1 | // |
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2 | // You received this file as part of RRLib |
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3 | // Robotics Research Library |
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4 | // |
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5 | // Copyright (C) Finroc GbR (finroc.org) |
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6 | // |
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7 | // This program is free software; you can redistribute it and/or |
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8 | // modify it under the terms of the GNU General Public License |
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9 | // as published by the Free Software Foundation; either version 2 |
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10 | // of the License, or (at your option) any later version. |
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11 | // |
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12 | // This program is distributed in the hope that it will be useful, |
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13 | // but WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 | // GNU General Public License for more details. |
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16 | // |
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17 | // You should have received a copy of the GNU General Public License |
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18 | // along with this program; if not, write to the Free Software |
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19 | // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 | // |
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21 | //---------------------------------------------------------------------- |
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22 | /*!\file tBezierCurve.hpp |
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23 | * |
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24 | * \author Tobias Foehst |
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25 | * |
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26 | * \date 2009-05-25 |
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27 | * |
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28 | */ |
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29 | //---------------------------------------------------------------------- |
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30 | |
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31 | //---------------------------------------------------------------------- |
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32 | // External includes (system with <>, local with "") |
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33 | //---------------------------------------------------------------------- |
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34 | #include "rrlib/util/variadic_templates.h" |
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35 | |
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36 | //---------------------------------------------------------------------- |
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37 | // Internal includes with "" |
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38 | //---------------------------------------------------------------------- |
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39 | |
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40 | //---------------------------------------------------------------------- |
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41 | // Debugging |
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42 | //---------------------------------------------------------------------- |
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43 | #include <cassert> |
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44 | |
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45 | //---------------------------------------------------------------------- |
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46 | // Namespace declaration |
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47 | //---------------------------------------------------------------------- |
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48 | namespace rrlib |
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49 | { |
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50 | namespace geometry |
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51 | { |
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52 | |
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53 | //---------------------------------------------------------------------- |
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54 | // Forward declarations / typedefs / enums |
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55 | //---------------------------------------------------------------------- |
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56 | |
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57 | //---------------------------------------------------------------------- |
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58 | // Const values |
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59 | //---------------------------------------------------------------------- |
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60 | |
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61 | //---------------------------------------------------------------------- |
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62 | // Implementation |
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63 | //---------------------------------------------------------------------- |
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64 | |
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65 | //---------------------------------------------------------------------- |
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66 | // tBezierCurve constructors |
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67 | //---------------------------------------------------------------------- |
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68 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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69 | tBezierCurve<Tdimension, TElement, Tdegree>::tBezierCurve() |
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70 | { |
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71 | static_assert(Tdegree > 0, "The degree of Bezier curves must be greater than zero"); |
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72 | memset(this->control_points, 0, sizeof(this->control_points)); |
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73 | } |
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74 | |
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75 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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76 | template <typename TIterator> |
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77 | tBezierCurve<Tdimension, TElement, Tdegree>::tBezierCurve(TIterator begin, TIterator end) |
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78 | { |
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79 | static_assert(Tdegree > 0, "The degree of Bezier curves must be greater than zero"); |
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80 | assert(static_cast<size_t>(std::distance(begin, end)) == this->NumberOfControlPoints() && "A Bezier curve must have degree + 1 control points"); |
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81 | size_t index = 0; |
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82 | for (TIterator it = begin; it != end; ++it) |
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83 | { |
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84 | this->control_points[index++] = *it; |
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85 | } |
