示例#1
0
		/// <summary>
		/// Compute spline coefficients for the specified x,y points.
		/// This does the "natural spline" style for ends.
		/// This can extrapolate off the ends of the splines.
		/// You must provide points in X sort order.
		/// </summary>
		/// <param name="x">Input. X coordinates to fit.</param>
		/// <param name="y">Input. Y coordinates to fit.</param>
		/// <param name="startSlope">Optional slope constraint for the first point. Single.NaN means no constraint.</param>
		/// <param name="endSlope">Optional slope constraint for the final point. Single.NaN means no constraint.</param>
		/// <param name="debug">Turn on console output. Default is false.</param>
		public void Fit(float[] x, float[] y, float startSlope = float.NaN, float endSlope = float.NaN, bool debug = false)
		{
			if (Single.IsInfinity(startSlope) || Single.IsInfinity(endSlope))
			{
				throw new Exception("startSlope and endSlope cannot be infinity.");
			}

			// Save x and y for eval
			this.xOrig = x;
			this.yOrig = y;

			int n = x.Length;
			float[] r = new float[n]; // the right hand side numbers: wikipedia page overloads b

			TriDiagonalMatrixF m = new TriDiagonalMatrixF(n);
			float dx1, dx2, dy1, dy2;

			// First row is different (equation 16 from the article)
			if (float.IsNaN(startSlope))
			{
				dx1 = x[1] - x[0];
				m.C[0] = 1.0f / dx1;
				m.B[0] = 2.0f * m.C[0];
				r[0] = 3 * (y[1] - y[0]) / (dx1 * dx1);
			}
			else
			{
				m.B[0] = 1;
				r[0] = startSlope;
			}

			// Body rows (equation 15 from the article)
			for (int i = 1; i < n - 1; i++)
			{
				dx1 = x[i] - x[i - 1];
				dx2 = x[i + 1] - x[i];

				m.A[i] = 1.0f / dx1;
				m.C[i] = 1.0f / dx2;
				m.B[i] = 2.0f * (m.A[i] + m.C[i]);

				dy1 = y[i] - y[i - 1];
				dy2 = y[i + 1] - y[i];
				r[i] = 3 * (dy1 / (dx1 * dx1) + dy2 / (dx2 * dx2));
			}

			// Last row also different (equation 17 from the article)
			if (float.IsNaN(endSlope))
			{
				dx1 = x[n - 1] - x[n - 2];
				dy1 = y[n - 1] - y[n - 2];
				m.A[n - 1] = 1.0f / dx1;
				m.B[n - 1] = 2.0f * m.A[n - 1];
				r[n - 1] = 3 * (dy1 / (dx1 * dx1));
			}
			else
			{
				m.B[n - 1] = 1;
				r[n - 1] = endSlope;
			}

			if (debug) Console.WriteLine("Tri-diagonal matrix:\n{0}", m.ToDisplayString(":0.0000", "  "));
			if (debug) Console.WriteLine("r: {0}", ArrayUtil.ToString<float>(r));

			// k is the solution to the matrix
			float[] k = m.Solve(r);
			if (debug) Console.WriteLine("k = {0}", ArrayUtil.ToString<float>(k));

			// a and b are each spline's coefficients
			this.a = new float[n - 1];
			this.b = new float[n - 1];

			for (int i = 1; i < n; i++)
			{
				dx1 = x[i] - x[i - 1];
				dy1 = y[i] - y[i - 1];
				a[i - 1] = k[i - 1] * dx1 - dy1; // equation 10 from the article
				b[i - 1] = -k[i] * dx1 + dy1; // equation 11 from the article
			}

