嗯，克里斯的工作很有用。
我意识到他指出的算法由于计算错误以 0 结尾而提前终止的问题是由于一个点重复并且计算出的切线是无限的。
我已经根据 Kris 的代码完成了 Java 的翻译，我相信它可以正常工作：
编辑：
我仍在努力并试图在算法上获得更好的行为。我意识到，在非常尖的角度上，贝塞尔曲线根本表现不佳。所以我尝试将 Bezier 曲线与 Lines 结合起来，结果如下：
import java.awt.Point;
import java.awt.Shape;
import java.awt.geom.CubicCurve2D;
import java.awt.geom.Line2D;
import java.awt.geom.Point2D;
import java.util.LinkedList;
import java.util.List;
import java.util.concurrent.atomic.AtomicInteger;
import javax.vecmath.Point2d;
import javax.vecmath.Tuple2d;
import javax.vecmath.Vector2d;
/*
An Algorithm for Automatically Fitting Digitized Curves
by Philip J. Schneider
from "Graphics Gems", Academic Press, 1990
*/
public class FitCurves
{
/* Fit the Bezier curves */
private final static int MAXPOINTS = 10000;
private final static double epsilon = 1.0e-6;
/**
* Rubén:
* This is the sensitivity. When it is 1, it will create a line if it is at least as long as the
* distance from the previous control point.
* When it is greater, it will create less lines, and when it is lower, more lines.
* This is based on the previous control point since I believe it is a good indicator of the curvature
* where it is coming from, and we don't want long and second derived constant curves to be modeled with
* many lines.
*/
private static final double lineSensitivity=0.75;
public interface ResultCurve {
public Point2D getStart();
public Point2D getEnd();
public Shape getShape();
}
public static class BezierCurve implements ResultCurve {
public Point start;
public Point end;
public Point ctrl1;
public Point ctrl2;
public BezierCurve(Point2D start, Point2D ctrl1, Point2D ctrl2, Point2D end) {
this.start=new Point((int)Math.round(start.getX()), (int)Math.round(start.getY()));
this.end=new Point((int)Math.round(end.getX()), (int)Math.round(end.getY()));
this.ctrl1=new Point((int)Math.round(ctrl1.getX()), (int)Math.round(ctrl1.getY()));
this.ctrl2=new Point((int)Math.round(ctrl2.getX()), (int)Math.round(ctrl2.getY()));
if(this.ctrl1.x<=1 || this.ctrl1.y<=1) {
throw new IllegalStateException("ctrl1 invalid");
}
if(this.ctrl2.x<=1 || this.ctrl2.y<=1) {
throw new IllegalStateException("ctrl2 invalid");
}
}
public Shape getShape() {
return new CubicCurve2D.Float(start.x, start.y, ctrl1.x, ctrl1.y, ctrl2.x, ctrl2.y, end.x, end.y);
}
public Point getStart() {
return start;
}
public Point getEnd() {
return end;
}
}
public static class CurveSegment implements ResultCurve {
Point2D start;
Point2D end;
public CurveSegment(Point2D startP, Point2D endP) {
this.start=startP;
this.end=endP;
}
public Shape getShape() {
return new Line2D.Float(start, end);
}
public Point2D getStart() {
return start;
}
public Point2D getEnd() {
return end;
}
}
public static List<ResultCurve> FitCurve(double[][] points, double error) {
Point[] allPoints=new Point[points.length];
for(int i=0; i < points.length; i++) {
allPoints[i]=new Point((int) Math.round(points[i][0]), (int) Math.round(points[i][1]));
}
return FitCurve(allPoints, error);
}
public static List<ResultCurve> FitCurve(Point[] d, double error)
{
Vector2d tHat1, tHat2; /* Unit tangent vectors at endpoints */
int first=0;
int last=d.length-1;
tHat1 = ComputeLeftTangent(d, first);
tHat2 = ComputeRightTangent(d, last);
List<ResultCurve> result = new LinkedList<ResultCurve>();
FitCubic(d, first, last, tHat1, tHat2, error, result);
return result;
}
private static void FitCubic(Point[] d, int first, int last, Vector2d tHat1, Vector2d tHat2, double error, List<ResultCurve> result)
{
PointE[] bezCurve; /*Control points of fitted Bezier curve*/
double[] u; /* Parameter values for point */
double[] uPrime; /* Improved parameter values */
double maxError; /* Maximum fitting error */
int nPts; /* Number of points in subset */
double iterationError; /*Error below which you try iterating */
int maxIterations = 4; /* Max times to try iterating */
Vector2d tHatCenter; /* Unit tangent vector at splitPoint */
int i;
double errorOnLine=error;
iterationError = error * error;
nPts = last - first + 1;
AtomicInteger outputSplitPoint=new AtomicInteger();
/**
* Rubén: Here we try to fit the form with a line, and we mark the split point if we find any line with a minimum length
*/
/*
* the minimum distance for a length (so we don't create a very small line, when it could be slightly modeled with the previous Bezier,
* will be proportional to the distance of the previous control point of the last Bezier.
