// Copyright (c) FIRST and other WPILib contributors.
// Open Source Software; you can modify and/or share it under the terms of
// the WPILib BSD license file in the root directory of this project.

package edu.wpi.first.math.spline;

import org.ejml.simple.SimpleMatrix;

public class CubicHermiteSpline extends Spline {
  private static SimpleMatrix hermiteBasis;
  private final SimpleMatrix m_coefficients;

  /**
   * Constructs a cubic hermite spline with the specified control vectors. Each control vector
   * contains info about the location of the point and its first derivative.
   *
   * @param xInitialControlVector The control vector for the initial point in the x dimension.
   * @param xFinalControlVector The control vector for the final point in the x dimension.
   * @param yInitialControlVector The control vector for the initial point in the y dimension.
   * @param yFinalControlVector The control vector for the final point in the y dimension.
   */
  @SuppressWarnings("ParameterName")
  public CubicHermiteSpline(
      double[] xInitialControlVector,
      double[] xFinalControlVector,
      double[] yInitialControlVector,
      double[] yFinalControlVector) {
    super(3);

    // Populate the coefficients for the actual spline equations.
    // Row 0 is x coefficients
    // Row 1 is y coefficients
    final var hermite = makeHermiteBasis();
    final var x = getControlVectorFromArrays(xInitialControlVector, xFinalControlVector);
    final var y = getControlVectorFromArrays(yInitialControlVector, yFinalControlVector);

    final var xCoeffs = (hermite.mult(x)).transpose();
    final var yCoeffs = (hermite.mult(y)).transpose();

    m_coefficients = new SimpleMatrix(6, 4);

    for (int i = 0; i < 4; i++) {
      m_coefficients.set(0, i, xCoeffs.get(0, i));
      m_coefficients.set(1, i, yCoeffs.get(0, i));

      // Populate Row 2 and Row 3 with the derivatives of the equations above.
      // Then populate row 4 and 5 with the second derivatives.
      // Here, we are multiplying by (3 - i) to manually take the derivative. The
      // power of the term in index 0 is 3, index 1 is 2 and so on. To find the
      // coefficient of the derivative, we can use the power rule and multiply
      // the existing coefficient by its power.
      m_coefficients.set(2, i, m_coefficients.get(0, i) * (3 - i));
      m_coefficients.set(3, i, m_coefficients.get(1, i) * (3 - i));
    }

    for (int i = 0; i < 3; i++) {
      // Here, we are multiplying by (2 - i) to manually take the derivative. The
      // power of the term in index 0 is 2, index 1 is 1 and so on. To find the
      // coefficient of the derivative, we can use the power rule and multiply
      // the existing coefficient by its power.
      m_coefficients.set(4, i, m_coefficients.get(2, i) * (2 - i));
      m_coefficients.set(5, i, m_coefficients.get(3, i) * (2 - i));
    }
  }

  /**
   * Returns the coefficients matrix.
   *
   * @return The coefficients matrix.
   */
  @Override
  protected SimpleMatrix getCoefficients() {
    return m_coefficients;
  }

  /**
   * Returns the hermite basis matrix for cubic hermite spline interpolation.
   *
   * @return The hermite basis matrix for cubic hermite spline interpolation.
   */
  private SimpleMatrix makeHermiteBasis() {
    if (hermiteBasis == null) {
      // Given P(i), P'(i), P(i+1), P'(i+1), the control vectors, we want to find
      // the coefficients of the spline P(t) = a3 * t^3 + a2 * t^2 + a1 * t + a0.
      //
      // P(i)    = P(0)  = a0
      // P'(i)   = P'(0) = a1
      // P(i+1)  = P(1)  = a3 + a2 + a1 + a0
      // P'(i+1) = P'(1) = 3 * a3 + 2 * a2 + a1
      //
      // [ P(i)    ] = [ 0 0 0 1 ][ a3 ]
      // [ P'(i)   ] = [ 0 0 1 0 ][ a2 ]
      // [ P(i+1)  ] = [ 1 1 1 1 ][ a1 ]
      // [ P'(i+1) ] = [ 3 2 1 0 ][ a0 ]
      //
      // To solve for the coefficients, we can invert the 4x4 matrix and move it
      // to the other side of the equation.
      //
      // [ a3 ] = [  2  1 -2  1 ][ P(i)    ]
      // [ a2 ] = [ -3 -2  3 -1 ][ P'(i)   ]
      // [ a1 ] = [  0  1  0  0 ][ P(i+1)  ]
      // [ a0 ] = [  1  0  0  0 ][ P'(i+1) ]
      hermiteBasis =
          new SimpleMatrix(
              4,
              4,
              true,
              new double[] {
                +2.0, +1.0, -2.0, +1.0, -3.0, -2.0, +3.0, -1.0, +0.0, +1.0, +0.0, +0.0, +1.0, +0.0,
                +0.0, +0.0
              });
    }
    return hermiteBasis;
  }

  /**
   * Returns the control vector for each dimension as a matrix from the user-provided arrays in the
   * constructor.
   *
   * @param initialVector The control vector for the initial point.
   * @param finalVector The control vector for the final point.
   * @return The control vector matrix for a dimension.
   */
  private SimpleMatrix getControlVectorFromArrays(double[] initialVector, double[] finalVector) {
    if (initialVector.length != 2 || finalVector.length != 2) {
      throw new IllegalArgumentException("Size of vectors must be 2");
    }
    return new SimpleMatrix(
        4,
        1,
        true,
        new double[] {
          initialVector[0], initialVector[1],
          finalVector[0], finalVector[1]
        });
  }
}