			if (debug) Console.WriteLine("a: {0}", ArrayUtil.ToString<float>(a));
			if (debug) Console.WriteLine("b: {0}", ArrayUtil.ToString<float>(b));
		}
示例#2
0
        /// <summary>
        /// Compute spline coefficients for the specified x,y points.
        /// This does the "natural spline" style for ends.
        /// This can extrapolate off the ends of the splines.
        /// You must provide points in X sort order.
        /// </summary>
        /// <param name="x">Input. X coordinates to fit.</param>
        /// <param name="y">Input. Y coordinates to fit.</param>
        /// <param name="startSlope">Optional slope constraint for the first point. Single.NaN means no constraint.</param>
        /// <param name="endSlope">Optional slope constraint for the final point. Single.NaN means no constraint.</param>
        /// <param name="debug">Turn on console output. Default is false.</param>
        public void Fit(float[] x, float[] y, float startSlope = float.NaN, float endSlope = float.NaN, bool debug = false)
        {
            if (Single.IsInfinity(startSlope) || Single.IsInfinity(endSlope))
            {
                throw new Exception("startSlope and endSlope cannot be infinity.");
            }

            // Save x and y for eval
            this.xOrig = x;
            this.yOrig = y;

            int n = x.Length;

            float[] r = new float[n];             // the right hand side numbers: wikipedia page overloads b

            TriDiagonalMatrixF m = new TriDiagonalMatrixF(n);
            float dx1, dx2, dy1, dy2;

            // First row is different (equation 16 from the article)
            if (float.IsNaN(startSlope))
            {
                dx1    = x[1] - x[0];
                m.C[0] = 1.0f / dx1;
                m.B[0] = 2.0f * m.C[0];
                r[0]   = 3 * (y[1] - y[0]) / (dx1 * dx1);
            }
            else
            {
                m.B[0] = 1;
                r[0]   = startSlope;
            }

            // Body rows (equation 15 from the article)
            for (int i = 1; i < n - 1; i++)
            {
                dx1 = x[i] - x[i - 1];
                dx2 = x[i + 1] - x[i];

                m.A[i] = 1.0f / dx1;
                m.C[i] = 1.0f / dx2;
                m.B[i] = 2.0f * (m.A[i] + m.C[i]);

                dy1  = y[i] - y[i - 1];
                dy2  = y[i + 1] - y[i];
                r[i] = 3 * (dy1 / (dx1 * dx1) + dy2 / (dx2 * dx2));
            }

            // Last row also different (equation 17 from the article)
            if (float.IsNaN(endSlope))
            {
                dx1        = x[n - 1] - x[n - 2];
                dy1        = y[n - 1] - y[n - 2];
                m.A[n - 1] = 1.0f / dx1;
                m.B[n - 1] = 2.0f * m.A[n - 1];
                r[n - 1]   = 3 * (dy1 / (dx1 * dx1));
            }
            else
            {
                m.B[n - 1] = 1;
                r[n - 1]   = endSlope;
            }

            if (debug)
            {
                Console.WriteLine("Tri-diagonal matrix:\n{0}", m.ToDisplayString(":0.0000", "  "));
            }
            if (debug)
            {
                Console.WriteLine("r: {0}", ArrayUtil.ToString <float>(r));
            }

            // k is the solution to the matrix
            float[] k = m.Solve(r);
            if (debug)
            {
                Console.WriteLine("k = {0}", ArrayUtil.ToString <float>(k));
            }

            // a and b are each spline's coefficients
            this.a = new float[n - 1];
            this.b = new float[n - 1];

            for (int i = 1; i < n; i++)
            {
                dx1      = x[i] - x[i - 1];
                dy1      = y[i] - y[i - 1];
                a[i - 1] = k[i - 1] * dx1 - dy1;              // equation 10 from the article
                b[i - 1] = -k[i] * dx1 + dy1;                 // equation 11 from the article
            }

            if (debug)
            {
                Console.WriteLine("a: {0}", ArrayUtil.ToString <float>(a));
            }
            if (debug)
            {
                Console.WriteLine("b: {0}", ArrayUtil.ToString <float>(b));
            }
        }