*/
BezierCurve res=null;
for(i=result.size()-1; i >0; i--) {
ResultCurve thisCurve=result.get(i);
if(thisCurve instanceof BezierCurve) {
res=(BezierCurve)thisCurve;
break;
}
}
Line seg=new Line(d[first], d[last]);
int nAcceptableTogether=0;
int startPoint=-1;
int splitPointTmp=-1;
if(Double.isInfinite(seg.getGradient())) {
for (i = first; i <= last; i++) {
double dist=Math.abs(d[i].x-d[first].x);
if(dist<errorOnLine) {
nAcceptableTogether++;
if(startPoint==-1) startPoint=i;
} else {
if(startPoint!=-1) {
double minLineLength=Double.POSITIVE_INFINITY;
if(res!=null) {
minLineLength=lineSensitivity * res.ctrl2.distance(d[startPoint]);
}
double thisFromStart=d[startPoint].distance(d[i]);
if(thisFromStart >= minLineLength) {
splitPointTmp=i;
startPoint=-1;
break;
}
}
nAcceptableTogether=0;
startPoint=-1;
}
}
} else {
//looking for the max squared error
for (i = first; i <= last; i++) {
Point thisPoint=d[i];
Point2D calculatedP=seg.getByX(thisPoint.getX());
double dist=thisPoint.distance(calculatedP);
if(dist<errorOnLine) {
nAcceptableTogether++;
if(startPoint==-1) startPoint=i;
} else {
if(startPoint!=-1) {
double thisFromStart=d[startPoint].distance(thisPoint);
double minLineLength=Double.POSITIVE_INFINITY;
if(res!=null) {
minLineLength=lineSensitivity * res.ctrl2.distance(d[startPoint]);
}
if(thisFromStart >= minLineLength) {
splitPointTmp=i;
startPoint=-1;
break;
}
}
nAcceptableTogether=0;
startPoint=-1;
}
}
}
if(startPoint!=-1) {
double minLineLength=Double.POSITIVE_INFINITY;
if(res!=null) {
minLineLength=lineSensitivity * res.ctrl2.distance(d[startPoint]);
}
if(d[startPoint].distance(d[last]) >= minLineLength) {
splitPointTmp=startPoint;
startPoint=-1;
} else {
nAcceptableTogether=0;
}
}
outputSplitPoint.set(splitPointTmp);
if(nAcceptableTogether==(last-first+1)) {
//This is a line!
