x(t).
+ /// Computes the derivative order N, \f$\frac{d^Nx(t)}{dt^N}\f$ of bezier curve of parametric equation x(t).
/// \param order : order of derivative.
- /// \return Derivative \f$\frac{d^Nx(t)}{dt^N}\f$.
+ /// \return \f$\frac{d^Nx(t)}{dt^N}\f$ derivative order N of the curve.
bezier_curve_t compute_derivate(const std::size_t order) const
{
if(order == 0) return *this;
@@ -177,10 +177,10 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
}
/// \brief Compute the primitive of the curve at order N.
- /// Computes the primitive at order N of bezier curve of parametric equation \f$x(t)\f$. At order \f$N=1\f$,
- /// the primitve \f$X(t)\f$ of \f$x(t)\f$ is such as \f$\frac{dX(t)}{dt} = x(t)\f$.
+ /// Computes the primitive at order N of bezier curve of parametric equation \f$x(t)\f$. <br>
+ /// At order \f$N=1\f$, the primitve \f$X(t)\f$ of \f$x(t)\f$ is such as \f$\frac{dX(t)}{dt} = x(t)\f$.
/// \param order : order of the primitive.
- /// \return Primitive at order N of x(t).
+ /// \return primitive at order N of x(t).
bezier_curve_t compute_primitive(const std::size_t order) const
{
if(order == 0) return *this;
@@ -199,12 +199,12 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
return integ.compute_primitive(order-1);
}
- /// \brief Evaluate the derivative of order N of curve at time t.
- /// If the derivative is to be evaluated several times, it is
+ /// \brief Evaluate the derivative order N of curve at time t.
+ /// If derivative is to be evaluated several times, it is
/// rather recommended to compute derivative curve using compute_derivate.
/// \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.
+ /// \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
{
@@ -215,9 +215,9 @@ 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$.<br/>
- /// Warning: the horner scheme is about 100 times faster than this method.
+ /// Warning: the horner scheme is about 100 times faster than this method.<br>
/// This method will probably be removed in the future as the computation of bernstein polynomial is very costly.
- /// \param t : unNormalized time
+ /// \param t : time when to evaluate the curve.
/// \return \f$x(t)\f$, point corresponding on curve at time t.
///
point_t evalBernstein(const Numeric t) const
@@ -232,15 +232,15 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
}
/// \brief Evaluate all Bernstein polynomes for a certain degree using Horner's scheme.
- /// A bezier curve with N control points is expressed as : \f$x(t) = \sum_{i=0}^{N} B_i^N(t) P_i\f$.
- /// To evaluate the position on curve at time t,we can apply the Horner's scheme :
- /// \f$ x(t) = (1-t)^N(\sum_{i=0}^{N} \binom{N}{i} \frac{1-t}{t}^i P_i) \f$.
- /// Horner's scheme : for a polynom of degree N expressed by :
+ /// A bezier curve with N control points is expressed as : \f$x(t) = \sum_{i=0}^{N} B_i^N(t) P_i\f$.<br>
+ /// To evaluate the position on curve at time t,we can apply the Horner's scheme : <br>
+ /// \f$ x(t) = (1-t)^N(\sum_{i=0}^{N} \binom{N}{i} \frac{1-t}{t}^i P_i) \f$.<br>
+ /// Horner's scheme : for a polynom of degree N expressed by : <br>
/// \f$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 :
+ /// where \f$number of additions = N\f$ / f$number of multiplication = N!\f$<br>
+ /// 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 : unNormalized time
+ /// \param t : time when to evaluate the curve.
/// \return \f$x(t)\f$, point corresponding on curve at time t.
///
point_t evalHorner(const Numeric t) const
@@ -264,7 +264,7 @@ 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.
- /// \param t : unNormalized time
+ /// \param t : time when to evaluate the curve.
/// \return \f$x(t)\f$, point corresponding on curve at time t.
///
point_t evalDeCasteljau(const Numeric t) const {
@@ -283,7 +283,7 @@ struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
/// \brief Compute de Casteljau's reduction of the given list of points at time t.
/// \param pts : list of points.
- /// \param u : NORMALIZED time.
+ /// \param u : NORMALIZED time when to evaluate the curve.
/// \return Reduced list of point (size of pts - 1).
///
t_point_t deCasteljauReduction(const t_point_t& pts, const Numeric u) const{
--
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