WIP: Doxygen comments

Interpolation.hpp

@@ -1,26 +1,120 @@
 
+/**
+ * @file Interpolation.hpp
+ * @brief Provides various interpolation methods, including linear, cubic Hermite, cubic Lagrange, and cubic B-spline interpolations.
+ *
+ * This file defines template structures and methods for performing different types of interpolation.
+ * Each interpolation method allows for smooth estimation of values between known data points
+ * using specific mathematical techniques:
+ * - Linear interpolation computes values by connecting points with straight lines.
+ * - Cubic Hermite interpolation provides smooth results with continuous first derivatives.
+ * - Cubic Lagrange interpolation uses Lagrange polynomials to approximate values between points.
+ * - Cubic B-spline interpolation uses B-spline basis functions to ensure smooth curves with continuity in function values and derivatives.
+ *
+ * The templates are designed to be flexible and accept various data types for interpolation, such as float or double.
+ */
+
 #ifndef INTERPOLATION_HPP
 #define INTERPOLATION_HPP
 
 // Enumeration of interpolation types
 
-enum class InterpType { None, Linear, CubicHermite, CubicLagrange, CubicBSpline };
+/**
+ * @enum InterpType
+ * @brief Defines different types of interpolation methods.
+ *
+ * This enumeration specifies various interpolation techniques that can be
+ * used to estimate values between known data points.
+ */
+enum class InterpType {
+    None,           /**< No interpolation applied. */
+        Linear,         /**< Linear interpolation. Computes the value by connecting data points with a straight line. */
+        CubicHermite,   /**< Cubic Hermite interpolation. Provides smooth results with continuity in both the function and its first derivative. */
+        CubicLagrange,  /**< Cubic Lagrange interpolation. Uses the Lagrange polynomial for approximating values. */
+        CubicBSpline    /**< Cubic B-Spline interpolation. Uses B-spline curves for smooth interpolation. */
+};
 
 // Linear
 
+/**
+ * @struct linear_interp
+ * @brief A template structure for performing linear interpolation.
+ *
+ * This structure provides a mechanism for calculating the linear interpolation
+ * of a given value between two points. The template parameter @p T represents
+ * the data type of the values being interpolated.
+ *
+ * @tparam T The type of the data points to be interpolated (e.g., float, double).
+ */
+
 template <class T>
 struct linear_interp
 {
+
+    /**
+     * @brief Performs linear interpolation between two values.
+     *
+     * This operator overload computes the linear interpolation between two values @p y0 and @p y1
+     * at a point @p x, where @p x is typically a fractional value between 0 and 1.
+     *
+     * @param x The interpolation factor. Typically a value between 0 and 1, representing
+     *          the relative position between @p y0 and @p y1.
+     * @param y0 The starting value (interpolated at @p x = 0).
+     * @param y1 The ending value (interpolated at @p x = 1).
+     * @return The interpolated value between @p y0 and @p y1.
+     */
+
     T operator()(const T& x, const T& y0, const T& y1) { return  (y0 + x * ((y1 - y0))); }
 };
 
 // Cubic Hermite
 
+/**
+ * @struct cubic_hermite_interp
+ * @brief A template structure for performing cubic Hermite interpolation.
+ *
+ * This structure provides a mechanism for calculating cubic Hermite interpolation,
+ * which is a method of interpolation that provides smooth curves with continuity
+ * in both the function values and their first derivatives.
+ *
+ * The template parameter @p T represents the data type of the values being interpolated.
+ *
+ * @tparam T The type of the data points to be interpolated (e.g., float, double).
+ */
+
 template <class T>
 struct cubic_hermite_interp
 {
+
+    /**
+     * @brief Default constructor for the cubic Hermite interpolation structure.
+     *
+     * Initializes constants used in the cubic Hermite interpolation process.
+     * These constants represent fractional coefficients that are used in the interpolation formula:
+     * - @p _5div2 is initialized to 2.5.
+     * - @p _3div2 is initialized to 1.5.
+     * - @p _1div2 is initialized to 0.5.
+     */
+
     cubic_hermite_interp() : _5div2(2.5), _3div2(1.5), _1div2(0.5) {}
 