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86 | } |
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87 | |
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88 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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89 | template <typename ... TPoints> |
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90 | tBezierCurve<Tdimension, TElement, Tdegree>::tBezierCurve(const typename tShape::tPoint &p1, const typename tShape::tPoint &p2, const TPoints &... rest) |
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91 | { |
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92 | static_assert(Tdegree > 0, "The degree of Bezier curves must be greater than zero"); |
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93 | static_assert(sizeof...(rest) + 1 == Tdegree, "A Bezier curve must have degree + 1 control points"); |
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94 | size_t index = 0; |
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95 | util::ProcessVariadicValues<typename tShape::tPoint>([this, index](const typename tShape::tPoint & x) mutable { this->control_points[index++] = x; }, p1, p2, rest...); |
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96 | } |
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97 | |
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98 | //---------------------------------------------------------------------- |
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99 | // tBezierCurve SetControlPoint |
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100 | //---------------------------------------------------------------------- |
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101 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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102 | void tBezierCurve<Tdimension, TElement, Tdegree>::SetControlPoint(size_t i, const typename tShape::tPoint &point) |
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103 | { |
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104 | assert(i < this->NumberOfControlPoints()); |
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105 | this->control_points[i] = point; |
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106 | this->SetChanged(); |
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107 | }; |
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108 | |
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109 | //---------------------------------------------------------------------- |
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110 | // tBezierCurve GetTwist |
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111 | //---------------------------------------------------------------------- |
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112 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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113 | const TElement tBezierCurve<Tdimension, TElement, Tdegree>::GetTwist() const |
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114 | { |
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115 | TElement twist = 0.0; |
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116 | for (size_t i = 0; i < Tdegree - 1; ++i) |
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117 | { |
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118 | twist = std::max(twist, ((this->control_points[i + 2] - this->control_points[i + 1]) - (this->control_points[i + 1] - this->control_points[i])).Length()); |
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119 | } |
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120 | return Tdegree * (Tdegree - 1) * twist; |
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121 | } |
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122 | |
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123 | //---------------------------------------------------------------------- |
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124 | // tBezierCurve GetSubdivision |
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125 | //---------------------------------------------------------------------- |
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126 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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127 | const typename tBezierCurve<Tdimension, TElement, Tdegree>::tSubdivision tBezierCurve<Tdimension, TElement, Tdegree>::GetSubdivision() const |
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128 | { |
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129 | typename tShape::tPoint left_half[this->NumberOfControlPoints()]; |
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130 | typename tShape::tPoint right_half[this->NumberOfControlPoints()]; |
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131 | typename tShape::tPoint temp_points[this->NumberOfControlPoints()]; |
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132 | std::memcpy(temp_points, this->control_points, this->NumberOfControlPoints() * sizeof(typename tShape::tPoint)); |
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133 | |
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134 | left_half[0] = temp_points[0]; |
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135 | right_half[Tdegree] = temp_points[Tdegree]; |
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136 | |
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137 | size_t k = 0; |
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138 | while (k < Tdegree) |
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139 | { |
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140 | for (size_t i = 0; i < Tdegree - k; ++i) |
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141 | { |
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142 | temp_points[i] = (temp_points[i] + temp_points[i + 1]) * 0.5; |
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143 | } |
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144 | ++k; |
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145 | left_half[k] = temp_points[0]; |
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146 | right_half[Tdegree - k] = temp_points[Tdegree - k]; |
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147 | } |
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148 | |
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149 | return std::make_pair(tBezierCurve(left_half, left_half + this->NumberOfControlPoints()), tBezierCurve(right_half, right_half + this->NumberOfControlPoints())); |
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150 | } |
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151 | |
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152 | //---------------------------------------------------------------------- |
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153 | // tBezierCurve Evaluation: operator () |
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154 | //---------------------------------------------------------------------- |
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155 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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156 | const typename tShape<Tdimension, TElement>::tPoint tBezierCurve<Tdimension, TElement, Tdegree>::operator()(tParameter t) const |
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157 | { |
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158 | assert((0.0 <= t) && (t <= 1.0)); |
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159 | |
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160 | typename tShape::tPoint temp_points[this->NumberOfControlPoints()]; |
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161 | std::memcpy(temp_points, this->control_points, (this->NumberOfControlPoints()) * sizeof(typename tShape::tPoint)); |
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162 | |
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163 | size_t k = 0; |
