50 lines
1.2 KiB
C++
50 lines
1.2 KiB
C++
#pragma once
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#include "autoopt/quadric.hpp"
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namespace autoopt {
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template <typename T>
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struct ellipse {
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T left_arm;
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T right_arm;
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T entrance_angle;
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constexpr quadric<T> to_quadric() const {
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T a = (left_arm + right_arm) / T{2};
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T a2 = a * a;
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T left_x = -left_arm * std::cos(entrance_angle);
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T left_y = left_arm * std::sin(entrance_angle);
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T right_x = right_arm * std::cos(entrance_angle);
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T right_y = right_arm * std::sin(entrance_angle);
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T c_x = (left_x + right_x) / T{2};
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T c_y = (left_y + right_y) / T{2};
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T c2 = (left_x - c_x) * (left_x - c_x) + (left_y - c_y) * (left_y - c_y);
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T b2 = a2 - c2;
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// source: https://en.wikipedia.org/wiki/Ellipse#General_ellipse
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T theta = std::atan2(right_y - left_y, right_x - left_x);
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T cos_t = std::cos(theta);
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T sin_t = std::sin(theta);
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T cos_t2 = cos_t * cos_t;
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T sin_t2 = sin_t * sin_t;
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T sico_t = sin_t * cos_t;
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T A = a2 * sin_t2 + b2 * cos_t2;
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T B = T{2} * (b2 - a2) * sico_t;
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T C = a2 * cos_t2 + b2 * sin_t2;
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T D = -T{2} * A * c_x - B * c_y;
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T E = -B * c_x - T{2} * C * c_y;
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T F = A * c_x * c_x + B * c_x * c_y + C * c_y * c_y - a2 * b2;
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return quadric<T>(A, B, C, D, E, F);
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}
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};
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} // namespace autoopt
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