用JFreeChart绘制光滑曲线，利用最小二乘法数学原理计算，供大家参考，具体内容如下

绘制图形：

代码：

FittingCurve.java

package org.jevy; import java.util.ArrayList; import java.util.List; import org.jfree.chart.ChartFactory; import org.jfree.chart.ChartPanel; import org.jfree.chart.JFreeChart; import org.jfree.chart.axis.ValueAxis; import org.jfree.chart.plot.PlotOrientation; import org.jfree.chart.plot.XYPlot; import org.jfree.chart.renderer.xy.XYItemRenderer; import org.jfree.chart.renderer.xy.XYLineAndShapeRenderer; import org.jfree.data.xy.XYDataset; import org.jfree.data.xy.XYSeries; import org.jfree.data.xy.XYSeriesCollection; import org.jfree.ui.ApplicationFrame; import org.jfree.ui.RefineryUtilities; public class FittingCurve extends ApplicationFrame{ List<Double> equation = null; //设置多项式的次数 int times = 2; public FittingCurve(String title) { super(title); //使用最小二乘法计算拟合多项式中各项前的系数。 //多项式的次数从高到低，该函数需要的参数：x轴数据<List>，y轴数据<List>，多项式的次数<2> this.equation = this.getCurveEquation(this.getData().get(0),this.getData().get(1),this.times); //生成Chart JFreeChart chart = this.getChart(); ChartPanel chartPanel = new ChartPanel(chart); chartPanel.setPreferredSize(new java.awt.Dimension(500, 270)); chartPanel.setMouseZoomable(true, false); setContentPane(chartPanel); } public static void main(String[] args) { // TODO Auto-generated method stub FittingCurve demo = new FittingCurve("XYFittingCurve"); demo.pack(); RefineryUtilities.centerFrameOnScreen(demo); demo.setVisible(true); } //生成chart public JFreeChart getChart(){ //获取X和Y轴数据集 XYDataset xydataset = this.getXYDataset(); //创建用坐标表示的折线图 JFreeChart xyChart = ChartFactory.createXYLineChart( "二次多项式拟合光滑曲线", "X轴", "Y轴", xydataset, PlotOrientation.VERTICAL, true, true, false); //生成坐标点点的形状 XYPlot plot = (XYPlot) xyChart.getPlot(); XYItemRenderer r = plot.getRenderer(); if (r instanceof XYLineAndShapeRenderer) { XYLineAndShapeRenderer renderer = (XYLineAndShapeRenderer) r; renderer.setBaseShapesVisible(false);//坐标点的形状是否可见 renderer.setBaseShapesFilled(false); } ValueAxis yAxis = plot.getRangeAxis(); yAxis.setLowerMargin(2); return xyChart; } //数据集按照逻辑关系添加到对应的集合 public XYDataset getXYDataset() { //预设数据点数据集 XYSeries s2 = new XYSeries("点点连线"); for(int i=0; i<data.get(0).size(); i++){ s2.add(data.get(0).get(i),data.get(1).get(i)); } // 拟合曲线绘制 数据集 XYSeries s1 = new XYSeries("拟合曲线"); //获取拟合多项式系数，equation在构造方法中已经实例化 List<Double> list = this.equation; //获取预设的点数据 List<List<Double>> data = this.getData(); //get Max and Min of x; List<Double> xList = data.get(0); double max =this.getMax(xList); double min = this.getMin(xList); double step = max - min; double x = min; double step2 = step/800.0; //按照多项式的形式 还原多项式，并利用多项式计算给定x时y的值 for(int i=0; i<800; i++){ x = x + step2; int num = list.size()-1; double temp = 0.0; for(int j=0; j<list.size(); j++){ temp = temp + Math.pow(x, (num-j))*list.get(j); } s1.add(x, temp); } //把预设数据集合拟合数据集添加到XYSeriesCollection XYSeriesCollection dataset = new XYSeriesCollection(); dataset.addSeries(s1); dataset.addSeries(s2); return dataset; } //模拟设置绘图数据（点） public List<List<Double>> getData(){ //x为x轴坐标 List<Double> x = new ArrayList<Double>(); List<Double> y = new ArrayList<Double>(); for(int i=0; i<10; i++){ x.add(-5.0+i); } y.add(26.0); y.add(17.1); y.add(10.01); y.add(5.0); y.add(2.01); y.add(1.0); y.add(2.0); y.add(5.01); y.add(10.1); y.add(17.001); List<List<Double>> list = new ArrayList<List<Double>>(); list.add(x); list.add(y); return list; } //以下代码为最小二乘法计算多项式系数 //最小二乘法多项式拟合 public List<Double> getCurveEquation(List<Double> x, List<Double> y, int m){ if(x.size() != y.size() || x.size() <= m+1){ return new ArrayList<Double>(); } List<Double> result = new ArrayList<Double>(); List<Double> S = new ArrayList<Double>(); List<Double> T = new ArrayList<Double>(); //计算S0 S1 …… S2m for(int i=0; i<=2*m; i++){ double si = 0.0; for(double xx:x){ si = si + Math.pow(xx, i); } S.add(si); } //计算T0 T1 …… Tm for(int j=0; j<=m; j++){ double ti = 0.0; for(int k=0; k<y.size(); k++){ ti = ti + y.get(k)*Math.pow(x.get(k), j); } T.add(ti); } //把S和T 放入二维数组，作为矩阵 double[][] matrix = new double[m+1][m+2]; for(int k=0; k<m+1; k++){ double[] matrixi = matrix[k]; for(int q=0; q<m+1; q++){ matrixi[q] = S.get(k+q); } matrixi[m+1] = T.get(k); } for(int p=0; p<matrix.length; p++){ for(int pp=0; pp<matrix[p].length; pp++){ System.out.print(" matrix["+p+"]["+pp+"]="+matrix[p][pp]); } System.out.println(); } //把矩阵转化为三角矩阵 matrix = this.matrixConvert(matrix); //计算多项式系数，多项式从高到低排列 result = this.MatrixCalcu(matrix); return result; } //矩阵转换为三角矩阵 public double[][] matrixConvert(double[][] d){ for(int i=0; i<d.length-1; i++){ double[] dd1 = d[i]; double num1 = dd1[i]; for(int j=i; j<d.length-1;j++ ){ double[] dd2 = d[j+1]; double num2 = dd2[i]; for(int k=0; k<dd2.length; k++){ dd2[k] = (dd2[k]*num1 - dd1[k]*num2); } } } for(int ii=0; ii<d.length; ii++){ for(int kk=0; kk<d[ii].length; kk++) System.out.print(d[ii][kk]+" "); System.out.println(); } return d; } //计算一元多次方程前面的系数， 其排列为 xm xm-1 …… x0（多项式次数从高到低排列） public List<Double> MatrixCalcu(double[][] d){ int i = d.length -1; int j = d[0].length -1; List<Double> list = new ArrayList<Double>(); double res = d[i][j]/d[i][j-1]; list.add(res); for(int k=i-1; k>=0; k--){ double num = d[k][j]; for(int q=j-1; q>k; q--){ num = num - d[k][q]*list.get(j-1-q); } res = num/d[k][k]; list.add(res); } return list; } //获取List中Double数据的最大最小值 public double getMax(List<Double> data){ double res = data.get(0); for(int i=0; i<data.size()-1; i++){ if(res<data.get(i+1)){ res = data.get(i+1); } } return res; } public double getMin(List<Double> data){ double res = data.get(0); for(int i=0; i<data.size()-1; i++){ if(res>data.get(i+1)){ res = data.get(i+1); } } return res; } }

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