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164 | while (k < Tdegree) |
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165 | { |
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166 | for (size_t i = 0; i < Tdegree - k; ++i) |
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167 | { |
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168 | temp_points[i] = ((1.0 - t) * temp_points[i]) + (t * temp_points[i + 1]); |
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169 | } |
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170 | ++k; |
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171 | } |
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172 | |
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173 | return temp_points[0]; |
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174 | } |
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175 | |
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176 | //---------------------------------------------------------------------- |
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177 | // tBezierCurve GetDerivative |
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178 | //---------------------------------------------------------------------- |
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179 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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180 | const typename tBezierCurve<Tdimension, TElement, Tdegree>::tDerivative tBezierCurve<Tdimension, TElement, Tdegree>::GetDerivative() const |
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181 | { |
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182 | typename tShape::tPoint temp[Tdegree]; |
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183 | for (size_t i = 0; i < Tdegree; ++i) |
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184 | { |
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185 | temp[i] = Tdegree * (this->control_points[i + 1] - this->control_points[i]); |
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186 | } |
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187 | return tDerivative(temp, temp + Tdegree); |
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188 | } |
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189 | |
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190 | //---------------------------------------------------------------------- |
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191 | // tBezierCurve GetIntersections |
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192 | //---------------------------------------------------------------------- |
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193 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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194 | template <unsigned int Tother_degree> |
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195 | const bool tBezierCurve<Tdimension, TElement, Tdegree>::GetIntersections(std::vector<typename tShape::tPoint> &intersection_points, std::vector<tParameter> &intersection_parameters, |
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196 | const tBezierCurve<Tdimension, TElement, Tother_degree> &other) const |
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197 | { |
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198 | return this->GetIntersections(intersection_points, intersection_parameters, other, 0.0, 1.0); |
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199 | } |
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200 | |
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201 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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202 | const bool tBezierCurve<Tdimension, TElement, Tdegree>::GetIntersections(std::vector<typename tShape::tPoint> &intersection_points, std::vector<tParameter> &intersection_parameters, |
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203 | const tLine<Tdimension, TElement> &line) const |
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204 | { |
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205 | return this->GetIntersections(intersection_points, intersection_parameters, line, 0.0, 1.0); |
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206 | } |
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207 | |
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208 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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209 | template <unsigned int Tother_degree> |
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210 | const bool tBezierCurve<Tdimension, TElement, Tdegree>::GetIntersections(std::vector<typename tShape::tPoint> &intersection_points, std::vector<tParameter> &intersection_parameters, |
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211 | const tBezierCurve<Tdimension, TElement, Tother_degree> &other, |
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212 | tParameter min_parameter, tParameter max_parameter) const |
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213 | { |
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214 | // check if bounding boxes intersect |
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215 | if (!this->BoundingBox().Intersects(other.BoundingBox())) |
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216 | { |
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217 | return false; |
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218 | } |
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219 | |
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220 | // subdivide curve with greater twist if necessary |
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221 | TElement own_twist = this->GetTwist(); |
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222 | TElement other_twist = other.GetTwist(); |
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223 | |
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224 | if (own_twist > other_twist && !math::IsEqual(own_twist, 0)) |
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225 | { |
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226 | tSubdivision subdivision(this->GetSubdivision()); |
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227 | tParameter middle_parameter(0.5 * (min_parameter + max_parameter)); |
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228 | bool result = false; |
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229 | result |= subdivision.first.GetIntersections(intersection_points, intersection_parameters, other, min_parameter, middle_parameter); |
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230 | result |= subdivision.second.GetIntersections(intersection_points, intersection_parameters, other, middle_parameter, max_parameter); |
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231 | return result; |
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232 | } |
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233 | else if (!math::IsEqual(other_twist, 0)) |
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234 | { |
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235 | tSubdivision subdivision(other.GetSubdivision()); |
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236 | bool result = false; |
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237 | result |= this->GetIntersections(intersection_points, intersection_parameters, subdivision.first, min_parameter, max_parameter); |
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238 | result |= this->GetIntersections(intersection_points, intersection_parameters, subdivision.second, min_parameter, max_parameter); |
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239 | return result; |
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240 | } |
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241 | |
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242 | // compute the intersection using the baselines of the two control polygons |
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243 | tLine<Tdimension, TElement> own_line_segment(this->control_points[0], this->control_points[Tdegree]); |
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244 | tLine<Tdimension, TElement> other_line_segment(other.ControlPoints()[0], other.ControlPoints()[Tother_degree]); |
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245 | typename tShape::tPoint intersection_point; |
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246 | if (own_line_segment.GetIntersection(intersection_point, other_line_segment) && !math::IsEqual(intersection_point, intersection_points.back(), 0.001)) |
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247 | { |
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248 | intersection_points.push_back(intersection_point); |
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249 | const tParameter baseline_parameter((intersection_points.back() - this->control_points[0]).Length() / (this->control_points[Tdegree] - this->control_points[0]).Length()); |
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250 | assert(!isnan(baseline_parameter)); |
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251 | intersection_parameters.push_back(min_parameter + (max_parameter - min_parameter) * baseline_parameter); |
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252 | return true; |
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253 | } |
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254 | return false; |
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255 | } |
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256 | |
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257 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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258 | const bool tBezierCurve<Tdimension, TElement, Tdegree>::GetIntersections(std::vector<typename tShape::tPoint> &intersection_points, std::vector<tParameter> &intersection_parameters, |
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259 | const tLine<Tdimension, TElement> &line, |
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260 | tParameter min_parameter, tParameter max_parameter) const |
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261 | { |
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262 | // check if intersection with line is possible |
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263 | typename tShape::tPoint center_of_bounding_box(math::tVector<Tdimension, TElement>(0.5 * (this->BoundingBox().Min() + this->BoundingBox().Max()))); |
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264 | double radius_of_bounding_sphere = 0.5 * (this->BoundingBox().Max() - this->BoundingBox().Min()).Length(); |
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265 | if (line.GetDistanceToPoint(center_of_bounding_box) > radius_of_bounding_sphere) |
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266 | { |
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267 | return false; |
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268 | } |
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269 | |
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270 | // subdivide curve if necessary |
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271 | if (!math::IsEqual(this->GetTwist(), 0)) |
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272 | { |
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273 | tSubdivision subdivision(this->GetSubdivision()); |
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274 | tParameter middle_parameter(0.5 * (min_parameter + max_parameter)); |
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275 | bool result = false; |
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276 | result |= subdivision.first.GetIntersections(intersection_points, intersection_parameters, line, min_parameter, middle_parameter); |
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277 | result |= subdivision.second.GetIntersections(intersection_points, intersection_parameters, line, middle_parameter, max_parameter); |
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278 | return result; |
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279 | } |
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280 | |
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281 | // compute the intersection using the baseline of the control polygon |
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282 | tLineSegment<Tdimension, TElement> own_line_segment(this->control_points[0], this->control_points[Tdegree]); |
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283 | typename tShape::tPoint intersection_point; |
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284 | if (own_line_segment.GetIntersection(intersection_point, line)) |
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285 | { |
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286 | intersection_points.push_back(intersection_point); |
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287 | const tParameter baseline_parameter((intersection_points.back() - this->control_points[0]).Length() / (this->control_points[Tdegree] - this->control_points[0]).Length()); |
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288 | assert(!isnan(baseline_parameter)); |
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289 | intersection_parameters.push_back(min_parameter + (max_parameter - min_parameter) * baseline_parameter); |
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290 | return true; |
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291 | } |
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292 | return false; |
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293 | } |
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294 | |
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295 | //---------------------------------------------------------------------- |
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296 | // tBezierCurve GetClosestPoint |
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297 | //---------------------------------------------------------------------- |
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298 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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299 | const typename tShape<Tdimension, TElement>::tPoint tBezierCurve<Tdimension, TElement, Tdegree>::GetClosestPoint(const typename tShape::tPoint &reference_point) const |
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300 | { |
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301 | tSubdivision subdivision(this->GetSubdivision()); |
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302 | |
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303 | double squared_distance_to_first_candidate = std::numeric_limits<double>::max(); |
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304 | double squared_distance_to_second_candidate = std::numeric_limits<double>::max(); |
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305 | |
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306 | for (unsigned int i = 0; i < Tdegree; ++i) |
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307 | { |
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308 | tLineSegment<Tdimension, TElement> first_segment_base_line(subdivision.first.ControlPoints()[i], subdivision.first.ControlPoints()[i + 1]); |
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309 | tLineSegment<Tdimension, TElement> second_segment_base_line(subdivision.second.ControlPoints()[i], subdivision.second.ControlPoints()[i + 1]); |
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310 | |
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311 | typename tShape::tPoint first_candidate = first_segment_base_line.GetClosestPoint(reference_point); |
