Loading...
Searching...
No Matches
cubic_hermite_spline.h
Go to the documentation of this file.
1
8#ifndef _CLASS_CUBICHERMITESPLINE
9#define _CLASS_CUBICHERMITESPLINE
10
11#include <boost/serialization/utility.hpp> // To serialize std::pair
12#include <iostream>
13#include <stdexcept>
14#include <vector>
15
16#include "MathDefs.h"
17#include "bezier_curve.h"
18#include "curve_abc.h"
19#include "piecewise_curve.h"
20
21namespace ndcurves {
32template <typename Time = double, typename Numeric = Time, bool Safe = false,
33 typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1> >
34struct cubic_hermite_spline : public curve_abc<Time, Numeric, Safe, Point> {
35 typedef Point point_t;
36 typedef std::pair<Point, Point> pair_point_tangent_t;
37 typedef std::vector<pair_point_tangent_t,
38 Eigen::aligned_allocator<pair_point_tangent_t> >
40 typedef std::vector<Time> vector_time_t;
41 typedef Time time_t;
42 typedef Numeric num_t;
50
51 public:
56
63 template <typename In>
64 cubic_hermite_spline(In PairsBegin, In PairsEnd,
65 const vector_time_t& time_control_points)
66 : size_(std::distance(PairsBegin, PairsEnd)), degree_(3) {
67 // Check size of pairs container.
68 if (Safe && size_ < 1) {
69 throw std::length_error(
70 "can not create cubic_hermite_spline, number of pairs is inferior to "
71 "2.");
72 }
73 // Set dimension according to size of points
74 dim_ = PairsBegin->first.size();
75 // Push all pairs in controlPoints
76 In it(PairsBegin);
77 for (; it != PairsEnd; ++it) {
78 if (Safe && (static_cast<size_t>(it->first.size()) != dim_ ||
79 static_cast<size_t>(it->second.size()) != dim_))
80 throw std::invalid_argument(
81 "All the control points and their derivatives must have the same "
82 "dimension.");
83 control_points_.push_back(*it);
84 }
85 // Set time
86 setTime(time_control_points);
87 }
88
90 : dim_(other.dim_),
94 T_min_(other.T_min_),
95 T_max_(other.T_max_),
96 size_(other.size_),
97 degree_(other.degree_) {}
98
101
102 /*Operations*/
103 public:
108 virtual Point operator()(const time_t t) const {
109 check_conditions();
110 if (Safe & !(T_min_ <= t && t <= T_max_)) {
111 throw std::invalid_argument(
112 "can't evaluate cubic hermite spline, out of range");
113 }
114 if (size_ == 1) {
115 return control_points_.front().first;
116 } else {
117 const bezier_t bezier = buildCurrentBezier(t);
118 return bezier(t);
119 }
120 }
121
132 const cubic_hermite_spline_t& other,
133 const Numeric prec = Eigen::NumTraits<Numeric>::dummy_precision()) const {
134 bool equal = ndcurves::isApprox<num_t>(T_min_, other.min()) &&
135 ndcurves::isApprox<num_t>(T_max_, other.max()) &&
136 dim_ == other.dim() && degree_ == other.degree() &&
137 size_ == other.size() &&
140 if (!equal) return false;
141 for (std::size_t i = 0; i < size_; ++i) {
142 if ((!control_points_[i].first.isApprox(other.control_points_[i].first,
143 prec)) ||
144 (!control_points_[i].second.isApprox(other.control_points_[i].second,
145 prec)))
146 return false;
147 }
148 return true;
149 }
150
151 virtual bool isApprox(
152 const curve_abc_t* other,
153 const Numeric prec = Eigen::NumTraits<Numeric>::dummy_precision()) const {
154 const cubic_hermite_spline_t* other_cast =
155 dynamic_cast<const cubic_hermite_spline_t*>(other);
156 if (other_cast)
157 return isApprox(*other_cast, prec);
158 else
159 return false;
160 }
161
162 virtual bool operator==(const cubic_hermite_spline_t& other) const {
163 return isApprox(other);
164 }
165
166 virtual bool operator!=(const cubic_hermite_spline_t& other) const {
167 return !(*this == other);
168 }
169
176 virtual Point derivate(const time_t t, const std::size_t order) const {
177 check_conditions();
178 if (Safe & !(T_min_ <= t && t <= T_max_)) {
179 throw std::invalid_argument(
180 "can't derivate cubic hermite spline, out of range");
181 }
182 if (size_ == 1) {
183 return control_points_.front().second;
184 } else {
185 const bezier_t bezier = buildCurrentBezier(t);
186 return bezier.derivate(t, order);
187 }
188 }
189
190 piecewise_bezier_t compute_derivate(const std::size_t order) const {
192 for (size_t i = 0; i < size_ - 1; ++i) {
193 const bezier_t curve = buildCurrentBezier(time_control_points_[i]);
194 res.add_curve(curve.compute_derivate(order));
195 }
196 return res;
197 }
198
203 piecewise_bezier_t* compute_derivate_ptr(const std::size_t order) const {
204 return new piecewise_bezier_t(compute_derivate(order));
205 }
206
213 void setTime(const vector_time_t& time_control_points) {
214 time_control_points_ = time_control_points;
217 if (time_control_points.size() != size()) {
218 throw std::length_error(
219 "size of time control points should be equal to number of control "
220 "points");
221 }
222 computeDurationSplines();
223 if (!checkDurationSplines()) {
224 throw std::invalid_argument(
225 "time_splines not monotonous, all spline duration should be superior "
226 "to 0");
227 }
228 }
229
234
239
243 std::size_t size() const { return size_; }
244
248 std::size_t numIntervals() const { return size() - 1; }
249
250 private:
255 std::size_t findInterval(const time_t t) const {
256 // time before first control point time.
257 if (t <= time_control_points_[0]) {
258 return 0;
259 }
260 // time is after last control point time
261 if (t >= time_control_points_[size_ - 1]) {
262 return size_ - 2;
263 }
264 std::size_t left_id = 0;
265 std::size_t right_id = size_ - 1;
266 while (left_id <= right_id) {
267 const std::size_t middle_id = left_id + (right_id - left_id) / 2;
268 if (time_control_points_.at(middle_id) < t) {
269 left_id = middle_id + 1;
270 } else if (time_control_points_.at(middle_id) > t) {
271 right_id = middle_id - 1;
272 } else {
273 return middle_id;
274 }
275 }
276 return left_id - 1;
277 }
278
286 bezier_t buildCurrentBezier(const time_t t) const {
287 size_t id_interval = findInterval(t);
288 const pair_point_tangent_t pair0 = control_points_.at(id_interval);
289 const pair_point_tangent_t pair1 = control_points_.at(id_interval + 1);
290 const Time& t0 = time_control_points_[id_interval];
291 const Time& t1 = time_control_points_[id_interval + 1];
292 t_point_t control_points;
293 control_points.reserve(4);
294 control_points.push_back(pair0.first);
295 control_points.push_back(pair0.first + pair0.second / 3. * (t1 - t0));
296 control_points.push_back(pair1.first - pair1.second / 3. * (t1 - t0));
297 control_points.push_back(pair1.first);
298 return bezier_t(control_points.begin(), control_points.end(), t0, t1);
299 }
300
304 void check_conditions() const {
305 if (control_points_.size() == 0) {
306 throw std::runtime_error(
307 "Error in cubic hermite : there is no control points set / did you "
308 "use empty constructor ?");
309 } else if (dim_ == 0) {
310 throw std::runtime_error(
311 "Error in cubic hermite : Dimension of points is zero / did you use "
312 "empty constructor ?");
313 }
314 }
315
321 void computeDurationSplines() {
322 duration_splines_.clear();
323 Time actual_time;
324 Time prev_time = *(time_control_points_.begin());
325 std::size_t i = 0;
326 for (i = 0; i < size() - 1; i++) {
327 actual_time = time_control_points_.at(i + 1);
328 duration_splines_.push_back(actual_time - prev_time);
329 prev_time = actual_time;
330 }
331 }
332
336 bool checkDurationSplines() const {
337 std::size_t i = 0;
338 bool is_positive = true;
339 while (is_positive && i < duration_splines_.size()) {
340 is_positive = (duration_splines_.at(i) > 0.);
341 i++;
342 }
343 return is_positive;
344 }
345 /*Operations*/
346
347 /*Helpers*/
348 public:
351 std::size_t virtual dim() const { return dim_; }
354 Time virtual min() const { return time_control_points_.front(); }
357 Time virtual max() const { return time_control_points_.back(); }
360 virtual std::size_t degree() const { return degree_; }
361 /*Helpers*/
362
363 /*Attributes*/
365 std::size_t dim_;
381 /*const*/ Time T_min_;
384 /*const*/ Time T_max_;
386 std::size_t size_;
388 std::size_t degree_;
389 /*Attributes*/
390
391 // Serialization of the class
393
394 template <class Archive>
395 void serialize(Archive& ar, const unsigned int version) {
396 if (version) {
397 // Do something depending on version ?
