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// // Copyright 2020 Olzhas Zhumabek // // Use, modification and distribution are subject to the Boost Software License, // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // #ifndef BOOST_GIL_EXTENSION_RASTERIZATION_CIRCLE_HPP #define BOOST_GIL_EXTENSION_RASTERIZATION_CIRCLE_HPP #include #include #include #include #include #include namespace boost { namespace gil { struct circle_rasterizer_t{}; /// \defgroup CircleRasterization /// \ingroup Rasterization /// \brief Circle rasterization algorithms /// /// The main problems are connectivity and equation following. Circle can be easily moved /// to new offset, and rotation has no effect on it (not recommended to do rotation). /// \ingroup CircleRasterization /// \brief Rasterize trigonometric circle according to radius by sine and radius by cosine /// /// This rasterizer is the one used that is used in standard Hough circle transform in /// the books. It is also quite expensive to compute. /// WARNING: the product of this rasterizer does not follow circle equation, even though it /// produces quite round like shapes. struct trigonometric_circle_rasterizer { using type = circle_rasterizer_t; /// \brief Creates a trigonometric circle rasterizer /// \param center_point - Point containing positive integer x co-ordinate and y co-ordinate of the /// center respectively. /// \param circle_radius - Radius of the circle trigonometric_circle_rasterizer(point_t center_point, std::ptrdiff_t circle_radius) : center(center_point), radius(circle_radius) {} /// \brief Calculates minimum angle step that is distinguishable when walking on circle /// /// It is important to not have disconnected circle and to not compute unnecessarily, /// thus the result of this function is used when rendering. double minimum_angle_step() const noexcept { const auto diameter = radius * 2 - 1; return std::atan2(1.0, diameter); } /// \brief Calculate the amount of points that rasterizer will output std::ptrdiff_t point_count() const noexcept { return 8 * static_cast( std::round(detail::pi / 4 / minimum_angle_step()) + 1); } /// \brief perform rasterization and output into d_first template void operator()(OutputIterator d_first) const { const double minimum_angle_step = std::atan2(1.0, radius); auto translate_mirror_points = [this, &d_first](point_t p) { *d_first++ = point_t{center.x + p.x, center.y + p.y}; *d_first++ = point_t{center.x + p.x, center.y - p.y}; *d_first++ = point_t{center.x - p.x, center.y + p.y}; *d_first++ = point_t{center.x - p.x, center.y - p.y}; *d_first++ = point_t{center.x + p.y, center.y + p.x}; *d_first++ = point_t{center.x + p.y, center.y - p.x}; *d_first++ = point_t{center.x - p.y, center.y + p.x}; *d_first++ = point_t{center.x - p.y, center.y - p.x}; }; const std::ptrdiff_t iteration_count = point_count() / 8; double angle = 0; // do note that + 1 was done inside count estimation, thus <= is not needed, only < for (std::ptrdiff_t i = 0; i < iteration_count; ++i, angle += minimum_angle_step) { std::ptrdiff_t x = static_cast(std::round(radius * std::cos(angle))); std::ptrdiff_t y = static_cast(std::round(radius * std::sin(angle))); translate_mirror_points({x, y}); } } point_t center; std::ptrdiff_t radius; }; /// \ingroup CircleRasterization /// \brief Perform circle rasterization according to Midpoint algorithm /// /// This algorithm givess reasonable output and is cheap to compute. /// reference: /// https://en.wikipedia.org/wiki/Midpoint_circle_algorithm struct midpoint_circle_rasterizer { using type = circle_rasterizer_t; /// \brief Creates a midpoint circle rasterizer /// \param center_point - Point containing positive integer x co-ordinate and y co-ordinate of the /// center respectively. /// \param circle_radius - Radius of the circle midpoint_circle_rasterizer(point_t center_point, std::ptrdiff_t circle_radius) : center(center_point), radius(circle_radius) {} /// \brief Calculate the amount of points that rasterizer will output std::ptrdiff_t point_count() const noexcept { // the reason for pulling 8 out is so that when the expression radius * cos(45 degrees) // is used, it would yield the same result as here // + 1 at the end is because the point at radius itself is computed as well return 8 * static_cast( std::round(radius * std::cos(boost::gil::detail::pi / 4)) + 1); } /// \brief perform rasterization and output into d_first template void operator()(OutputIterator d_first) const { auto translate_mirror_points = [this, &d_first](point_t p) { *d_first++ = point_t{center.x + p.x, center.y + p.y}; *d_first++ = point_t{center.x + p.x, center.y - p.y}; *d_first++ = point_t{center.x - p.x, center.y + p.y}; *d_first++ = point_t{center.x - p.x, center.y - p.y}; *d_first++ = point_t{center.x + p.y, center.y + p.x}; *d_first++ = point_t{center.x + p.y, center.y - p.x}; *d_first++ = point_t{center.x - p.y, center.y + p.x}; *d_first++ = point_t{center.x - p.y, center.y - p.x}; }; std::ptrdiff_t iteration_distance = point_count() / 8; std::ptrdiff_t y_current = radius; std::ptrdiff_t r_squared = radius * radius; translate_mirror_points({0, y_current}); for (std::ptrdiff_t x = 1; x < iteration_distance; ++x) { std::ptrdiff_t midpoint = x * x + y_current * y_current - y_current - r_squared; if (midpoint > 0) { --y_current; } translate_mirror_points({x, y_current}); } } point_t center; std::ptrdiff_t radius; }; namespace detail { template struct apply_rasterizer_op { void operator()( View const& view, Rasterizer const& rasterizer, Pixel const& pixel) { std::vector trajectory(rasterizer.point_count()); rasterizer(std::begin(trajectory)); for (auto const& point : trajectory) { view(point) = pixel; } } }; } //namespace detail }} // namespace boost::gil #endif