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312 | typename tShape::tPoint second_candidate = second_segment_base_line.GetClosestPoint(reference_point); |
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313 | |
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314 | double squared_distance_to_first = (reference_point - first_candidate).SquaredLength(); |
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315 | double squared_distance_to_second = (reference_point - second_candidate).SquaredLength(); |
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316 | |
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317 | if (squared_distance_to_first < squared_distance_to_first_candidate) |
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318 | { |
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319 | squared_distance_to_first_candidate = squared_distance_to_first; |
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320 | } |
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321 | |
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322 | if (squared_distance_to_second < squared_distance_to_second_candidate) |
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323 | { |
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324 | squared_distance_to_second_candidate = squared_distance_to_second; |
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325 | } |
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326 | } |
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327 | |
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328 | if (squared_distance_to_first_candidate < squared_distance_to_second_candidate) |
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329 | { |
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330 | if (subdivision.first.GetTwist() < 1E-6) |
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331 | { |
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332 | tLineSegment<Tdimension, TElement> first_segment_base_line(subdivision.first.ControlPoints()[0], subdivision.first.ControlPoints()[Tdegree]); |
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333 | return first_segment_base_line.GetClosestPoint(reference_point); |
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334 | } |
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335 | return subdivision.first.GetClosestPoint(reference_point); |
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336 | } |
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337 | |
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338 | if (subdivision.second.GetTwist() < 1E-6) |
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339 | { |
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340 | tLineSegment<Tdimension, TElement> second_segment_base_line(subdivision.second.ControlPoints()[0], subdivision.second.ControlPoints()[Tdegree]); |
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341 | return second_segment_base_line.GetClosestPoint(reference_point); |
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342 | } |
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343 | return subdivision.second.GetClosestPoint(reference_point); |
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344 | } |
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345 | |
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346 | //---------------------------------------------------------------------- |
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347 | // tBezierCurve Translate |
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348 | //---------------------------------------------------------------------- |
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349 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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350 | tBezierCurve<Tdimension, TElement, Tdegree> &tBezierCurve<Tdimension, TElement, Tdegree>::Translate(const math::tVector<Tdimension, TElement> &translation) |
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351 | { |
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352 | for (size_t i = 0; i < this->NumberOfControlPoints(); ++i) |
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353 | { |
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354 | this->control_points[i] += translation; |
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355 | } |
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356 | this->SetChanged(); |
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357 | return *this; |
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358 | } |
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359 | |
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360 | //---------------------------------------------------------------------- |
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361 | // tBezierCurve Rotate |
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362 | //---------------------------------------------------------------------- |
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363 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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364 | tBezierCurve<Tdimension, TElement, Tdegree> &tBezierCurve<Tdimension, TElement, Tdegree>::Rotate(const math::tMatrix<Tdimension, Tdimension, TElement> &rotation) |
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365 | { |
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366 | for (size_t i = 0; i < this->NumberOfControlPoints(); ++i) |
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367 | { |
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368 | this->control_points[i] = rotation * this->control_points[i]; |
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369 | } |
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370 | this->SetChanged(); |
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371 | return *this; |
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372 | } |
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373 | |
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374 | //---------------------------------------------------------------------- |
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375 | // tBezierCurve Transform |
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376 | //---------------------------------------------------------------------- |
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377 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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378 | tBezierCurve<Tdimension, TElement, Tdegree> &tBezierCurve<Tdimension, TElement, Tdegree>::Transform(const math::tMatrix < Tdimension + 1, Tdimension + 1, TElement > &transformation) |
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379 | { |
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380 | #ifndef NDEBUG |
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381 | for (size_t i = 0; i < Tdimension; ++i) |
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382 | { |
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383 | assert(math::IsEqual(transformation[Tdimension][i], 0)); |
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384 | } |
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385 | assert(math::IsEqual(transformation[Tdimension][Tdimension], 1)); |
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386 | math::tMatrix<Tdimension, Tdimension, TElement> rotation; |
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387 | for (size_t row = 0; row < Tdimension; ++row) |
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388 | { |
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389 | for (size_t column = 0; column < Tdimension; ++column) |
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390 | { |
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391 | rotation[row][column] = transformation[row][column]; |
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392 | } |
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393 | } |