398 }
399 ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(curve_abc_t);
400 ar& boost::serialization::make_nvp("dim", dim_);
401 ar& boost::serialization::make_nvp("control_points", control_points_);
402 ar& boost::serialization::make_nvp("time_control_points",
404 ar& boost::serialization::make_nvp("duration_splines", duration_splines_);
405 ar& boost::serialization::make_nvp("T_min", T_min_);
406 ar& boost::serialization::make_nvp("T_max", T_max_);
407 ar& boost::serialization::make_nvp("size", size_);
408 ar& boost::serialization::make_nvp("degree", degree_);
409 }
410}; // End struct Cubic hermite spline
411} // namespace ndcurves
412
414 SINGLE_ARG(typename Time, typename Numeric, bool Safe, typename Point),
416#endif //_CLASS_CUBICHERMITESPLINE
#define DEFINE_CLASS_TEMPLATE_VERSION(Template, Type)
Definition: archive.hpp:27
#define SINGLE_ARG(...)
Definition: archive.hpp:23
class allowing to create a Bezier curve of dimension 1 <= n <= 3.
interface for a Curve of arbitrary dimension.
Eigen::Matrix< Numeric, Eigen::Dynamic, 1 > Point
Definition: effector_spline.h:28
double Numeric
Definition: effector_spline.h:26
double Time
Definition: effector_spline.h:27
Definition: bernstein.h:20
class allowing to create a piecewise curve.
Definition: bezier_curve.h:31
std::vector< point_t, Eigen::aligned_allocator< point_t > > t_point_t
Definition: bezier_curve.h:38
bezier_curve_t compute_derivate(const std::size_t order) const
Compute the derived curve at order N. Computes the derivative order N, of bezier curve of parametric...
Definition: bezier_curve.h:206
virtual point_t derivate(const time_t t, const std::size_t order) const
Evaluate the derivative order N of curve at time t. If derivative is to be evaluated several times,...
Definition: bezier_curve.h:308
Definition: cubic_hermite_spline.h:34
piecewise_bezier_t compute_derivate(const std::size_t order) const
Definition: cubic_hermite_spline.h:190
void serialize(Archive &ar, const unsigned int version)
Definition: cubic_hermite_spline.h:395
Time time_t
Definition: cubic_hermite_spline.h:41
virtual std::size_t degree() const
Get the degree of the curve.
Definition: cubic_hermite_spline.h:360
virtual Time max() const
Get the maximum time for which the curve is defined.
Definition: cubic_hermite_spline.h:357
Time T_max_
Definition: cubic_hermite_spline.h:384
bezier_t::t_point_t t_point_t
Definition: cubic_hermite_spline.h:47
bezier_curve< Time, Numeric, Safe, point_t > bezier_t
Definition: cubic_hermite_spline.h:46
std::size_t degree_
Degree (Cubic so degree 3)
Definition: cubic_hermite_spline.h:388
std::size_t dim_
Dim of curve.
