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#! /usr/bin/python3
"""
3-D spline interpolation
(with graph drawing by matplotlib)
"""
import matplotlib.pyplot as plt
import sys
import os
import traceback

class SplineInterpolation:
    def __init__(self, ts, ds):
        """ Initialization

        :param list ts: item number list of given points
        :param list ds: coordinate list of given points
        """
        self.ts, self.ds = ts, ds
        self.n = len(self.ts) - 1
        h = self.__calc_h()
        w = self.__calc_w(h)
        matrix = self.__gen_matrix(h, w)
        v = [0] + self.__gauss_jordan(matrix) + [0]
        self.b = self.__calc_b(v)
        self.a = self.__calc_a(v)
        self.d = self.__calc_d()
        self.c = self.__calc_c(v)

    def interpolate(self, t):
        """ Interpolation

        :param  float t: value for a interpolate target
        :return float  : computated y-value
        """
        try:
            i = self.__search_i(t)
            return self.a[i] * (t - self.ts[i]) ** 3 \
                 + self.b[i] * (t - self.ts[i]) ** 2 \
                 + self.c[i] * (t - self.ts[i]) \
                 + self.d[i]
        except Exception as e:
            raise

    def __calc_h(self):
        """ H calculation

        :return list: h-values
        """
        try:
            return [self.ts[i + 1] - self.ts[i] for i in range(self.n)]
        except Exception as e:
            raise

    def __calc_w(self, h):
        """ W calculation

        :param  list h: h-values
        :return list  : w-values
        """
        try:
            return [
                6 * ((self.ds[i + 1] - self.ds[i]) / h[i]
                   - (self.ds[i] - self.ds[i - 1]) / h[i - 1])
                for i in range(1, self.n)
            ]
        except Exception as e:
            raise

    def __gen_matrix(self, h, w):
        """ Matrix generation

        :param  list   h: h-values
        :param  list   w: w-values
        :return list mtx: generated 2-D matrix
        """
        mtx = [[0 for _ in range(self.n)] for _ in range(self.n - 1)]
        try:
            for i in range(self.n - 1):
                mtx[i][i]     = 2 * (h[i] + h[i + 1])
                mtx[i][-1]    = w[i]
                if i == 0:
                    continue
                mtx[i - 1][i] = h[i]
                mtx[i][i - 1] = h[i]
            return mtx
        except Exception as e:
            raise

    def __gauss_jordan(self, matrix):
        """ Solving of simultaneous linear equations
            with Gauss-Jordan's method

        :param  list mtx: list of 2-D matrix
        :return list   v: answers list of simultaneous linear equations
        """
        v = []
        n = self.n - 1
        try:
            for k in range(n):
                p = matrix[k][k]
                for j in range(k, n + 1):
                    matrix[k][j] /= p
                for i in range(n):
                    if i == k:
                        continue
                    d = matrix[i][k]
                    for j in range(k, n + 1):
                        matrix[i][j] -= d * matrix[k][j]
            for row in matrix:
                v.append(row[-1])
            return v
        except Exception as e:
            raise

    def __calc_a(self, v):
        """ A calculation

        :param  list v: v-values
        :return list  : a-values
        """
        try:
            return [
                (v[i + 1] - v[i])
              / (6 * (self.ts[i + 1] - self.ts[i]))
                for i in range(self.n)
            ]
        except Exception as e:
            raise

    def __calc_b(self, v):
        """ B calculation

        :param  list v: v-values
        :return list  : b-values
        """
        try:
            return [v[i] / 2.0 for i in range(self.n)]
        except Exception as e:
            raise

    def __calc_c(self, v):
        """ C calculation

        :param  list v: v-values
        :return list  : c-values
        """
        try:
            return [
                (self.ds[i + 1] - self.ds[i]) / (self.ts[i + 1] - self.ts[i]) \
              - (self.ts[i + 1] - self.ts[i]) * (2 * v[i] + v[i + 1]) / 6
                for i in range(self.n)
            ]
        except Exception as e:
            raise

    def __calc_d(self):
        """ D calculation

        :return list: c-values
        """
        try:
            return self.ds
        except Exception as e:
            raise

    def __search_i(self, t):
        """ Index searching

        :param float t: t-value
        :return  int i: index
        """
        i, j = 0, len(self.ts) - 1
        try:
            while i < j:
                k = (i + j) // 2
                if self.ts[k] < t:
                    i = k + 1
                else:
                    j = k
            if i > 0:
                i -= 1
            return i
        except Exception as e:
            raise


class Graph:
    def __init__(self, xs_0, ys_0, zs_0, xs_1, ys_1, zs_1):
        self.xs_0, self.ys_0, self.zs_0, self.xs_1, self.ys_1, self.zs_1 = xs_0, ys_0, zs_0, xs_1, ys_1, zs_1

    def plot2d(self):
        try:
            plt.title("2-D Spline Interpolation in XY/XZ")
            plt.scatter(
                self.xs_1, self.ys_1, c = "g",
                label = "interpolated points XY", marker = "+"
            )
            plt.scatter(
                self.xs_0, self.ys_0, c = "r",
                label = "given points XY"
            )

            plt.scatter(
                self.xs_1, self.zs_1, c = "b",
                label = "interpolated points XZ", marker = "+"
            )
            plt.scatter(
                self.xs_0, self.zs_0, c = "k",
                label = "given points XZ"
            )
            plt.xlabel("x")
            plt.ylabel("y,z")
            plt.legend(loc = 2)
            plt.grid(color = "gray", linestyle = "--")
            #plt.show()
            #plt.savefig("spline_interpolation.png")
        except Exception as e:
            raise


    def plot3d(self):
        ax = plt.figure().add_subplot(projection='3d')

        x = self.xs_1
        y = self.ys_1
        z = self.zs_1

        ax.scatter(x, y, z, c='b', label='Interpolated points')
        ax.scatter(X, Y, Z, c='r', label='Given points')

        # Make legend, set axes limits and labels
        ax.legend()
        ax.set_xlim(min(X),max(X))
        ax.set_ylim(min(Y),max(Y))
        ax.set_zlim(min(Z),max(Z))
        ax.set_xlabel('X')
        ax.set_ylabel('Y')
        ax.set_zlabel('Z')

        # Customize the view angle so it's easier to see that the scatter points lie
        # on the plane y=0
        ax.view_init(elev=20., azim=-35)

        plt.show()


if __name__ == '__main__':
    # (N + 1) points
    T,X,Y,Z,A = [],[],[],[],[]
    fileName  = './points_input.txt'
    import csv
    with open(fileName, 'r') as f:
        reader = csv.reader(f)
        point_data = list(reader)
        for line in point_data:
            X.append(float(line[0]))
            Y.append(float(line[1]))
            Z.append(float(line[2]))
            A.append(float(line[3]))

    print('X:', X)
    print('Y:', Y)
    print('Z:', Z)
    print('A:', A)
    n=0
    for x in X:
        T.append(n+1.0)   
        n += 1
    print('T: ', T)
        
    #T = [1.0,2.0,3.0,4.0,5.0,6.0]
    #X = [0.0, 2.0, 3.0, 5.0, 7.0, 8.0]
    #Y = [0.8, 2.8, 3.2, 1.9, 4.5, 2.5]
    #Z = [-0.5, 1.8, 2.2, 0.9, 3.5, -1.5]

    S   = 0.1        # Step for interpolation
    S_1 = 1 / S      # Inverse of S
    xs_g, ys_g, zs_g, as_g = [], [], [], []  # List for graph
    try:
        # 3-D spline interpolation
        si = SplineInterpolation(T, X)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            x= si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, x))
            xs_g.append(x)        
        si = SplineInterpolation(T, Y)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            y = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, y))
            ys_g.append(y)
        si = SplineInterpolation(T, Z)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            z = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, z))
            zs_g.append(z)
        si = SplineInterpolation(T, A)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            a = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, z))
            as_g.append(a)

        # Write output to file
        file_out = 'output_file.txt'
        print('Writing output to ',file_out)
        n=0
        output = open(file_out, 'w')
        for x in xs_g:
            string=("G1 X{:4.2f} Y{:4.2f} Z{:4.2f} A{:4.2f}\n".format(xs_g[n], ys_g[n], zs_g[n], as_g[n]))
            output.write(string)
            n += 1
        # Closing file
        output.close()

        # Graph drawing
        g = Graph(X, Y, Z, xs_g, ys_g, zs_g)
        g.plot2d()
        g.plot3d()

    except Exception as e:
        traceback.print_exc()
        sys.exit(1)

#! /usr/bin/python3
"""
3-D spline interpolation
(with graph drawing by matplotlib)
"""
import matplotlib.pyplot as plt
import sys
import os
import traceback

class SplineInterpolation:
    def __init__(self, ts, ds):
        """ Initialization