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394 | assert(math::IsEqual(rotation.Determinant(), 1)); |
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395 | #endif |
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396 | |
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397 | for (size_t i = 0; i < this->NumberOfControlPoints(); ++i) |
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398 | { |
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399 | this->control_points[i] = transformation.MultiplyHomogeneously(this->control_points[i]); |
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400 | } |
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401 | this->SetChanged(); |
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402 | return *this; |
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403 | } |
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404 | |
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405 | //---------------------------------------------------------------------- |
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406 | // tBezierCurve UpdateBoundingBox |
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407 | //---------------------------------------------------------------------- |
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408 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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409 | void tBezierCurve<Tdimension, TElement, Tdegree>::UpdateBoundingBox(typename tShape::tBoundingBox &bounding_box) const |
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410 | { |
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411 | for (size_t i = 0; i < this->NumberOfControlPoints(); ++i) |
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412 | { |
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413 | bounding_box.Add(this->control_points[i]); |
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414 | } |
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415 | } |
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416 | |
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417 | //---------------------------------------------------------------------- |
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418 | // tBezierCurve UpdateCenterOfGravity |
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419 | //---------------------------------------------------------------------- |
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420 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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421 | void tBezierCurve<Tdimension, TElement, Tdegree>::UpdateCenterOfGravity(typename tShape::tPoint ¢er_of_gravity) const |
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422 | { |
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423 | for (size_t i = 0; i < this->NumberOfControlPoints(); ++i) |
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424 | { |
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425 | center_of_gravity += this->control_points[i]; |
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426 | } |
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427 | center_of_gravity /= this->NumberOfControlPoints(); |
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428 | } |
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429 | |
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430 | //---------------------------------------------------------------------- |
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431 | // Operators for rrlib_canvas |
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432 | //---------------------------------------------------------------------- |
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433 | #ifdef _LIB_RRLIB_CANVAS_PRESENT_ |
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434 | |
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435 | template <typename TElement, unsigned int Tdegree> |
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436 | canvas::tCanvas2D &operator << (canvas::tCanvas2D &canvas, const tBezierCurve<2, TElement, Tdegree> &bezier_curve) |
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437 | { |
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438 | canvas.DrawBezierCurve(bezier_curve.ControlPoints(), bezier_curve.ControlPoints() + bezier_curve.NumberOfControlPoints()); |
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439 | |
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440 | return canvas; |
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441 | } |
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442 | |
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443 | #endif |
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444 | |
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445 | //---------------------------------------------------------------------- |
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446 | // Operators for rrlib_serialization |
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447 | //---------------------------------------------------------------------- |
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448 | #ifdef _LIB_RRLIB_SERIALIZATION_PRESENT_ |
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449 | |
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450 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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451 | serialization::tOutputStream &operator << (serialization::tOutputStream &stream, const tBezierCurve<Tdimension, TElement, Tdegree> &curve) |
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452 | { |
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453 | for (size_t i = 0; i < curve.NumberOfControlPoints(); ++i) |
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454 | { |
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455 | stream << curve.ControlPoints()[i]; |
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456 | } |
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457 | return stream; |
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458 | } |
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459 | |
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460 | template <size_t Tdimension, typename TElement, unsigned int Tdegree> |
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461 | serialization::tInputStream &operator >> (serialization::tInputStream &stream, tBezierCurve<Tdimension, TElement, Tdegree> &curve) |
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462 | { |
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463 | for (size_t i = 0; i < curve.NumberOfControlPoints(); ++i) |
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464 | { |
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465 | typename tBezierCurve<Tdimension, TElement, Tdegree>::tPoint control_point; |
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466 | stream >> control_point; |
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467 | curve.SetControlPoint(i, control_point); |
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468 | } |
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469 | return stream; |
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470 | } |
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471 | |
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472 | #endif |
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473 | |
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474 | //---------------------------------------------------------------------- |
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475 | // End of namespace declaration |
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476 | //---------------------------------------------------------------------- |
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477 | } |
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478 | } |
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