src/geometry.cpp

Sun, 16 May 2021 22:41:00 +0300

author
Teemu Piippo <teemu@hecknology.net>
date
Sun, 16 May 2021 22:41:00 +0300
changeset 103
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parent 71
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child 115
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permissions
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update

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1 #include <glm/gtc/matrix_transform.hpp>
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2 #include "geometry.h"
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3
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4 /**
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5 * @brief Computes line-plane intersection
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6 * @param line
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7 * @param plane
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8 * @return point of intersection. Does not return a value if the line is in parallel to the plane.
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9 */
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10 std::optional<glm::vec3> geom::linePlaneIntersection(
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11 const geom::Line<3>& line,
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12 const geom::Plane& plane,
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13 const float epsilon)
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14 {
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15 const float denominator = glm::dot(line.direction, plane.normal);
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16 if (std::abs(denominator) < epsilon)
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17 {
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18 return {};
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19 }
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20 else
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21 {
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22 const float d = glm::dot(plane.anchor - line.anchor, plane.normal) / denominator;
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23 return line.anchor + d * line.direction;
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24 }
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25 }
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26
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27 /**
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28 * @brief Computes the plane of a triangle
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29 * @param triangle
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30 * @return plane
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31 */
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32 geom::Plane geom::planeFromTriangle(const geom::Triangle& triangle)
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33 {
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34 return geom::Plane{normalVector(triangle), triangle.points[0]};
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35 }
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36
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37 /**
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38 * @brief Computes the normal vector of a triangle
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39 * @param triangle
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40 * @return normal vector
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41 */
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42 glm::vec3 geom::normalVector(const geom::Triangle& triangle)
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43 {
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44 return glm::normalize(
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45 glm::cross(
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46 triangle.points[1] - triangle.points[0],
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47 triangle.points[2] - triangle.points[0]));
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48 }
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49
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50 /**
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51 * @brief Extracts the scaling component of the specified matrix into a vector and returns both the scaling
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52 * components as well as the unscaled matrix.
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53 * @param matrix Matrix to compute
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54 * @return scaling vector and unscaled matrix
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55 */
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56 geom::ScalingExtract geom::extractScaling(const glm::mat4& matrix)
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57 {
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58 geom::ScalingExtract result;
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59 result.scaling = geom::scalingVector(matrix);
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60 result.unscaled = glm::scale(matrix, 1.0f / result.scaling);
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61 return result;
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62 }
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63
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64 /**
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65 * @brief Computes the scaling vector, which contains the scaling of the specified matrix
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66 * @param matrix
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67 * @return scaling vector
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68 */
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69 glm::vec3 geom::scalingVector(const glm::mat4 matrix)
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70 {
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71 auto component = [](const glm::mat4& matrix, const int i) -> float
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72 {
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73 return std::hypot(std::hypot(matrix[i][0], matrix[i][1]), matrix[i][2]);
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74 };
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75 return glm::vec3{component(matrix, 0), component(matrix, 1), component(matrix, 2)};
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76 }
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77
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78 std::optional<glm::vec2> geom::lineLineIntersection(const Line<2>& line_1, const Line<2>& line_2)
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79 {
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80 const float denominator = (line_1.direction.x * line_2.direction.y) - (line_1.direction.y * line_2.direction.x);
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81 constexpr float epsilon = 1e-6f;
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82 if (std::abs(denominator) < epsilon)
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83 {
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84 return {};
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85 }
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86 else
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87 {
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88 const glm::vec2 p1 = line_1.anchor + line_1.direction;
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89 const glm::vec2& p2 = line_1.anchor;
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90 const glm::vec2 p3 = line_2.anchor + line_2.direction;
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91 const glm::vec2& p4 = line_2.anchor;
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92 const float a = glm::determinant(glm::mat2{{p1.x, p2.x}, {p1.y, p2.y}});
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93 const float b = glm::determinant(glm::mat2{{p3.x, p4.x}, {p3.y, p4.y}});