        :param list ts: item number list of given points
        :param list ds: coordinate list of given points
        """
        self.ts, self.ds = ts, ds
        self.n = len(self.ts) - 1
        h = self.__calc_h()
        w = self.__calc_w(h)
        matrix = self.__gen_matrix(h, w)
        v = [0] + self.__gauss_jordan(matrix) + [0]
        self.b = self.__calc_b(v)
        self.a = self.__calc_a(v)
        self.d = self.__calc_d()
        self.c = self.__calc_c(v)

    def interpolate(self, t):
        """ Interpolation

        :param  float t: value for a interpolate target
        :return float  : computated y-value
        """
        try:
            i = self.__search_i(t)
            return self.a[i] * (t - self.ts[i]) ** 3 \
                 + self.b[i] * (t - self.ts[i]) ** 2 \
                 + self.c[i] * (t - self.ts[i]) \
                 + self.d[i]
        except Exception as e:
            raise

    def __calc_h(self):
        """ H calculation

        :return list: h-values
        """
        try:
            return [self.ts[i + 1] - self.ts[i] for i in range(self.n)]
        except Exception as e:
            raise

    def __calc_w(self, h):
        """ W calculation

        :param  list h: h-values
        :return list  : w-values
        """
        try:
            return [
                6 * ((self.ds[i + 1] - self.ds[i]) / h[i]
                   - (self.ds[i] - self.ds[i - 1]) / h[i - 1])
                for i in range(1, self.n)
            ]
        except Exception as e:
            raise

    def __gen_matrix(self, h, w):
        """ Matrix generation

        :param  list   h: h-values
        :param  list   w: w-values
        :return list mtx: generated 2-D matrix
        """
        mtx = [[0 for _ in range(self.n)] for _ in range(self.n - 1)]
        try:
            for i in range(self.n - 1):
                mtx[i][i]     = 2 * (h[i] + h[i + 1])
                mtx[i][-1]    = w[i]
                if i == 0:
                    continue
                mtx[i - 1][i] = h[i]
                mtx[i][i - 1] = h[i]
            return mtx
        except Exception as e:
            raise

    def __gauss_jordan(self, matrix):
        """ Solving of simultaneous linear equations
            with Gauss-Jordan's method

        :param  list mtx: list of 2-D matrix
        :return list   v: answers list of simultaneous linear equations
        """
        v = []
        n = self.n - 1
        try:
            for k in range(n):
                p = matrix[k][k]
                for j in range(k, n + 1):
                    matrix[k][j] /= p
                for i in range(n):
                    if i == k:
                        continue
                    d = matrix[i][k]
                    for j in range(k, n + 1):
                        matrix[i][j] -= d * matrix[k][j]
            for row in matrix:
                v.append(row[-1])
            return v
        except Exception as e:
            raise

    def __calc_a(self, v):
        """ A calculation

        :param  list v: v-values
        :return list  : a-values
        """
        try:
            return [
                (v[i + 1] - v[i])
              / (6 * (self.ts[i + 1] - self.ts[i]))
                for i in range(self.n)
            ]
        except Exception as e:
            raise

    def __calc_b(self, v):
        """ B calculation

        :param  list v: v-values
        :return list  : b-values
        """
        try:
            return [v[i] / 2.0 for i in range(self.n)]
        except Exception as e:
            raise

    def __calc_c(self, v):
        """ C calculation

        :param  list v: v-values
        :return list  : c-values
        """
        try:
            return [
                (self.ds[i + 1] - self.ds[i]) / (self.ts[i + 1] - self.ts[i]) \
              - (self.ts[i + 1] - self.ts[i]) * (2 * v[i] + v[i + 1]) / 6
                for i in range(self.n)
            ]
        except Exception as e:
            raise

    def __calc_d(self):
        """ D calculation

        :return list: c-values
        """
        try:
            return self.ds
        except Exception as e:
            raise

    def __search_i(self, t):
        """ Index searching

        :param float t: t-value
        :return  int i: index
        """
        i, j = 0, len(self.ts) - 1
        try:
            while i < j:
                k = (i + j) // 2
                if self.ts[k] < t:
                    i = k + 1
                else:
                    j = k
            if i > 0:
                i -= 1
            return i
        except Exception as e:
            raise


