Java曲线拟合库

Question

我希望找到一个简单的库，可以接受一系列二维点，并给我返回更多的点以建模曲线。基本上，我想获得像JFreeChart中这个示例所示的拟合效果： 。

但是 JFreeChart 的问题在于代码没有提供这种类型的API。我甚至查看了源代码，发现算法与实际绘图紧密耦合。

- Russell Leggett

---

问题被“挂起”：可以重新措辞问题，以在Java中提供曲线拟合代码的示例（当然，该代码将引入一些库，因此可以将其视为建议）。这个问题不是关于JFreeChart的，它只是接收点并显示它们，但不会生成额外的点。我实际上很惊讶Linked和Related没有显示出那个问题。 - David Tonhofer

Answer 1

Apache Commons Math 提供了一系列不错的算法，尤其是 "SplineInterpolator"，详情请见 API 文档

以下是一个使用 Groovy 调用插值函数 alpha(x) 和 beta(x) 的示例:

package example.com

import org.apache.commons.math3.analysis.interpolation.SplineInterpolator
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction

import statec.Extrapolate.Value;

class Interpolate {

    enum Value {
        ALPHA, BETA
    }

    def static xValues     = [
        -284086,
        -94784,
        31446,
        354837,
        667782,
        982191
    ]
    def static alphaValues = [
        71641,
        78245,
        80871,
        94045,
        105780,
        119616
    ]
    def static betaValues = [
        95552,
        103413,
        108667,
        128456,
        144686,
        171953
    ]

    static def getValueByName(Value value, int i) {
        def res
        switch (value) {
            case Value.ALPHA:
                res = alphaValues[i]
                break
            case Value.BETA:
                res = betaValues[i]
                break
            default:
                assert false
        }
        return res
    }

    static PolynomialSplineFunction interpolate(Value value) {
        def yValues = []
        int i = 0
        xValues.each {
            def y = getValueByName(value, i++)
            yValues << (y as Double)
        }
        SplineInterpolator spi = new SplineInterpolator()
        return spi.interpolate(xValues as double[], yValues as double[])
    }

    static void main(def argv) {
        //
        // Create a map mapping a Value instance to its interpolating function
        //
        def interpolations = [:]
        Value.values().each {
            interpolations[it] = interpolate(it)
        }
        //
        // Create an array of new x values to compute display.
        // Make sure the last "original" value is in there!
        // Note that the newxValues MUST stay within the range of the original xValues!
        //
        def newxValues = []
        for (long x = xValues[0] ; x < xValues[-1] ; x+=25000) {
            newxValues << x
        }
        newxValues << xValues[-1]
        //
        // Write interpolated values for ALPHA and BETA, adding the original values in columns 4 and 5
        //
        System.out << "X , ALPHA, BETA, X_orig, ALPHA_orig, BETA_orig" << "\n"
        int origIndex = 0
        newxValues.each { long x ->
            def alpha_ipol = interpolations[Value.ALPHA].value(x)
            def beta_ipol  = interpolations[Value.BETA].value(x)
            String out = "${x} ,  ${alpha_ipol} , ${beta_ipol}"
            if (x >= xValues[origIndex]) {
                out += ", ${xValues[origIndex]}, ${alphaValues[origIndex]}, ${betaValues[origIndex]}"
                origIndex++
            }
            System.out << out << "\n"
        }
    }
}

现在举个与主题无关但很有趣的EXTRAPOLATIONS实例。这里我们使用与上面相同的数据，但是使用一个二次多项式进行外推。当然，还要选择适当的类。再次用Groovy语言编写：

package example.com

import org.apache.commons.math3.analysis.polynomials.PolynomialFunction
import org.apache.commons.math3.fitting.PolynomialFitter
import org.apache.commons.math3.fitting.WeightedObservedPoint
import org.apache.commons.math3.optim.SimpleVectorValueChecker
import org.apache.commons.math3.optim.nonlinear.vector.jacobian.GaussNewtonOptimizer