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94 const float c_x = glm::determinant(glm::mat2{{p1.x, p2.x}, {1, 1}});
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95 const float c_y = glm::determinant(glm::mat2{{p1.y, p2.y}, {1, 1}});
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96 const float d_x = glm::determinant(glm::mat2{{p3.x, p4.x}, {1, 1}});
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97 const float d_y = glm::determinant(glm::mat2{{p3.y, p4.y}, {1, 1}});
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98 const float x = glm::determinant(glm::mat2{{a, b}, {c_x, d_x}});
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99 const float y = glm::determinant(glm::mat2{{a, b}, {c_y, d_y}});
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100 return glm::vec2{x / denominator, y / denominator};
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101 }
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102 }
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103
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104 std::optional<glm::vec2> geom::rayLineSegmentIntersection(const Ray<2>& ray, const LineSegment2D& line)
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105 {
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106 std::optional<glm::vec2> result = lineLineIntersection(rayToLine(ray), lineFromPoints(line.points[0], line.points[1]));
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107 if (result.has_value())
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108 {
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109 const float d1 = glm::dot(*result - ray.anchor, ray.direction);
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110 if (d1 < 0)
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111 {
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112 result.reset();
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113 }
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114 else
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115 {
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116 const float d2 = glm::dot(*result - line.points[0], *result - line.points[1]);
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117 if (d2 > 0)
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118 {
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119 result.reset();
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120 }
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121 }
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122 }
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123 return result;
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124 }
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125
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126 std::optional<geom::PointOnRectagle> geom::rayRectangleIntersection(const Ray<2>& ray, const QRectF& rectangle)
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127 {
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128 std::optional<glm::vec2> position;
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129 std::optional<PointOnRectagle> result;
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130 // Try top
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131 position = rayLineSegmentIntersection(ray, top(rectangle));
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132 if (position.has_value())
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133 {
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134 result = {*position, RectangleSide::Top};
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135 }
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136 else
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137 {
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138 // Try bottom
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139 position = rayLineSegmentIntersection(ray, bottom(rectangle));
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140 if (position.has_value())
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141 {
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142 result = {*position, RectangleSide::Bottom};
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143 }
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144 else
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145 {
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146 // Try left
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147 position = rayLineSegmentIntersection(ray, left(rectangle));
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148 if (position.has_value())
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149 {
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150 result = {*position, RectangleSide::Left};
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151 }
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152 else
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153 {
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154 // Try right
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155 position = rayLineSegmentIntersection(ray, right(rectangle));
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156 if (position.has_value())
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157 {
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158 result = {*position, RectangleSide::Right};
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159 }
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160 }
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161 }
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162 }
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163 return result;
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164 }
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165
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166 geom::LineSegment2D geom::top(const QRectF& rectangle)
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167 {
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168 return {
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169 glm::vec2{rectangle.left(), rectangle.top()},
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170 glm::vec2{rectangle.right(), rectangle.top()}
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171 };
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172 }
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173
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174 geom::LineSegment2D geom::bottom(const QRectF& rectangle)
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175 {
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176 return {
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177 glm::vec2{rectangle.left(), rectangle.bottom()},
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178 glm::vec2{rectangle.right(), rectangle.bottom()}
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179 };
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180 }
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181
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182 geom::LineSegment2D geom::left(const QRectF& rectangle)
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183 {
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184 return {
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185 glm::vec2{rectangle.left(), rectangle.top()},
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186 glm::vec2{rectangle.left(), rectangle.bottom()}
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187 };
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188 }
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189
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190 geom::LineSegment2D geom::right(const QRectF& rectangle)
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191 {
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192 return {
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193 glm::vec2{rectangle.right(), rectangle.top()},
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194 glm::vec2{rectangle.right(), rectangle.bottom()}
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195 };
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196 }

mercurial