class Graph:
    def __init__(self, xs_0, ys_0, zs_0, xs_1, ys_1, zs_1):
        self.xs_0, self.ys_0, self.zs_0, self.xs_1, self.ys_1, self.zs_1 = xs_0, ys_0, zs_0, xs_1, ys_1, zs_1

    def plot2d(self):
        try:
            plt.title("2-D Spline Interpolation in XY/XZ")
            plt.scatter(
                self.xs_1, self.ys_1, c = "g",
                label = "interpolated points XY", marker = "+"
            )
            plt.scatter(
                self.xs_0, self.ys_0, c = "r",
                label = "given points XY"
            )

            plt.scatter(
                self.xs_1, self.zs_1, c = "b",
                label = "interpolated points XZ", marker = "+"
            )
            plt.scatter(
                self.xs_0, self.zs_0, c = "k",
                label = "given points XZ"
            )
            plt.xlabel("x")
            plt.ylabel("y,z")
            plt.legend(loc = 2)
            plt.grid(color = "gray", linestyle = "--")
            #plt.show()
            #plt.savefig("spline_interpolation.png")
        except Exception as e:
            raise


    def plot3d(self):
        ax = plt.figure().add_subplot(projection='3d')

        x = self.xs_1
        y = self.ys_1
        z = self.zs_1

        ax.scatter(x, y, z, c='b', label='Interpolated points')
        ax.scatter(X, Y, Z, c='r', label='Given points')

        # Make legend, set axes limits and labels
        ax.legend()
        ax.set_xlim(min(X),max(X))
        ax.set_ylim(min(Y),max(Y))
        ax.set_zlim(min(Z),max(Z))
        ax.set_xlabel('X')
        ax.set_ylabel('Y')
        ax.set_zlabel('Z')

        # Customize the view angle so it's easier to see that the scatter points lie
        # on the plane y=0
        ax.view_init(elev=20., azim=-35)

        plt.show()


if __name__ == '__main__':
    # (N + 1) points
    T,X,Y,Z,B,C = [],[],[],[],[],[]
    fileName  = './points_input.txt'
    import csv
    with open(fileName, 'r') as f:
        reader = csv.reader(f)
        point_data = list(reader)
        for line in point_data:
            X.append(float(line[0]))
            Y.append(float(line[1]))
            Z.append(float(line[2]))
            B.append(float(line[3]))
            C.append(float(line[4]))

    print('X:', X)
    print('Y:', Y)
    print('Z:', Z)
    print('B:', B)
    print('C:', C)
    n=0
    for x in X:
        T.append(n+1.0)   
        n += 1
    print('T: ', T)
        
    #T = [1.0,2.0,3.0,4.0,5.0,6.0]
    #X = [0.0, 2.0, 3.0, 5.0, 7.0, 8.0]
    #Y = [0.8, 2.8, 3.2, 1.9, 4.5, 2.5]
    #Z = [-0.5, 1.8, 2.2, 0.9, 3.5, -1.5]

    S   = 0.1        # Step for interpolation
    S_1 = 1 / S      # Inverse of S
    xs_g, ys_g, zs_g, bs_g, cs_g = [], [], [], [], []  # List for graph
    try:
        # 3-D spline interpolation
        si = SplineInterpolation(T, X)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            x= si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, x))
            xs_g.append(x)        
        si = SplineInterpolation(T, Y)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            y = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, y))
            ys_g.append(y)
        si = SplineInterpolation(T, Z)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            z = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, z))
            zs_g.append(z)
        si = SplineInterpolation(T, B)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            b = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, b))
            bs_g.append(b)
        si = SplineInterpolation(T, C)
        for t in [t / S_1 for t in range(int(T[0] / S), int(T[-1] / S) + 1)]:
            c = si.interpolate(t)
            #print("{:8.4f}, {:8.4f}".format(t, c))
            cs_g.append(c)

        # Write output to file
        file_out = 'output_file.txt'
        print('Writing output to ',file_out)
        n=0
        output = open(file_out, 'w')
        for x in xs_g:
            string=("G1 X{:4.2f} Y{:4.2f} Z{:4.2f} B{:4.2f} C{:4.2f}\n".format(xs_g[n], ys_g[n], zs_g[n], bs_g[n], cs_g[n]))
            output.write(string)
            n += 1
        # Closing file
        output.close()

        # Graph drawing
        g = Graph(X, Y, Z, xs_g, ys_g, zs_g)
        g.plot2d()
        g.plot3d()

    except Exception as e:
        traceback.print_exc()
        sys.exit(1)