#include <polynomial_solver.hpp>
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| auto | solveLinearEquation (const double a, const double b, const double min_value=0, const double max_value=1) const -> std::vector< double > |
| | solve linear equation a*x + b = 0 More...
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| auto | solveQuadraticEquation (const double a, const double b, const double c, const double min_value=0, const double max_value=1) const -> std::vector< double > |
| | solve quadratic equation a*x^2 + b*x + c = 0 More...
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| auto | solveCubicEquation (const double a, const double b, const double c, const double d, const double min_value=0, const double max_value=1) const -> std::vector< double > |
| | solve cubic function a*t^3 + b*t^2 + c*t + d = 0 More...
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| auto | linear (const double a, const double b, const double t) const -> double |
| | calculate result of linear function a*t + b More...
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| auto | quadratic (const double a, const double b, const double c, const double t) const -> double |
| | calculate result of quadratic function a*t^2 + b*t + c More...
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| auto | cubic (const double a, const double b, const double c, const double d, const double t) const -> double |
| | calculate result of cubic function a*t^3 + b*t^2 + c*t + d More...
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| constexpr static double | tolerance = 1e-7 |
| | Hard coded parameter, tolerance of calculation results of the PolynomialSolver. This value was determined by Masaya Kataoka (@hakuturu583). The reason this value is not std::numeric_limits<double>::epsilon is that when using this set of functions to find the intersection of a Catmull-Rom spline curve and a line segment, it was confirmed that when the solution is very close to the endpoints of the Hermite curves that make up the Catmull-Rom spline, the solution could not calculated. When considering a 1 km long Catmull-Rom spline (assuming a very long lanelet) with a tolerance of 1e-7, the error in calculating the intersection position in a tangentially distorted coordinate system was ±0.0001 m. This value is sufficiently small that it was tentatively determined to be 1e-7. More...
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◆ cubic()
| auto math::geometry::PolynomialSolver::cubic |
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const double |
a, |
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const double |
b, |
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const double |
c, |
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const double |
d, |
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const double |
t |
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| const -> double |
calculate result of cubic function a*t^3 + b*t^2 + c*t + d
- Parameters
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- Returns
- double result of cubic function
◆ linear()
| auto math::geometry::PolynomialSolver::linear |
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const double |
a, |
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const double |
b, |
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const double |
t |
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| const -> double |
calculate result of linear function a*t + b
- Parameters
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- Returns
- double result of linear function
◆ quadratic()
| auto math::geometry::PolynomialSolver::quadratic |
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const double |
a, |
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const double |
b, |
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const double |
c, |
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const double |
t |
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| const -> double |
calculate result of quadratic function a*t^2 + b*t + c
- Parameters
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- Returns
- double result of quadratic function
◆ solveCubicEquation()
| auto math::geometry::PolynomialSolver::solveCubicEquation |
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const double |
a, |
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const double |
b, |
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const double |
c, |
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const double |
d, |
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const double |
min_value = 0, |
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const double |
max_value = 1 |
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| const -> std::vector<double> |
solve cubic function a*t^3 + b*t^2 + c*t + d = 0
- Parameters
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- Returns
- std::vector<double> real solution of the cubic functions (from min_value to max_value)
- Note
- Function that takes a complex number as input and returns the real part if it is a real number (imaginary part is 0) or std::nullopt if it is an imaginary or complex number.
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Iterate all complex values and check the value is real value or not.
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Function that takes a std::vector of complex numbers and selects only real numbers from it and returns them
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Finds the complex solution of the monic cubic equation and returns only those that are real numbers.
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Fallback to quadratic equation solver if a = 0
◆ solveLinearEquation()
| auto math::geometry::PolynomialSolver::solveLinearEquation |
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const double |
a, |
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const double |
b, |
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const double |
min_value = 0, |
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const double |
max_value = 1 |
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) |
| const -> std::vector<double> |
solve linear equation a*x + b = 0
- Parameters
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- Returns
- std::vector<double> real solution of the quadratic functions (from min_value to max_value)
- Note
- In this case, ax*b = 0 (a=0) can cause division by zero. So give special treatment to this case.
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In this case, ax*b = 0 (a=0,b!=0) so any x cannot satisfy this equation.
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In this case, ax*b = 0 (a!=0, b!=0) so x = -b/a is a only solution.
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No fallback because of the order cannot be lowered any further.
◆ solveQuadraticEquation()
| auto math::geometry::PolynomialSolver::solveQuadraticEquation |
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const double |
a, |
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const double |
b, |
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const double |
c, |
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const double |
min_value = 0, |
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const double |
max_value = 1 |
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) |
| const -> std::vector<double> |
solve quadratic equation a*x^2 + b*x + c = 0
- Parameters
-
- Returns
- std::vector<double> real solution of the quadratic functions (from min_value to max_value)
- Note
- Fallback to linear equation solver if a = 0
◆ tolerance
| constexpr static double math::geometry::PolynomialSolver::tolerance = 1e-7 |
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staticconstexpr |
Hard coded parameter, tolerance of calculation results of the PolynomialSolver. This value was determined by Masaya Kataoka (@hakuturu583). The reason this value is not std::numeric_limits<double>::epsilon is that when using this set of functions to find the intersection of a Catmull-Rom spline curve and a line segment, it was confirmed that when the solution is very close to the endpoints of the Hermite curves that make up the Catmull-Rom spline, the solution could not calculated. When considering a 1 km long Catmull-Rom spline (assuming a very long lanelet) with a tolerance of 1e-7, the error in calculating the intersection position in a tangentially distorted coordinate system was ±0.0001 m. This value is sufficiently small that it was tentatively determined to be 1e-7.
The documentation for this class was generated from the following files:
