add spline segments classes

src/decition/decition_brain/decition/adc_math/coordinate_conversion.h

@@ -1,122 +0,0 @@
-/****************************************
- * Functions:  Convert coordinates between GPS (longitude, latitude) system and UTM system.
- * Purpose:    Vehicle localization
- * Author:     Zhao Liang
- * Last Updated:  2021/01/20
- * Update note:  call third-party lib 'proj4' to do the conversionseee.
-*****************************************
-*
-* Convention: East is the X-axis, North is the Y-axis, Up (sky) is the Z-axis,
-* the pair (longitude, latitude) are in degrees: longitude ~ (-180, 180) and
-* latitude ~(-90, 90).
-*
-* Online tool: https://www.latlong.net/lat-long-utm.html
-*
-* Basically the convertion procedure can be splitted into three steps:
-* 1. Declare two `projPJ` objects for the source system and the target system.
-* 2. Put your projection params in two strings.
-* 3. Call `pj_transform` to do the conversion.
-*
-* String used by Apollo:
-*
-* "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs"
-*
-* 1. +proj=longlat means we are projecting from (longitude, latitude).
-* 2. +ellps=GRS80 means the ellipsoid model is GRS80.
-* 3. +towgs84=0,0,0,0,0,0,0 gives the 7 params for datum transformation.
-* 4. +no_defs means we don't want proj to read the default config file,
-* this option is obsolete since proj 6.x
-*/
-
-#ifndef COORDINATE_CONVERSION_H
-#define COORDINATE_CONVERSION_H
-
-#include <string>
-#include <proj_api.h>
-
-namespace iv {
-namespace math {
-
-/**
- * @brief: Convert (lon, lat) coordinates to UTM coordinates.
- * @param: longitude in degrees, range ~ (-180, 180).
- * @param: latitude in degrees, range ~ (-90, 90).
- * @param: x coordinate (East direction).
- * @param: y coordinate (North direction).
- * @return: Return true if the conversion between the two systems is valid.
-*/
-bool LatLonToUtmXY(double longitude, double latitude, double &x, double &y)
-{
-    projPJ pj_latlon;
-    projPJ pj_utm;
-    int zone = static_cast<int>((longitude + 180) / 6) + 1;
-    std::string latlon_src =
-        "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs";
-    std::string utm_dst =
-        "+proj=utm +zone=" + std::to_string(zone) + " +ellps=GRS80 +units=m +no_defs";
-
-    if (!(pj_latlon = pj_init_plus(latlon_src.c_str())))
-    {
-        return false;
-    }
-
-    if (!(pj_utm = pj_init_plus(utm_dst.c_str())))
-    {
-        return false;
-    }
-
-    // the pj_transform requires the (lon, lat) are in radians
-    double lon = longitude * DEG_TO_RAD;
-    double lat = latitude * DEG_TO_RAD;
-
-    // do the actual conversion
-    pj_transform(pj_latlon, pj_utm, 1, 1, &lon, &lat, nullptr);
-
-    x = lon;
-    y = lat;
-    pj_free(pj_latlon);
-    pj_free(pj_utm);
-    return true;
-}
-
-/**
- * @brief: Convert UTM coordinates to (lon, lat) coordinates.
- * @param: x coordinate (East direction).
- * @param: y coordinate (North direction).
- * @param: zone number.
- * @param: longitude in degrees, range ~ (-180, 180).
- * @param: latitude in degrees, range ~ (-90, 90).
- * @return: Return true if the conversion between the two systems is valid.
-*/
-bool UtmXYToLatLon(double x, double y, int zone, double &longitude, double &latitude)
-{
-    projPJ pj_latlon;
-    projPJ pj_utm;
-    std::string latlon_src =
-        "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs";
-    std::string utm_dst =
-        "+proj=utm +zone=" + std::to_string(zone) + " +ellps=GRS80 +units=m +no_defs";
-
-    if (!(pj_latlon = pj_init_plus(latlon_src.c_str())))
-    {
-        return false;
-    }
-
-    if (!(pj_utm = pj_init_plus(utm_dst.c_str())))
-    {
-        return false;
-    }
-
-    // do the actual conversion
-    pj_transform(pj_utm, pj_latlon, 1, 1, &x, &y, nullptr);
-
-    // the result given by pj_transform are in radians
-    longitude = x * RAD_TO_DEG;
-    latitude = y * RAD_TO_DEG;
-    pj_free(pj_latlon);
-    pj_free(pj_utm);
-    return true;
-}
-}
-}
-#endif // COORDINATE_CONVERSION_H

src/decition/decition_brain/decition/adc_math/core/include/splines/PolynomialXd.h

@@ -0,0 +1,130 @@
+#ifndef POLYNOMIALXD_H
+#define POLYNOMIALXD_H
+
+#pragma once
+
+#include <vector>
+
+#include "absl/strings/str_cat.h"
+#include "absl/strings/str_join.h"
+
+namespace adtoolbox {
+namespace core {
+
+class PolynomialXd
+{
+public:
+    PolynomialXd() = default;
+    explicit PolynomialXd(const size_t order);
+    explicit PolynomialXd(const std::vector<double> &params);
+    double operator()(const double value) const;
+    double operator[](const size_t index) const;
+    void setParams(const std::vector<double> &params);
+
+    static PolynomialXd derivedFrom(const PolynomialXd &other);
+    static PolynomialXd integratedFrom(const PolynomialXd &other, const double c);
+
+    size_t order() const;
+    const std::vector<double> &params() const;
+    std::string toString() const;
+
+private:
+    std::vector<double> params_;
+};
+
+// ----------------------------------------
+
+PolynomialXd::PolynomialXd(const size_t order)
+    : params_(order + 1, 0.0) {}
+
+// ----------------------------------------
+
+PolynomialXd::PolynomialXd(const std::vector<double> &params)
+    : params_(params) {}
+
+// ----------------------------------------
+
+size_t PolynomialXd::order() const
+{
+    return params_.size() - 1;
+}
+
+// ----------------------------------------
+
+void PolynomialXd::setParams(const std::vector<double> &params)
+{
+    params_ = params;
+}
+
+// ----------------------------------------
+
+const std::vector<double> &PolynomialXd::params() const
+{
+    return params_;
+}
+
+// ----------------------------------------
+
+double PolynomialXd::operator()(const double value) const
+{
+    double result = 0.0;
+    for (auto rit = params_.rbegin(); rit != params_.rend(); ++rit)
+    {
+        result = result * value + (*rit);
+    }
+    return result;
+}
+
+// ----------------------------------------
+
+double PolynomialXd::operator[](const size_t index) const
+{
+    return index >= params_.size() ? 0.0 : params_[index];
+}
+
+// ----------------------------------------
+
+PolynomialXd PolynomialXd::derivedFrom(const PolynomialXd &other)
+{
+    std::vector<double> params;
+    if (other.order() <= 0)
+    {
+        params.clear();
+    }
+    else
+    {
+        params.resize(other.params().size() - 1);
+        for (size_t i = 1; i < other.order() + 1; i++)
+        {
+            params[i - 1] = other[i] * i;
+        }
+    }
+    return PolynomialXd(params);
+}
+
+// ----------------------------------------
+
+PolynomialXd PolynomialXd::integratedFrom(const PolynomialXd &other, const double c)
+{
+    std::vector<double> params;
+    params.resize(other.params().size() + 1);
+    params[0] = c;
+    for (size_t i = 0; i < other.params().size(); i++)
+    {
+        params[i + 1] = other[i] / (i + 1);
+    }
+    return PolynomialXd(params);
+}
+
+// ----------------------------------------
+
+std::string PolynomialXd::toString() const
+{
+    return absl::StrCat("PolynomailXd(", absl::StrJoin(params_, ", "), ")");
+}
+// ----------------------------------------
+// Ends class PolynomialXd
+}
+}
+
+#endif // POLYNOMIALXD_H

src/decition/decition_brain/decition/adc_math/quartic_polynomail.cpp → src/decition/decition_brain/decition/adc_math/core/include/splines/QuarticPolynomial.h

@@ -1,9 +1,47 @@
-#include "quartic_polynomial.h"
+#ifndef QUARTICPOLYNOMIAL_H
+#define QUARTICPOLYNOMIAL_H
+
+#pragma once
+
+#include <array>
 #include "absl/strings/str_cat.h"
 #include "absl/strings/str_join.h"
 
-namespace iv {
-namespace math {
+namespace adtoolbox {
+namespace core {
+
+class QuarticPolynomial
+{
+public:
+    QuarticPolynomial() = default;
+    virtual ~QuarticPolynomial() = default;
+
+    QuarticPolynomial(const double x0, const double dx0, const double ddx0,
+                      const double dx1, const double ddx1,
+                      const double t);
+
+    QuarticPolynomial(const std::array<double, 3> &start,
+                      const std::array<double, 2> &end,
+                      const double t);
+
+    double evaluate(const size_t order, const double t) const;
+    size_t order() const;
+    double paramLength() const;
+    double coef(const size_t order) const;
+    std::string toString() const;
+
+private:
+    void computeCoefficients(const double x0, const double dx0, const double ddx0,
+                             const double dx1, const double ddx1,
+                             const double t);
+
+    double t_;
+    std::array<double, 3> start_condition_;
+    std::array<double, 2> end_condition_;
+    std::array<double, 5> coef_;
+};
+
+// ----------------------------------------
 
 QuarticPolynomial::QuarticPolynomial(const double x0, const double dx0, const double ddx0,
                                      const double dx1, const double ddx1,
@@ -18,30 +56,15 @@ QuarticPolynomial::QuarticPolynomial(const double x0, const double dx0, const do
     computeCoefficients(x0, dx0, ddx0, dx1, ddx1, t);
 }
 
+// ----------------------------------------
+
 QuarticPolynomial::QuarticPolynomial(const std::array<double, 3> &start,
                                      const std::array<double, 2> &end,
                                      const double t)
     : QuarticPolynomial::QuarticPolynomial(start[0], start[1], start[2],
                                            end[0], end[1], t) {}
 
-void QuarticPolynomial::computeCoefficients(const double x0, const double dx0, const double ddx0,
-                                            const double dx1, const double ddx1,
-                                            const double t)
-{
-    coef_[0] = x0;
-    coef_[1] = dx0;
-    coef_[2] = ddx0 * 0.5;
-
-    double b0 = dx1 - ddx0 * t - dx0;
-    double b1 = ddx1 - ddx0;
-    double t2 = t * t;
-    double t3 = t2 * t;
-
-    coef_[3] = (3 * b0 - b1 * t) / (3 * t2);
-    coef_[4] = (-2 * b0 + b1 * t) / (4 * t3);
-}
-
-double QuarticPolynomial::evaluate(const std::uint32_t order, const double p) const
+double QuarticPolynomial::evaluate(const size_t order, const double p) const
 {
     switch (order)
     {
@@ -60,19 +83,45 @@ double QuarticPolynomial::evaluate(const std::uint32_t order, const double p) co
     }
 }
 
-double QuarticPolynomial::coef(const size_t order) const
-{
-    return coef_[order];
-}
+// ----------------------------------------
+
+size_t QuarticPolynomial::order() const { return 4; }
+
+// ----------------------------------------
+
+double QuarticPolynomial::coef(const size_t order) const { return coef_[order];}
+
+// ----------------------------------------
 
-const std::array<double, 5> &QuarticPolynomial::coef() const
+double QuarticPolynomial::paramLength() const { return t_; }
+
+// ----------------------------------------
+
+std::string QuarticPolynomial::toString() const
 {
-    return coef_;
+    return absl::StrCat("QuarticPoly(", absl::StrJoin(coef_, ", "), ")");
 }
 
-std::string QuarticPolynomial::toString() const
+// ----------------------------------------
+
+void QuarticPolynomial::computeCoefficients(const double x0, const double dx0, const double ddx0,
+                                            const double dx1, const double ddx1,
+                                            const double t)
 {
-    return absl::StrCat("QuarticPolynomial(", absl::StrJoin(coef_, ", "), ")");
+    coef_[0] = x0;
+    coef_[1] = dx0;
+    coef_[2] = ddx0 * 0.5;
+
+    double b0 = dx1 - ddx0 * t - dx0;
+    double b1 = ddx1 - ddx0;
+    double t2 = t * t;
+    double t3 = t2 * t;
+
+    coef_[3] = (3 * b0 - b1 * t) / (3 * t2);
+    coef_[4] = (-2 * b0 + b1 * t) / (4 * t3);
 }
+// ----------------------------------------
+// Ends class QuarticPolynomial
 }
 }
+#endif // QUARTICPOLYNOMIAL_H

src/decition/decition_brain/decition/adc_math/quintic_polynomial.cpp → src/decition/decition_brain/decition/adc_math/core/include/splines/QuinticPolynomial.h

@@ -1,9 +1,51 @@
-#include "quintic_polynomial.h"
+#ifndef QUINTICPOLYNOMIAL_H
+#define QUINTICPOLYNOMIAL_H
+
+#pragma once
+
+#include <array>
 #include "absl/strings/str_cat.h"
 #include "absl/strings/str_join.h"
 
-namespace iv {
-namespace math {
+namespace adtoolbox {
+namespace core {
+
+class QuinticPolynomial
+{
+public:
+    QuinticPolynomial() = default;
+    virtual ~QuinticPolynomial() = default;
+
+    QuinticPolynomial(const double x0, const double dx0, const double ddx0,
+                      const double x1, const double dx1, const double ddx1,
+                      const double t);
+
+    QuinticPolynomial(const std::array<double, 3> &start,
+                      const std::array<double, 3> &end,
+                      const double t);
+
+    void fitBoundaryConditions(const double x0, const double dx0, const double ddx0,
+                               const double x1, const double dx1, const double ddx1,
+                               const double t);
+
+    double evaluate(const size_t order, const double t) const;
+    size_t order() const;
+    double paramLength() const;
+    double coef(const size_t order) const;
+    std::string toString() const;
+
+private:
+    void computeCoefficients(const double x0, const double dx0, const double ddx0,
+                             const double x1, const double dx1, const double ddx1,
+                             const double t);
+
+    double t_;
+    std::array<double, 3> start_condition_;
+    std::array<double, 3> end_condition_;
+    std::array<double, 6> coef_;
+};
+
+// ----------------------------------------
 
 QuinticPolynomial::QuinticPolynomial(const double x0, const double dx0, const double ddx0,
                                      const double x1, const double dx1, const double ddx1,
@@ -19,13 +61,31 @@ QuinticPolynomial::QuinticPolynomial(const double x0, const double dx0, const do
     computeCoefficients(x0, dx0, ddx0, x1, dx1, ddx1, t);
 }
 
+// ----------------------------------------
+
 QuinticPolynomial::QuinticPolynomial(const std::array<double, 3> &start,
                                      const std::array<double, 3> &end,
                                      const double t)
     : QuinticPolynomial::QuinticPolynomial(start[0], start[1], start[2],
                                            end[0], end[1], end[2], t) {}
 
-double QuinticPolynomial::evaluate(std::uint32_t order, const double p) const
+void QuinticPolynomial::fitBoundaryConditions(const double x0, const double dx0, const double ddx0,
+                                              const double x1, const double dx1, const double ddx1,
+                                              const double t)
+{
+    t_ = t;
+    start_condition_[0] = x0;
+    start_condition_[1] = dx0;
+    start_condition_[2] = ddx0;
+    end_condition_[0] = x1;
+    end_condition_[1] = dx1;
+    end_condition_[2] = ddx1;
+    computeCoefficients(x0, dx0, ddx0, x1, dx1, ddx1, t);
+}
+
+// ----------------------------------------
+
+double QuinticPolynomial::evaluate(const size_t order, const double p) const
 {
     switch (order)
     {
@@ -46,30 +106,36 @@ double QuinticPolynomial::evaluate(std::uint32_t order, const double p) const
     }
 }
 
-void QuinticPolynomial::fitByBoundaryConditions(const double x0, const double dx0, const double ddx0,
-                                                const double x1, const double dx1, const double ddx1,
-                                                const double t)
+// ----------------------------------------
+
+size_t QuinticPolynomial::order() const
 {
-    t_ = t;
-    start_condition_[0] = x0;
-    start_condition_[1] = dx0;
-    start_condition_[2] = ddx0;
-    end_condition_[0] = x1;
-    end_condition_[1] = dx1;
-    end_condition_[2] = ddx1;
-    computeCoefficients(x0, dx0, ddx0, x1, dx1, ddx1, t);
+    return 5;
 }
 
+// ----------------------------------------
+
 double QuinticPolynomial::coef(const size_t order) const
 {
     return coef_[order];
 }
 
-const std::array<double, 6> &QuinticPolynomial::coef() const
+// ----------------------------------------
+
+double QuinticPolynomial::paramLength() const
+{
+    return t_;
+}
+
+// ----------------------------------------
+
+std::string QuinticPolynomial::toString() const
 {
-    return coef_;
+    return absl::StrCat("QuinticPoly(", absl::StrJoin(coef_, ", "), ")");
 }
 
+// ----------------------------------------
+
 void QuinticPolynomial::computeCoefficients(const double x0, const double dx0, const double ddx0,
                                             const double x1, const double dx1, const double ddx1,
                                             const double t)
@@ -89,10 +155,8 @@ void QuinticPolynomial::computeCoefficients(const double x0, const double dx0, c
     coef_[4] = (-15.0 * c0 + 7.0 * c1 - c2) / t;
     coef_[5] = (6.0 * c0 - 3.0 * c1 + 0.5 * c2) / t2;
 }
-
-std::string QuinticPolynomial::toString() const
-{
-    return absl::StrCat("QuinticPolynomial(", absl::StrJoin(coef_, ", "), ")");
-}
+// ----------------------------------------
+// Ends class QuinticPolynomial
 }
 }
+#endif // QUINTICPOLYNOMIAL_H

src/decition/decition_brain/decition/adc_math/core/include/splines/Spline1dSegment.h

@@ -0,0 +1,120 @@
+#ifndef SPLINE1DSEGMENT_H
+#define SPLINE1DSEGMENT_H
+
+#pragma once
+
+#include <vector>
+#include <eigen3/Eigen/Core>
+
+#include "core/include/splines/PolynomialXd.h"
+
+namespace adtoolbox {
+namespace core {
+
+class Spline1dSegment
+{
+public:
+    explicit Spline1dSegment(const size_t order);
+    explicit Spline1dSegment(const std::vector<double> &params);
+    ~Spline1dSegment() = default;
+
+    void setParams(const std::vector<double> &params);
+    double operator()(const double x) const;
+    double derivative(const double x) const;
+    double secondOrderDerivative(const double x) const;
+    double thirdOrderDerivative(const double x) const;
+
+    const PolynomialXd &splineFunc() const;
+    const PolynomialXd &derivativeFunc() const;
+    const PolynomialXd &secondOrderDerivativeFunc() const;
+    const PolynomialXd &thirdOrderDerivativeFunc() const;
+
+private:
+    void setSplineFunc(const PolynomialXd &spline_func);
+
+    PolynomialXd f_;
+    PolynomialXd df_;
+    PolynomialXd ddf_;
+    PolynomialXd dddf_;
+};
+
+// ----------------------------------------
+
+Spline1dSegment::Spline1dSegment(const size_t order)
+{
+    setSplineFunc(PolynomialXd(order));
+}
+
+// ----------------------------------------
+
+Spline1dSegment::Spline1dSegment(const std::vector<double> &params)
+{
+    setSplineFunc(PolynomialXd(params));
+}
+
+// ----------------------------------------
+
+void Spline1dSegment::setParams(const std::vector<double> &params)
+{
+    setSplineFunc(PolynomialXd(params));
+}
+
+// ----------------------------------------
+
+void Spline1dSegment::setSplineFunc(const PolynomialXd &spline_func)
+{
+    f_ = spline_func;
+    df_ = PolynomialXd::derivedFrom(f_);
+    ddf_ = PolynomialXd::derivedFrom(df_);
+    dddf_ = PolynomialXd::derivedFrom(ddf_);
+}
+
+// ----------------------------------------
+
+double Spline1dSegment::operator()(const double x) const
+{
+    return f_(x);
+}
+
+double Spline1dSegment::derivative(const double x) const
+{
+    return df_(x);
+}
+
+double Spline1dSegment::secondOrderDerivative(const double x) const
+{
+    return ddf_(x);
+}
+
+double Spline1dSegment::thirdOrderDerivative(const double x) const
+{
+    return dddf_(x);
+}
+
+// ----------------------------------------
+
+const PolynomialXd& Spline1dSegment::splineFunc() const
+{
+    return f_;
+}
+
+const PolynomialXd& Spline1dSegment::derivativeFunc() const
+{
+    return df_;
+}
+
+const PolynomialXd& Spline1dSegment::secondOrderDerivativeFunc() const
+{
+    return ddf_;
+}
+
+const PolynomialXd& Spline1dSegment::thirdOrderDerivativeFunc() const
+{
+    return dddf_;
+}
+// ----------------------------------------
+// Ends class Spline1dSegment
+}
+}
+
+#endif // SPLINE1DSEGMENT_H

src/decition/decition_brain/decition/adc_math/core/include/splines/Spline2dSegment.h

@@ -0,0 +1,133 @@
+#ifndef SPLINE2DSEGMENT_H
+#define SPLINE2DSEGMENT_H
+
+#pragma once
+
+#include <vector>
+#include <eigen3/Eigen/Core>
+
+#include "core/include/splines/PolynomialXd.h"
+
+namespace adtoolbox {
+namespace core {
+
+class Spline2dSegment
+{
+public:
+    explicit Spline2dSegment(const size_t order);
+    Spline2dSegment(const std::vector<double> &x_param,
+                    const std::vector<double> &y_param);
+    ~Spline2dSegment() = default;
+
+    bool setParams(const std::vector<double> &x_param,
+                   const std::vector<double> &y_param);
+
+    std::pair<double, double> operator()(const double t) const;
+    double x(const double t) const;
+    double y(const double t) const;
+    double derivativeX(const double t) const;
+    double derivativeY(const double t) const;
+    double secondOrderDerivativeX(const double t) const;
+    double secondOrderDerivativeY(const double t) const;
+    double thirdOrderDerivativeX(const double t) const;
+    double thirdOrderDerivativeY(const double t) const;
+
+    const PolynomialXd& splineFuncX() const;
+    const PolynomialXd& splineFuncY() const;
+    const PolynomialXd& derivativeFuncX() const;
+    const PolynomialXd& derivativeFuncY() const;
+    const PolynomialXd& secondOrderDerivativeFuncX() const;
+    const PolynomialXd& secondOrderDerivativeFuncY() const;
+    const PolynomialXd& thirdOrderDerivativeFuncX() const;
+    const PolynomialXd& thirdOrderDerivativeFuncY() const;
+
+private:
+    PolynomialXd fx_;
+    PolynomialXd fy_;
+    PolynomialXd dfx_;
+    PolynomialXd dfy_;
+    PolynomialXd ddfx_;
+    PolynomialXd ddfy_;
+    PolynomialXd dddfx_;
+    PolynomialXd dddfy_;
+};
+
+// ----------------------------------------
+
+Spline2dSegment::Spline2dSegment(const size_t order)
+    : fx_(order), fy_(order)
+{
+    dfx_ = PolynomialXd::derivedFrom(fx_);
+    dfy_ = PolynomialXd::derivedFrom(fy_);
+    ddfx_ = PolynomialXd::derivedFrom(dfx_);
+    ddfy_ = PolynomialXd::derivedFrom(dfy_);
+    dddfx_ = PolynomialXd::derivedFrom(ddfx_);
+    dddfy_ = PolynomialXd::derivedFrom(ddfy_);
+}
+
+// ----------------------------------------
+
+Spline2dSegment::Spline2dSegment(const std::vector<double>& x_param,
+                                 const std::vector<double>& y_param)
+    : fx_(x_param), fy_(y_param)
+{
+    dfx_ = PolynomialXd::derivedFrom(fx_);
+    dfy_ = PolynomialXd::derivedFrom(fy_);
+    ddfx_ = PolynomialXd::derivedFrom(dfx_);
+    ddfy_ = PolynomialXd::derivedFrom(dfy_);
+    dddfx_ = PolynomialXd::derivedFrom(ddfx_);
+    dddfy_ = PolynomialXd::derivedFrom(ddfy_);
+}
+
+// ----------------------------------------
+
+bool Spline2dSegment::setParams(const std::vector<double> &x_param,
+                                const std::vector<double> &y_param)
+{
+    if (x_param.size() != y_param.size())
+        return false;
+
+    fx_ = PolynomialXd(x_param);
+    fy_ = PolynomialXd(y_param);
+    dfx_ = PolynomialXd::derivedFrom(fx_);
+    dfy_ = PolynomialXd::derivedFrom(fy_);
+    ddfx_ = PolynomialXd::derivedFrom(dfx_);
+    ddfy_ = PolynomialXd::derivedFrom(dfy_);
+    dddfx_ = PolynomialXd::derivedFrom(ddfx_);
+    dddfy_ = PolynomialXd::derivedFrom(ddfy_);
+    return true;
+}
+
+// ----------------------------------------
+
+std::pair<double, double> Spline2dSegment::operator()(const double t) const
+{
+    return std::make_pair(fx_(t), fy_(t));
+}
+
+// ----------------------------------------
+
+double Spline2dSegment::x(const double t) const { return fx_(t); }
+double Spline2dSegment::y(const double t) const { return fy_(t); }
+double Spline2dSegment::derivativeX(const double t) const { return dfx_(t); }
+double Spline2dSegment::derivativeY(const double t) const { return dfy_(t); }
+double Spline2dSegment::secondOrderDerivativeX(const double t) const { return ddfx_(t); }
+double Spline2dSegment::secondOrderDerivativeY(const double t) const { return ddfy_(t); }
+double Spline2dSegment::thirdOrderDerivativeX(const double t) const { return dddfx_(t); }
+double Spline2dSegment::thirdOrderDerivativeY(const double t) const { return dddfy_(t); }
+
+// ----------------------------------------
+
+const PolynomialXd& Spline2dSegment::splineFuncX() const { return fx_; }
+const PolynomialXd& Spline2dSegment::splineFuncY() const { return fy_; }
+const PolynomialXd& Spline2dSegment::derivativeFuncX() const { return dfx_; }
+const PolynomialXd& Spline2dSegment::derivativeFuncY() const { return dfy_; }
+const PolynomialXd& Spline2dSegment::secondOrderDerivativeFuncX() const { return ddfx_; }
+const PolynomialXd& Spline2dSegment::secondOrderDerivativeFuncY() const { return ddfy_; }
+const PolynomialXd& Spline2dSegment::thirdOrderDerivativeFuncX() const { return dddfx_; }
+const PolynomialXd& Spline2dSegment::thirdOrderDerivativeFuncY() const { return dddfy_; }
+// ----------------------------------------
+// Ends class Spline2dSegment
+}
+}
+#endif // SPLINE2DSEGMENT_H