System.out.println("line, length: " + d[first].distance(d[last]));
result.add(new CurveSegment(d[first], d[last]));
return;
}
/*********************** END of the Line approach, lets try the normal algorithm *******************************************/
if(splitPointTmp < 0) {
if(nPts == 2) {
double dist = d[first].distance(d[last]) / 3.0; //sqrt((last.x-first.x)^2 + (last.y-first.y)^2) / 3.0
bezCurve = new PointE[4];
bezCurve[0] = new PointE(d[first]);
bezCurve[3] = new PointE(d[last]);
bezCurve[1]=new PointE(tHat1).scaleAdd(dist, bezCurve[0]); //V2Add(&bezCurve[0], V2Scale(&tHat1, dist), &bezCurve[1]);
bezCurve[2]=new PointE(tHat2).scaleAdd(dist, bezCurve[3]); //V2Add(&bezCurve[3], V2Scale(&tHat2, dist), &bezCurve[2]);
result.add(new BezierCurve(bezCurve[0],bezCurve[1],bezCurve[2],bezCurve[3]));
return;
}
/* Parameterize points, and attempt to fit curve */
u = ChordLengthParameterize(d, first, last);
bezCurve = GenerateBezier(d, first, last, u, tHat1, tHat2);
/* Find max deviation of points to fitted curve */
maxError = ComputeMaxError(d, first, last, bezCurve, u, outputSplitPoint);
if(maxError < error) {
result.add(new BezierCurve(bezCurve[0],bezCurve[1],bezCurve[2],bezCurve[3]));
return;
}
/* If error not too large, try some reparameterization */
/* and iteration */
if(maxError < iterationError)
{
for(i = 0; i < maxIterations; i++) {
uPrime = Reparameterize(d, first, last, u, bezCurve);
bezCurve = GenerateBezier(d, first, last, uPrime, tHat1, tHat2);
maxError = ComputeMaxError(d, first, last, bezCurve, uPrime, outputSplitPoint);
if(maxError < error) {
result.add(new BezierCurve(bezCurve[0],bezCurve[1],bezCurve[2],bezCurve[3]));
return;
}
u = uPrime;
}
}
}
/* Fitting failed -- split at max error point and fit recursively */
tHatCenter = ComputeCenterTangent(d, outputSplitPoint.get());
FitCubic(d, first, outputSplitPoint.get(), tHat1, tHatCenter, error,result);
tHatCenter.negate();
FitCubic(d, outputSplitPoint.get(), last, tHatCenter, tHat2, error,result);
}
//Checked!!
static PointE[] GenerateBezier(Point2D[] d, int first, int last, double[] uPrime, Vector2d tHat1, Vector2d tHat2)
{
int i;
Vector2d[][] A = new Vector2d[MAXPOINTS][2]; /* Precomputed rhs for eqn */
int nPts; /* Number of pts in sub-curve */
double[][] C = new double[2][2]; /* Matrix C */
double[] X = new double[2]; /* Matrix X */
double det_C0_C1, /* Determinants of matrices */
det_C0_X,
det_X_C1;
double alpha_l, /* Alpha values, left and right */
alpha_r;
PointE[] bezCurve = new PointE[4]; /* RETURN bezier curve ctl pts */
nPts = last - first + 1;
/* Compute the A's */
for (i = 0; i < nPts; i++) {
Vector2d v1=new Vector2d(tHat1);
Vector2d v2=new Vector2d(tHat2);
v1.scale(B1(uPrime[i]));
v2.scale(B2(uPrime[i]));
A[i][0] = v1;
A[i][1] = v2;
}
/* Create the C and X matrices */
C[0][0] = 0.0;
C[0][1] = 0.0;
C[1][0] = 0.0;
C[1][1] = 0.0;
X[0] = 0.0;
X[1] = 0.0;
for (i = 0; i < nPts; i++) {
C[0][0] += A[i][0].dot(A[i][0]); //C[0][0] += V2Dot(&A[i][0], &A[i][0]);
C[0][1] += A[i][0].dot(A[i][1]); //C[0][1] += V2Dot(&A[i][0], &A[i][1]);
/* C[1][0] += V2Dot(&A[i][0], &A[i][9]);*/
C[1][0] = C[0][1]; //C[1][0] = C[0][1]
C[1][1] += A[i][1].dot(A[i][1]); //C[1][1] += V2Dot(&A[i][1], &A[i][1]);