Definition: cubic_hermite_spline.h:365
std::vector< pair_point_tangent_t, Eigen::aligned_allocator< pair_point_tangent_t > > t_pair_point_tangent_t
Definition: cubic_hermite_spline.h:39
cubic_hermite_spline(const cubic_hermite_spline &other)
Definition: cubic_hermite_spline.h:89
bool isApprox(const cubic_hermite_spline_t &other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
isApprox check if other and *this are approximately equals. Only two curves of the same class can be ...
Definition: cubic_hermite_spline.h:131
vector_time_t getTime()
Get vector of Time corresponding to Time for each control point.
Definition: cubic_hermite_spline.h:238
std::size_t size_
Number of control points (pairs).
Definition: cubic_hermite_spline.h:386
virtual Time min() const
Get the minimum time for which the curve is defined.
Definition: cubic_hermite_spline.h:354
std::pair< Point, Point > pair_point_tangent_t
Definition: cubic_hermite_spline.h:36
Numeric num_t
Definition: cubic_hermite_spline.h:42
Time T_min_
Definition: cubic_hermite_spline.h:381
void setTime(const vector_time_t &time_control_points)
Set time of each control point of cubic hermite spline. Set duration of each spline,...
Definition: cubic_hermite_spline.h:213
virtual Point operator()(const time_t t) const
Evaluation of the cubic hermite spline at time t.
Definition: cubic_hermite_spline.h:108
virtual std::size_t dim() const
Get dimension of curve.
Definition: cubic_hermite_spline.h:351
std::size_t size() const
Get number of control points contained in the trajectory.
Definition: cubic_hermite_spline.h:243
std::vector< Time > vector_time_t
Definition: cubic_hermite_spline.h:40
vector_time_t time_control_points_
Definition: cubic_hermite_spline.h:372
virtual bool operator!=(const cubic_hermite_spline_t &other) const
Definition: cubic_hermite_spline.h:166
t_pair_point_tangent_t control_points_
Vector of pair < Point, Tangent >.
Definition: cubic_hermite_spline.h:367
virtual Point derivate(const time_t t, const std::size_t order) const
Evaluate the derivative of order N of spline at time t.
Definition: cubic_hermite_spline.h:176
std::size_t numIntervals() const
Get number of intervals (subsplines) contained in the trajectory.
Definition: cubic_hermite_spline.h:248
vector_time_t duration_splines_
Definition: cubic_hermite_spline.h:378
cubic_hermite_spline(In PairsBegin, In PairsEnd, const vector_time_t &time_control_points)
Constructor.
Definition: cubic_hermite_spline.h:64
piecewise_curve< Time, Numeric, Safe, point_t, point_t, bezier_t > piecewise_bezier_t
Definition: cubic_hermite_spline.h:49
curve_abc< Time, Numeric, Safe, point_t > curve_abc_t
Definition: cubic_hermite_spline.h:43
friend class boost::serialization::access
Definition: cubic_hermite_spline.h:392
virtual ~cubic_hermite_spline()
Destructor.
Definition: cubic_hermite_spline.h:100
Point point_t
Definition: cubic_hermite_spline.h:35
cubic_hermite_spline()
Empty constructor. Curve obtained this way can not perform other class functions.
Definition: cubic_hermite_spline.h:55
virtual bool operator==(const cubic_hermite_spline_t &other) const
Definition: cubic_hermite_spline.h:162
cubic_hermite_spline< Time, Numeric, Safe, point_t > cubic_hermite_spline_t
Definition: cubic_hermite_spline.h:45
piecewise_bezier_t * compute_derivate_ptr(const std::size_t order) const
Compute the derived curve at order N.
Definition: cubic_hermite_spline.h:203
t_pair_point_tangent_t getControlPoints()
Get vector of pair (positition, derivative) corresponding to control points.
Definition: cubic_hermite_spline.h:233
virtual bool isApprox(const curve_abc_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
Definition: cubic_hermite_spline.h:151
Represents a curve of dimension Dim. If value of parameter Safe is false, no verification is made on ...
Definition: curve_abc.h:37
Definition: piecewise_curve.h:37
void add_curve(const Curve &curve)
Definition: piecewise_curve.h:176