src/decition/decition_brain/decition/adc_math/quartic_polynomial.h

@@ -1,100 +0,0 @@
-/****************************************
- * Class:    Quartic Polynomial class
- * Purpose:  Fitting a quartic polynomial on interval [0, t] by given
- *     boundary conditions.
- * Author:   Zhao Liang
- * Last Updated:  2021/02/23
-*****************************************
-*
-* Note: The polynomial is defined on interval [0, t] and has form
-*
-*     f(t) = a0 + a1*t + a2*t^2 + a3*t^3 + a4*t^4
-*
-* Boundary conditions are given by:
-* 1. x0=f(0), dx0=f'(0), ddx0=f''(0)
-* 2. dx1=f'(t), ddx1=f''(t)
-*/
-
-#ifndef QUARTIC_POLYNOMIAL_H
-#define QUARTIC_POLYNOMIAL_H
-
-#pragma once
-
-#include <array>
-
-namespace iv {
-namespace math {
-
-class QuarticPolynomial
-{
-public:
-    QuarticPolynomial() = default;
-    ~QuarticPolynomial() = default;
-
-    /**
-    * @brief Initialize a quartic polynomial by given boundary conditions.
-    * @param x0: start point at x=0
-    * @param dx0: first order derivative at the start point
-    * @param ddx0: second order derivative at the start point
-    * @param dx1: first order derivative at the end point x=t.
-    * @param ddx1: second order derivative at the end point x=t.
-    * @param t: parameter length.
-    */
-    QuarticPolynomial(const double x0, const double dx0, const double ddx0,
-                      const double dx1, const double ddx1,
-                      const double t);
-
-    /**
-    * @brief You can also pack the boundary conditions into two arrays.
-    */
-    QuarticPolynomial(const std::array<double, 3> &start,
-                      const std::array<double, 2> &end,
-                      const double t);
-
-    /**
-    * @brief Evaluate the n-th derivative of this polynomial at a given point p.
-    * @param order: the order of the derivative to be evaluated.
-    * @param p: the point to be evaluated.
-    */
-    double evaluate(const std::uint32_t order, const double p) const;
-
-    /**
-    * @brief Return the coefficient of the k-th term.
-    */
-    double coef(const size_t order) const;
-
-    /**
-    * @brief Return all coefficients as a std::array.
-    */
-    const std::array<double, 5> &coef() const;
-
-    /**
-    * @brief Return a pretty string representation of this polynomial
-    */
-    std::string toString() const;
-
-    size_t order() const { return 4; }
-
-    /**
-    * @brief Return the length of the fitting interval [0, t]
-    */
-    double paramLength() const { return t_; }
-
-private:
-
-    /**
-    * @brief Compute the coefficients array.
-    */
-    void computeCoefficients(const double x0, const double dx0, const double ddx0,
-                             const double dx1, const double ddx1,
-                             const double t);
-
-    double t_;
-    std::array<double, 3> start_condition_;
-    std::array<double, 2> end_condition_;
-    std::array<double, 5> coef_;
-};
-}
-}
-
-#endif // QUARTIC_POLYNOMIAL_H