Tuple2d scaleLastB2=new Vector2d(PointE.getPoint2d(d[last])); scaleLastB2.scale(B2(uPrime[i])); // V2ScaleIII(d[last], B2(uPrime[i]))
Tuple2d scaleLastB3=new Vector2d(PointE.getPoint2d(d[last])); scaleLastB3.scale(B3(uPrime[i])); // V2ScaleIII(d[last], B3(uPrime[i]))
Tuple2d dLastB2B3Sum=new Vector2d(scaleLastB2); dLastB2B3Sum.add(scaleLastB3); //V2AddII(V2ScaleIII(d[last], B2(uPrime[i])), V2ScaleIII(d[last], B3(uPrime[i]))
Tuple2d scaleFirstB1=new Vector2d(PointE.getPoint2d(d[first])); scaleFirstB1.scale(B1(uPrime[i])); //V2ScaleIII(d[first], B1(uPrime[i]))
Tuple2d sumScaledFirstB1andB2B3=new Vector2d(scaleFirstB1); sumScaledFirstB1andB2B3.add(dLastB2B3Sum); //V2AddII(V2ScaleIII(d[first], B1(uPrime[i])), V2AddII(V2ScaleIII(d[last], B2(uPrime[i])), V2ScaleIII(d[last], B3(uPrime[i])))
Tuple2d scaleFirstB0=new Vector2d(PointE.getPoint2d(d[first])); scaleFirstB0.scale(B0(uPrime[i])); //V2ScaleIII(d[first], B0(uPrime[i])
Tuple2d sumB0Rest=new Vector2d(scaleFirstB0); sumB0Rest.add(sumScaledFirstB1andB2B3); //V2AddII(V2ScaleIII(d[first], B0(uPrime[i])), V2AddII( V2ScaleIII(d[first], B1(uPrime[i])), V2AddII(V2ScaleIII(d[last], B2(uPrime[i])), V2ScaleIII(d[last], B3(uPrime[i]))))));
Vector2d tmp=new Vector2d(PointE.getPoint2d(d[first + i]));
tmp.sub(sumB0Rest);
X[0] += A[i][0].dot(tmp);
X[1] += A[i][1].dot(tmp);
}
/* Compute the determinants of C and X */
det_C0_C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1];
det_C0_X = C[0][0] * X[1] - C[1][0] * X[0];
det_X_C1 = X[0] * C[1][1] - X[1] * C[0][1];
/* Finally, derive alpha values */
alpha_l = (det_C0_C1 == 0) ? 0.0 : det_X_C1 / det_C0_C1;
alpha_r = (det_C0_C1 == 0) ? 0.0 : det_C0_X / det_C0_C1;
/* If alpha negative, use the Wu/Barsky heuristic (see text) */
/* (if alpha is 0, you get coincident control points that lead to
* divide by zero in any subsequent NewtonRaphsonRootFind() call. */
double segLength = d[first].distance(d[last]); //(d[first] - d[last]).Length;
double epsilonRel = epsilon * segLength;
if (alpha_l < epsilonRel || alpha_r < epsilonRel) {
/* fall back on standard (probably inaccurate) formula, and subdivide further if needed. */
double dist = segLength / 3.0;
bezCurve[0] = new PointE(d[first]);
bezCurve[3] = new PointE(d[last]);
Vector2d b1Tmp=new Vector2d(tHat1); b1Tmp.scaleAdd(dist, bezCurve[0].getPoint2d());
bezCurve[1] = new PointE(b1Tmp); //(tHat1 * dist) + bezCurve[0];
Vector2d b2Tmp=new Vector2d(tHat2); b2Tmp.scaleAdd(dist, bezCurve[3].getPoint2d());
bezCurve[2] = new PointE(b2Tmp); //(tHat2 * dist) + bezCurve[3];
return (bezCurve);
}
/* First and last control points of the Bezier curve are */
/* positioned exactly at the first and last data points */
/* Control points 1 and 2 are positioned an alpha distance out */
/* on the tangent vectors, left and right, respectively */
bezCurve[0] = new PointE(d[first]);
bezCurve[3] = new PointE(d[last]);
Vector2d alphaLTmp=new Vector2d(tHat1); alphaLTmp.scaleAdd(alpha_l, bezCurve[0].getPoint2d());
bezCurve[1] = new PointE(alphaLTmp); //(tHat1 * alpha_l) + bezCurve[0]
Vector2d alphaRTmp=new Vector2d(tHat2); alphaRTmp.scaleAdd(alpha_r, bezCurve[3].getPoint2d());
bezCurve[2] = new PointE(alphaRTmp); //(tHat2 * alpha_r) + bezCurve[3];
return (bezCurve);
}
/*
* Reparameterize:
* Given set of points and their parameterization, try to find
* a better parameterization.
