curve_conversion.h
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1 #ifndef _CLASS_CURVE_CONVERSION
2 #define _CLASS_CURVE_CONVERSION
3 
4 #include <iostream>
5 #include <stdexcept>
6 #include <vector>
7 
8 #include "MathDefs.h"
9 #include "bernstein.h"
10 #include "curve_abc.h"
11 #include "curve_constraint.h"
12 
13 namespace ndcurves {
17 template <typename Polynomial>
19  const typename Polynomial::curve_abc_t& curve) {
20  typedef typename Polynomial::t_point_t t_point_t;
21  typedef typename Polynomial::num_t num_t;
22  t_point_t coefficients;
23  coefficients.push_back(curve(curve.min()));
24  num_t fact = 1;
25  for (std::size_t i = 1; i <= curve.degree(); ++i) {
26  fact *= (num_t)i;
27  coefficients.push_back(curve.derivate(curve.min(), i) / fact);
28  }
29 
30  return Polynomial(coefficients, curve.min(), curve.max());
31 }
32 
37 template <typename Bezier>
38 Bezier bezier_from_curve(const typename Bezier::curve_abc_t& curve) {
39  if (curve.degree() > 3)
40  throw std::invalid_argument(
41  "bezier_from_curve is only implemented for curves of degree <= 3.");
42  typedef typename Bezier::point_t point_t;
43  typedef typename Bezier::t_point_t t_point_t;
44  typedef typename Bezier::num_t num_t;
45  num_t T_min = curve.min();
46  num_t T_max = curve.max();
47  num_t T = T_max - T_min;
48  // Positions and derivatives
49  point_t p0 = curve(T_min);
50  point_t p1 = curve(T_max);
51  point_t m0 = curve.derivate(T_min, 1);
52  point_t m1 = curve.derivate(T_max, 1);
53  // Convert to bezier control points
54  // for t in [Tmin,Tmax] and T=Tmax-Tmin : x'(0)=3(b_p1-b_p0)/T and
55  // x'(1)=3(b_p3-b_p2)/T so : m0=3(b_p1-b_p0)/T and m1=3(b_p3-b_p2)/T
56  // <=> b_p1=T(m0/3)+b_p0 and b_p2=-T(m1/3)+b_p3
57  point_t b_p0 = p0;
58  point_t b_p3 = p1;
59  point_t b_p1 = T * m0 / 3 + b_p0;
60  point_t b_p2 = -T * m1 / 3 + b_p3;
61  t_point_t control_points;
62  control_points.push_back(b_p0);
63  control_points.push_back(b_p1);
64  control_points.push_back(b_p2);
65  control_points.push_back(b_p3);
66  return Bezier(control_points.begin(), control_points.end(), curve.min(),
67  curve.max());
68 }
69 
74 template <typename Hermite>
75 Hermite hermite_from_curve(const typename Hermite::curve_abc_t& curve) {
76  if (curve.degree() > 3)
77  throw std::invalid_argument(
78  "hermite_from_curve is only implemented for curves of degree <= 3.");
79  typedef typename Hermite::pair_point_tangent_t pair_point_tangent_t;
80  typedef typename Hermite::t_pair_point_tangent_t t_pair_point_tangent_t;
81  typedef typename Hermite::point_t point_t;
82  typedef typename Hermite::num_t num_t;
83  num_t T_min = curve.min();
84  num_t T_max = curve.max();
85  // Positions and derivatives
86  point_t p0 = curve(T_min);
87  point_t p1 = curve(T_max);
88  point_t m0 = curve.derivate(T_min, 1);
89  point_t m1 = curve.derivate(T_max, 1);
90  // Create pairs pos/vel
91  pair_point_tangent_t pair0(p0, m0);
92  pair_point_tangent_t pair1(p1, m1);
93  t_pair_point_tangent_t control_points;
94  control_points.push_back(pair0);
95  control_points.push_back(pair1);
96  std::vector<double> time_control_points;
97  time_control_points.push_back(T_min);
98  time_control_points.push_back(T_max);
99  return Hermite(control_points.begin(), control_points.end(),
100  time_control_points);
101 }
102 } // namespace ndcurves
103 #endif //_CLASS_CURVE_CONVERSION
interface for a Curve of arbitrary dimension.
struct to define constraints on start / end velocities and acceleration on a curve
Definition: bernstein.h:20
curve_abc< double, double, true, pointX_t, pointX_t > curve_abc_t
Definition: fwd.h:85
Hermite hermite_from_curve(const typename Hermite::curve_abc_t &curve)
Converts a polynomial of order 3 or less/cubic bezier curve to a cubic hermite spline.
Definition: curve_conversion.h:75
Bezier bezier_from_curve(const typename Bezier::curve_abc_t &curve)
Converts a cubic hermite spline or polynomial of order 3 or less to a cubic bezier curve.
Definition: curve_conversion.h:38
Polynomial polynomial_from_curve(const typename Polynomial::curve_abc_t &curve)
Converts a cubic hermite spline or a bezier curve to a polynomial.
Definition: curve_conversion.h:18