class Extrapolate {

    enum Value {
        ALPHA, BETA
    }

    def static xValues     = [
        -284086,
        -94784,
        31446,
        354837,
        667782,
        982191
    ]
    def static alphaValues = [
        71641,
        78245,
        80871,
        94045,
        105780,
        119616
    ]
    def static betaValues = [
        95552,
        103413,
        108667,
        128456,
        144686,
        171953
    ]

    static def getValueByName(Value value, int i) {
        def res
        switch (value) {
            case Value.ALPHA:
                res = alphaValues[i]
                break
            case Value.BETA:
                res = betaValues[i]
                break
            default:
                assert false
        }
        return res
    }

    static PolynomialFunction extrapolate(Value value) {
        //
        // how to check that we converged
        //
        def checker
        A: {
            double relativeThreshold = 0.01
            double absoluteThreshold = 10
            int maxIter = 1000
            checker = new SimpleVectorValueChecker(relativeThreshold, absoluteThreshold, maxIter)
        }
        //
        // how to fit
        //
        def fitter
        B: {
            def useLUdecomposition = true
            def optimizer = new GaussNewtonOptimizer(useLUdecomposition, checker)
            fitter = new PolynomialFitter(optimizer)
            int i = 0
            xValues.each {
                def weight = 1.0
                def y = getValueByName(value, i++)
                fitter.addObservedPoint(new WeightedObservedPoint(weight, it, y))
            }
        }
        //
        // fit using a 2-degree polynomial; guess at a linear function at first
        // "a0 + (a1 * x) + (a2 * x²)"; a linear guess mean a2 == 0
        //
        def params
        C: {
            def mStart = getValueByName(value,0)
            def mEnd   = getValueByName(value,-1)
            def xStart = xValues[0]
            def xEnd   = xValues[-1]
            def a2 = 0
            def a1 = (mEnd - mStart) / (xEnd - xStart) // slope
            def a0 = mStart - (xStart * a1) // 0-intersection
            def guess = [a0 , a1 , a2]
            params = fitter.fit(guess as double[])
        }
        //
        // make polynomial
        //
        return new PolynomialFunction(params)
    }

    static void main(def argv) {
        //
        // Create a map mapping a Value instance to its interpolating function
        //
        def extrapolations = [:]
        Value.values().each {
            extrapolations[it] = extrapolate(it)
        }
        //
        // New x, this times reaching out past the range of the original xValues
        //
        def newxValues = []
        for (long x = xValues[0] - 400000L ; x < xValues[-1] + 400000L ; x += 10000) {
            newxValues << x
        }
        //
        // Write the extrapolated series ALPHA and BETA, adding the original values in columns 4 and 5
        //
        System.out << "X , ALPHA, BETA, X_orig, ALPHA_orig, BETA_orig" << "\n"
        int origIndex = 0
        newxValues.each { long x ->
            def alpha_xpol = extrapolations[Value.ALPHA].value(x)
            def beta_xpol  = extrapolations[Value.BETA].value(x)
            String out = "${x} ,  ${alpha_xpol} , ${beta_xpol}"
            if (origIndex < xValues.size() && x >= xValues[origIndex]) {
                out += ", ${xValues[origIndex]}, ${alphaValues[origIndex]}, ${betaValues[origIndex]}"
                origIndex++
            }
            System.out << out << "\n"
        }
    }
}

- David Tonhofer

Answer 2

我从未这样做过，但快速的谷歌搜索显示Bezier曲线已经在http://java.sun.com/j2se/1.5.0/docs/api/java/awt/geom/QuadCurve2D.Double.html中实现。

然后，您可以从该曲线获取getPathIterator()，根据文档所说，您将获得“形状边界的坐标”，这可能是您要寻找的内容。

- jbasko

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不，他不想这样做。他需要使用样条插值或一些启发式方法计算曲线的控制点。 - Matej

我建议您最好阅读http://en.wikipedia.org/wiki/Spline_(mathematics)和http://en.wikipedia.org/wiki/B%C3%A9zier_curve。贝塞尔曲线是建模这些曲线的一种方式。通过拥有此曲线上点的坐标，他有效地获得了所需的内容。 - jbasko