src/decition/decition_brain/decition/adc_math/quintic_polynomial.h

@@ -1,93 +0,0 @@
-/****************************************
- * Class:    Quintic Polynomial class
- * Purpose:  Fitting a quinticc polynomial on interval [0, t] by given
- *     boundary conditions.
- * Author:   Zhao Liang
- * Last Updated:  2021/02/24
-*****************************************
-*
-* Note: The polynomial is defined on interval [0, t] and has form
-*
-*     f(t) = a0 + a1*t + a2*t^2 + a3*t^3 + a4*t^4 + a5*t^5
-*
-* Boundary conditions are given by:
-* 1. x0=f(0), dx0=f'(0), ddx0=f''(0)
-* 2. x1=f(t), dx1=f'(t), ddx1=f''(t)
-*/
-#ifndef QUINTIC_POLYNOMIAL_H
-#define QUINTIC_POLYNOMIAL_H
-
-#pragma once
-
-#include <array>
-
-namespace iv {
-namespace math {
-
-class QuinticPolynomial
-{
-public:
-    QuinticPolynomial() = default;
-    ~QuinticPolynomial() = default;
-
-    /**
-    * @brief Initialize a quintic polynomial by given boundary conditions.
-    * @param x0: start point at x=0
-    * @param dx0: first order derivative at the start point
-    * @param ddx0: second order derivative at the start point
-    * @param x1: end point at x=t
-    * @param dx1: first order derivative at the end point x=t.
-    * @param ddx1: second order derivative at the end point x=t.
-    * @param t: parameter length.
-    */
-    QuinticPolynomial(const double x0, const double dx0, const double ddx0,
-                      const double x1, const double dx1, const double ddx1,
-                      const double t);
-
-    QuinticPolynomial(const std::array<double, 3> &start,
-                      const std::array<double, 3> &end,
-                      const double t);
-
-    void fitByBoundaryConditions(const double x0, const double dx0, const double ddx0,
-                                 const double x1, const double dx1, const double ddx1,
-                                 const double t);
-
-    /**
-    * @brief Evaluate the n-th derivative of this polynomial at a given point p.
-    * @param order: the order of the derivative to be evaluated.
-    * @param p: the point to be evaluated.
-    */
-    double evaluate(const std::uint32_t order, const double p) const;
-
-    /**
-    * @brief Return the coefficient of the k-th term.
-    */
-    double coef(const size_t order) const;
-
-    /**
-    * @brief Return all coefficients as a std::array.
-    */
-    const std::array<double, 6> &coef() const;
-
-    /**
-    * @brief Return a pretty string representation of this polynomial
-    */
-    std::string toString() const;
-
-    size_t order() const { return 5; }
-    double paramLength() const { return t_; }
-
-private:
-    void computeCoefficients(const double x0, const double dx0, const double ddx0,
-                             const double x1, const double dx1, const double ddx1,
-                             const double t);
-
-    double t_;
-    std::array<double, 3> start_condition_;
-    std::array<double, 3> end_condition_;
-    std::array<double, 6> coef_;
-};
-}
-}
-
-#endif // QUINTIC_POLYNOMIAL_H