+    /**
+     * @brief Performs cubic Hermite interpolation between four values.
+     *
+     * This operator overload computes the cubic Hermite interpolation between four points
+     * @p y0, @p y1, @p y2, and @p y3 at a given point @p x. The values @p y1 and @p y2
+     * represent the interval over which interpolation occurs, while @p y0 and @p y3 are
+     * used to compute the tangent at the interval boundaries, ensuring smooth transitions.
+     *
+     * @param x The interpolation factor, typically between 0 and 1, representing the relative
+     *          position between @p y1 and @p y2.
+     * @param y0 The value before the starting point of interpolation, used to calculate the slope at @p y1.
+     * @param y1 The starting value of the interpolation interval (interpolated at @p x = 0).
+     * @param y2 The ending value of the interpolation interval (interpolated at @p x = 1).
+     * @param y3 The value after the ending point of interpolation, used to calculate the slope at @p y2.
+     * @return The interpolated value between @p y1 and @p y2 using cubic Hermite interpolation.
+     */
+
     T operator()(const T& x, const T& y0, const T& y1, const T& y2, const T& y3)
     {
         const T c0 = y1;
@@ -33,18 +127,81 @@ struct cubic_hermite_interp
 
 private:
 
+    /**
+     * @brief A constant representing the value 5/2 (or 2.5), used in cubic Hermite interpolation calculations.
+     *
+     * This constant is used internally in the cubic Hermite interpolation formula to scale the results
+     * based on specific mathematical operations.
+     */
+
     const T _5div2;
+
+    /**
+     * @brief A constant representing the value 3/2 (or 1.5), used in cubic Hermite interpolation calculations.
+     *
+     * This constant is utilized in the cubic Hermite interpolation formula to help scale and calculate
+     * the interpolated value between points.
+     */
+
     const T _3div2;
+
+    /**
+     * @brief A constant representing the value 1/2 (or 0.5), used in cubic Hermite interpolation calculations.
+     *
+     * This constant is used as part of the cubic Hermite interpolation formula to help adjust the scaling
+     * of the interpolated value between points.
+     */
+
     const T _1div2;
 };
 
 // Cubic Lagrange
 
+/**
+ * @struct cubic_lagrange_interp
+ * @brief A template structure for performing cubic Lagrange interpolation.
+ *
+ * This structure provides a mechanism for calculating cubic Lagrange interpolation,
+ * which approximates a smooth curve through four data points using Lagrange polynomials.
+ * The template parameter @p T represents the data type of the values being interpolated.
+ *
+ * @tparam T The type of the data points to be interpolated (e.g., float, double).
+ */
+
 template <class T>
 struct cubic_lagrange_interp
 {
+
+    /**
+     * @brief Default constructor for the cubic Lagrange interpolation structure.
+     *
+     * Initializes constants used in the cubic Lagrange interpolation process.
+     * These constants represent fractional coefficients that are used in the interpolation formula:
+     * - @p _1div3 is initialized to 1/3.
+     * - @p _1div6 is initialized to 1/6.
+     * - @p _1div2 is initialized to 0.5.
+     *
+     * The values are computed based on the template parameter type @p T.
+     */
+
     cubic_lagrange_interp() : _1div3(T(1)/T(3)), _1div6(T(1)/T(6)), _1div2(0.5) {}
 
+    /**
+     * @brief Performs cubic Lagrange interpolation between four values.
+     *
+     * This operator overload computes the cubic Lagrange interpolation between four points
+     * @p y0, @p y1, @p y2, and @p y3 at a given point @p x. Lagrange interpolation uses
+     * polynomials to estimate the value at @p x based on these four surrounding points.
+     *
+     * @param x The interpolation factor, typically between 0 and 1, representing the relative position
+     *          within the interval between @p y1 and @p y2.
+     * @param y0 The value before the starting point of interpolation, used to calculate the Lagrange polynomial.
+     * @param y1 The starting value of the interpolation interval (interpolated at @p x = 0).
+     * @param y2 The ending value of the interpolation interval (interpolated at @p x = 1).
+     * @param y3 The value after the ending point of interpolation, used to calculate the Lagrange polynomial.
+     * @return The interpolated value between @p y1 and @p y2 using cubic Lagrange interpolation.
+     */
+
     T operator()(const T& x, const T& y0, const T& y1, const T& y2, const T& y3)
     {
         const T c0 = y1;
@@ -57,18 +214,83 @@ struct cubic_lagrange_interp
 
 private:
 
+    /**
+     * @brief A constant representing the value 1/3, used in cubic Lagrange interpolation calculations.
+     *
+     * This constant is utilized as part of the cubic Lagrange interpolation formula to scale
+     * and compute the interpolated value between points.
+     */
+
     const T _1div3;
+
+    /**
+     * @brief A constant representing the value 1/6, used in cubic Lagrange interpolation calculations.
+     *
+     * This constant is part of the cubic Lagrange interpolation formula, helping to scale and
+     * compute the interpolated value between data points.
+     */
+
     const T _1div6;
+
+    /**
+     * @brief A constant representing the value 1/2 (or 0.5), used in cubic Lagrange interpolation calculations.
+     *
+     * This constant is utilized in the cubic Lagrange interpolation formula to help adjust
+     * and scale the interpolated value between data points.
+     */
+
     const T _1div2;
 };
 
 // Cubic B-spline
 
+/**
+ * @struct cubic_bspline_interp
+ * @brief A template structure for performing cubic B-spline interpolation.
+ *
+ * This structure provides a mechanism for calculating cubic B-spline interpolation,
+ * which produces smooth curves through control points using B-spline basis functions.
+ * The cubic B-spline method ensures continuity in both the function and its first two derivatives.
+ * The template parameter @p T represents the data type of the values being interpolated.
+ *
+ * @tparam T The type of the data points to be interpolated (e.g., float, double).
+ */
+
 template <class T>
 struct cubic_bspline_interp
 {
+
+    /**
+     * @brief Default constructor for the cubic B-spline interpolation structure.
+     *
+     * Initializes constants used in the cubic B-spline interpolation process.
+     * These constants represent fractional coefficients that are used in the B-spline interpolation formula:
+     * - @p _2div3 is initialized to 2/3.
+     * - @p _1div6 is initialized to 1/6.
+     * - @p _1div2 is initialized to 0.5.
+     *
+     * The values are computed based on the template parameter type @p T.
+     */
+
     cubic_bspline_interp() : _2div3(T(2)/T(3)), _1div6(T(1)/T(6)), _1div2(0.5) {}
 
+    /**
+     * @brief Performs cubic B-spline interpolation between four values.
+     *
+     * This operator overload computes the cubic B-spline interpolation between four control points
+     * @p y0, @p y1, @p y2, and @p y3 at a given point @p x. B-spline interpolation uses basis functions
+     * to create a smooth curve through the control points, ensuring continuity in both the function
+     * and its first two derivatives.
+     *
+     * @param x The interpolation factor, typically between 0 and 1, representing the relative position
+     *          within the interval between @p y1 and @p y2.
+     * @param y0 The value before the starting point of interpolation, used to define the curve.
+     * @param y1 The starting value of the interpolation interval (interpolated at @p x = 0).
+     * @param y2 The ending value of the interpolation interval (interpolated at @p x = 1).
+     * @param y3 The value after the ending point of interpolation, used to define the curve.
+     * @return The interpolated value between @p y1 and @p y2 using cubic B-spline interpolation.
+     */
+
     T operator()(const T& x, const T& y0, const T& y1, const T& y2, const T& y3)
     {
         const T y0py2 = y0 + y2;
@@ -82,8 +304,31 @@ struct cubic_bspline_interp
 
 private:
 
+    /**
+     * @brief A constant representing the value 2/3, used in cubic B-spline interpolation calculations.
+     *
+     * This constant is part of the cubic B-spline interpolation formula, used to scale and compute
+     * the interpolated value between control points.
+     */
+
     const T _2div3;
+
+    /**
+     * @brief A constant representing the value 1/6, used in cubic B-spline interpolation calculations.
+     *
+     * This constant is utilized as part of the cubic B-spline interpolation formula to help scale
+     * and compute the interpolated value between control points.
+     */
+
     const T _1div6;
+
+    /**
+     * @brief A constant representing the value 1/2 (or 0.5), used in cubic B-spline interpolation calculations.
+     *
+     * This constant is part of the cubic B-spline interpolation formula and is used to help scale
+     * the interpolated value between control points.
+     */
+
     const T _1div2;
 };