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AnimationHelper.cc
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49 
50 #define ANIMATIONHELPER_CC
51 
52 #include "AnimationHelper.hh"
53 #include <cmath>
54 #include <cassert>
55 
56 #define APPROXIMATION_EPSILON 1.0e-09
57 #define VERYSMALL 1.0e-20
58 #define MAXIMUM_ITERATIONS 1000
59 
60 template<typename Scalar>
61 Scalar AnimationHelper::clampTo01Interval(Scalar _value) {
62  if (_value < 0.0)
63  return 0.0;
64  else if (_value > 1.0)
65  return 1.0;
66  else
67  return _value;
68 }
69 
70 template<typename Scalar>
71 Scalar AnimationHelper::abs(Scalar _value) {
72  if (_value < 0.0)
73  return _value * -1.0;
74  else
75  return _value;
76 }
77 
78 template<typename Scalar>
79 float AnimationHelper::approximateCubicBezierParameter(Scalar _atX, Scalar _P0X, Scalar _P1X, Scalar _C0X, Scalar _C1X) {
80  if (_atX - _P0X < VERYSMALL)
81  return 0.0;
82 
83  if (_P1X - _atX < VERYSMALL)
84  return 1.0;
85 
86  long iterationStep = 0;
87 
88  float u = 0.0f; float v = 1.0f;
89 
90  //iteratively apply subdivision to approach value atX
91  while (iterationStep < MAXIMUM_ITERATIONS) {
92 
93  // de Casteljau Subdivision.
94  Scalar a = (_P0X + _C0X)*0.5;
95  Scalar b = (_C0X + _C1X)*0.5;
96  Scalar c = (_C1X + _P1X)*0.5;
97  Scalar d = (a + b)*0.5;
98  Scalar e = (b + c)*0.5;
99  Scalar f = (d + e)*0.5; //this one is on the curve!
100 
101  //The curve point is close enough to our wanted atX
102  if (abs<Scalar>(f - _atX) < APPROXIMATION_EPSILON)
103  return clampTo01Interval<Scalar>((u + v)*0.5f);
104 
105  //dichotomy
106  if (f < _atX) {
107  _P0X = f;
108  _C0X = e;
109  _C1X = c;
110  u = (u + v)*0.5f;
111  } else {
112  _C0X = a; _C1X = d; _P1X = f; v = (u + v)*0.5f;
113  }
114 
115  iterationStep++;
116  }
117 
118  return clampTo01Interval<Scalar>((u + v)*0.5f);
119 }
120 
121 template<typename Scalar>
122 std::vector<Scalar> AnimationHelper::evaluateBezier(float at, std::vector<Scalar> _P0, std::vector<Scalar> _P1, std::vector<Scalar> _C0, std::vector<Scalar> _C1) {
123  unsigned int size = _P0.size();
124  assert(size == _P1.size() && size == _C0.size() && size == _C1.size());
125 
126  float s = at;
127  float sinv = (1-s);
128 
129  std::vector<Scalar> result;
130 
131  for (unsigned int i=0;i<size;++i) {
132  result.push_back( _P0[i]*sinv*sinv*sinv + 3*_C0[i]*s*sinv*sinv + 3*_C1[i]*s*s*sinv + _P1[i]*s*s*s );
133  }
134 
135  return result;
136 }
static float approximateCubicBezierParameter(Scalar _atX, Scalar _P0X, Scalar _P1X, Scalar _C0X, Scalar _C1X)
Approximates the parameter value for a Bezier curve to get a certain x value Does an iterative DeCast...
static std::vector< Scalar > evaluateBezier(float at, std::vector< Scalar > _P0, std::vector< Scalar > _P1, std::vector< Scalar > _C0, std::vector< Scalar > _C1)
Evaluates the cubic Bezier curve parameterized by P0, P1, C0 and C1 at the parameter value "at"...