src/decition/decition_brain/decition/adc_math/vec2.h

@@ -1,289 +0,0 @@
-/****************************************
-* Class:    2D vector class
-* Purpose:  A single header file handling 2D vector computations.
-* Author:   Zhao Liang
-* Last Updated:  2021/01/20
-*****************************************
-*
-* Note: Need to add error handling procedures in divisions.
-*
-*/
-
-#ifndef VEC2_H
-#define VEC2_H
-
-#pragma once
-
-#include <cmath>
-#include <iostream>
-
-namespace iv {
-namespace math {
-
-constexpr double _EPSILON = 1e-12;
-
-class Vec2
-{
-public:
-
-    // ----------------------------------------
-
-    /*
-     * Constructors.
-    */
-
-    Vec2() : x_(0), y_(0) {}
-
-    explicit Vec2(double a) : x_(a), y_(a) {}
-
-    Vec2(double a, double b) : x_(a), y_(b) {}
-
-    // ----------------------------------------
-
-    // Compare to another vector
-    bool operator == (const Vec2 &v) const
-    {
-        return (std::abs(x_ - v.x()) < _EPSILON &&
-                std::abs(y_ - v.y()) < _EPSILON);
-    }
-
-    // ----------------------------------------
-
-    /*
-     * Return the unit vector Vec2(cos(angle), sin(angle)),
-     * The param 'angle' should be in radians.
-    */
-    static Vec2 unitVec2(const double angle)
-    {
-        return Vec2(cos(angle), sin(angle));
-    }
-
-    // ----------------------------------------
-
-    /*
-     * Access x and y components
-    */
-    double x() const { return x_; }
-    double y() const { return y_; }
-
-    // ----------------------------------------
-
-    /*
-     * Set x and y components
-    */
-    void set_x(const double x) { x_ = x; }
-    void set_y(const double y) { y_ = y; }
-
-    // ----------------------------------------
-
-    /*
-     * Operations with other scalars,
-     * vec2 is the left operand, scalar is the right operand.
-    */
-
-    // ----------------------------------------
-
-    // add a scalar
-    Vec2 operator + (double c) const { return Vec2(x() + c, y() + c); }
-    // subtract a scalar
-    Vec2 operator - (double c) const { return Vec2(x() - c, y() - c); }
-    // multiply a scalar
-    Vec2 operator * (double c) const { return Vec2(x() * c, y() * c); }
-    // divide by a scalar
-    Vec2 operator / (double c) const { return Vec2(x() / c, y() / c); }
-    // in-place add a scalar
-    Vec2 operator += (double c) { x_ += c; y_ += c; return (*this); }
-    // in-place subtract a scalar
-    Vec2 operator -= (double c) { x_ -= c; y_ -= c; return (*this); }
-    // in-place multiply a scalar
-    Vec2 operator *= (double c) { x_ *= c; y_ *= c; return (*this); }
-    // in-place divide by a scalar
-    Vec2 operator /= (double c) { x_ /= c; y_ /= c; return (*this); }
-
-    // ----------------------------------------
-
-    /*
-     * Operations with other vec2
-    */
-
-    // ----------------------------------------
-
-    // add two vectors
-    Vec2 operator + (const Vec2 &v) const { return Vec2(x() + v.x(), y() + v.y()); }
-    // subtract another vector
-    Vec2 operator - (const Vec2 &v) const { return Vec2(x() - v.x(), y() - v.y()); }
-    // multiply two vectors as complex numbers
-    Vec2 operator * (const Vec2 &v) const
-    {
-        double x1 = x() * v.x() - y() * v.y();
-        double y1 = x() * v.y() + y() * v.x();
-        return Vec2(x1, y1);
-    }
-    // division as complex numbers
-    Vec2 operator / (const Vec2 &v) const
-    {
-        double snorm = v.squared_norm();
-        return Vec2(this->dot(v) / snorm, -this->cross(v) / snorm);
-    }
-    // in-place vector addition
-    Vec2 operator += (const Vec2 &v) { x_ += v.x(); y_ += v.y(); return (*this); }
-    // in-place vector subtraction
-    Vec2 operator -= (const Vec2 &v) { x_ -= v.x(); y_ -= v.y(); return (*this); }
-    // in-place vector multiplication as complex numbers
-    Vec2 operator *= (const Vec2 &v)
-    {
-        double x1 = x() * v.x() - y() * v.y();
-        double y1 = x() * v.y() + y() * v.x();
-        x_ = x1;
-        y_ = y1;
-        return (*this);
-    }
-    // in-place vector division as complex numbers
-    Vec2 operator /= (const Vec2 &v)
-    {
-        double snorm = v.squared_norm();
-        double x1 = this->dot(v) / snorm;
-        double y1 = -this->cross(v) / snorm;
-        x_ = x1;
-        y_ = y1;
-        return (*this);
-    }
-
-    // ----------------------------------------
-
-    /*
-     * Vector util functions
-    */
-
-    // ----------------------------------------
-
-    // Return squared norm
-    double squared_norm() const { return x() * x() + y() * y(); }
-
-    // Return the usual Euclidean norm
-    double norm() const { return sqrt(x() * x() + y() * y()); }
-
-    // Inner product of two vectors
-    double dot(const Vec2 &v) const { return x() * v.x() + y() * v.y(); }
-
-    // Angle with the positive x-axis in radians
-    double angle() const { return atan2(y(), x()); }
-
-    // Angle between two vectors
-    double angle(const Vec2 &v) const
-    {
-        return acos(this->dot(v) / (norm() * v.norm()));
-    }
-
-    // Distance between two vectors
-    double dist(const Vec2 &v) const { return (*this - v).norm(); }
-
-    // Squared distance between two vectors
-    double squared_dist(const Vec2 &v) const { return (*this - v).squared_norm(); }
-
-    // Cross product of two vectors
-    double cross(const Vec2 &v) const { return x() * v.y() - y() * v.x(); }
-
-    // Return a normalized version of this vector
-    Vec2 normalize() const
-    {
-        double s = norm();
-        return (*this) / s;
-    }
-
-    // Translate a vector
-    Vec2 translate(double tx, double ty) const { return Vec2(x() + tx, y() + ty); }
-
-    // Rotate a vector by angle
-    Vec2 rotate(const double theta) const
-    {
-        double ct = cos(theta), st = sin(theta);
-        double x1 = x() * ct - y() * st;
-        double y1 = x() * ct + y() * st;
-        return Vec2(x1, y1);
-    }
-
-    // return a perpendicular vector to this one
-    Vec2 perp() const { return Vec2(-y(), x()); }
-
-private:
-    double x_;
-    double y_;
-};
-
-// ----------------------------------------
-
-/*
- * Vec2 operations as right operand
-*/
-
-// ----------------------------------------
-
-// print formatting
-std::ostream & operator << (std::ostream &out, const Vec2 &v)
-{
-    out << "Vec2(" << v.x() << ", " << v.y() << ")";
-    return out;
-}
-
-// add another scalar
-Vec2 operator + (double c, const Vec2 &v) { return Vec2(v.x() + c, v.y() + c); }
-// subtract another scalar
-Vec2 operator - (double c, const Vec2 &v) { return Vec2(c - v.x(), c - v.y()); }
-// multiply another scalar
-Vec2 operator * (double c, const Vec2 &v) { return Vec2(v.x() * c, v.y() * c); }
-// divide another scalar
-Vec2 operator / (double c, const Vec2 &v)
-{
-    double snorm = v.squared_norm();
-    return Vec2(v.x() * c / snorm, -v.y() * c / snorm);
-}
-
-// ----------------------------------------
-
-/*
- * Vector util functions
-*/
-
-// ----------------------------------------
-
-// Inner product
-double vdot(const Vec2 &v1, const Vec2 &v2) { return v1.dot(v2); }
-
-// Cross
-double vcross(const Vec2 &v1, const Vec2 &v2) { return v1.cross(v2); }
-
-// Vector length
-double vlength(const Vec2 &v) { return v.norm(); }
-
-// Angle with positive x-axis
-double vangle(const Vec2 &v) { return v.angle(); }
-
-// Angle between two vectors
-double vangle(const Vec2 &v1, const Vec2 &v2) { return v1.angle(v2); }
-
-// distance between two vectors
-double vdist(const Vec2 &v1, const Vec2 &v2) { return v1.dist(v2); }
-
-// squared distance between two vectors
-double vsquared_dist(const Vec2 &v1, const Vec2 &v2) { return v1.squared_dist(v2); }
-
-// normalize a vector
-Vec2 vnormalize(const Vec2 &v) { return v.normalize(); }
-
-// return a perpendicular one
-Vec2 vperp(const Vec2 &v) { return v.perp(); }
-
-// rotate a vector
-Vec2 vrotate(const Vec2 &v, double theta) { return v.rotate(theta); }
-
-// return a unit vector of given direction
-Vec2 vdir(const double angle) { return Vec2::unitVec2(angle); }
-
-// return a linear combination of two vectors
-Vec2 vinterp(const Vec2 &v1, const Vec2 &v2, double t) { return v1 * (1 - t) + v2 * t; }
-
-}
-}
-
-#endif // VEC2_H