*
*/
static double[] Reparameterize(Point2D[] d,int first,int last,double[] u, Point2D[] bezCurve)
{
int nPts = last-first+1;
int i;
double[] uPrime = new double[nPts]; /* New parameter values */
for (i = first; i <= last; i++) {
uPrime[i-first] = NewtonRaphsonRootFind(bezCurve, d[i], u[i-first]);
}
return uPrime;
}
/*
* NewtonRaphsonRootFind :
* Use Newton-Raphson iteration to find better root.
*/
static double NewtonRaphsonRootFind(Point2D[] Q, Point2D P, double u)
{
double numerator, denominator;
Point2D[] Q1 = new Point2D[3]; //Q'
Point2D[] Q2 = new Point2D[2]; //Q''
Point2D Q_u, Q1_u, Q2_u; /*u evaluated at Q, Q', & Q'' */
double uPrime; /* Improved u */
int i;
/* Compute Q(u) */
Q_u = BezierII(3, Q, u);
/* Generate control vertices for Q' */
for (i = 0; i <= 2; i++) {
double qXTmp=(Q[i+1].getX() - Q[i].getX()) * 3.0; //Q1[i].x = (Q[i+1].x - Q[i].x) * 3.0;
double qYTmp=(Q[i+1].getY() - Q[i].getY()) * 3.0; //Q1[i].y = (Q[i+1].y - Q[i].y) * 3.0;
Q1[i]=new Point2D.Double(qXTmp, qYTmp);
}
/* Generate control vertices for Q'' */
for (i = 0; i <= 1; i++) {
double qXTmp=(Q1[i+1].getX() - Q1[i].getX()) * 2.0; //Q2[i].x = (Q1[i+1].x - Q1[i].x) * 2.0;
double qYTmp=(Q1[i+1].getY() - Q1[i].getY()) * 2.0; //Q2[i].y = (Q1[i+1].y - Q1[i].y) * 2.0;
Q2[i]=new Point2D.Double(qXTmp, qYTmp);
}
/* Compute Q'(u) and Q''(u) */
Q1_u = BezierII(2, Q1, u);
Q2_u = BezierII(1, Q2, u);
/* Compute f(u)/f'(u) */
numerator = (Q_u.getX() - P.getX()) * (Q1_u.getX()) + (Q_u.getY() - P.getY()) * (Q1_u.getY());
denominator = (Q1_u.getX()) * (Q1_u.getX()) + (Q1_u.getY()) * (Q1_u.getY()) + (Q_u.getX() - P.getX()) * (Q2_u.getX()) + (Q_u.getY() - P.getY()) * (Q2_u.getY());
if (denominator == 0.0f) return u;
/* u = u - f(u)/f'(u) */
uPrime = u - (numerator/denominator);
return (uPrime);
}
/*
* Bezier :
* Evaluate a Bezier curve at a particular parameter value
*
*/
static Point2D BezierII(int degree, Point2D[] V, double t)
{
int i, j;
Point2D Q; /* Point on curve at parameter t */
Point2D[] Vtemp; /* Local copy of control points */
/* Copy array */
Vtemp = new Point2D[degree+1];
for (i = 0; i <= degree; i++) {
Vtemp[i] = new Point2D.Double(V[i].getX(), V[i].getY());
}
/* Triangle computation */
for (i = 1; i <= degree; i++) {
for (j = 0; j <= degree-i; j++) {
double tmpX, tmpY;
tmpX = (1.0 - t) * Vtemp[j].getX() + t * Vtemp[j+1].getX();
tmpY = (1.0 - t) * Vtemp[j].getY() + t * Vtemp[j+1].getY();
Vtemp[j].setLocation(tmpX, tmpY);
}
}
Q = Vtemp[0];
return Q;
}
/*
* B0, B1, B2, B3 :
* Bezier multipliers
*/
static double B0(double u)
{
double tmp = 1.0 - u;
return (tmp * tmp * tmp);
}
static double B1(double u)
{
double tmp = 1.0 - u;
return (3 * u * (tmp * tmp));
}
static double B2(double u)
{
double tmp = 1.0 - u;
return (3 * u * u * tmp);
}
static double B3(double u)
{
return (u * u * u);
}
/*
* ComputeLeftTangent, ComputeRightTangent, ComputeCenterTangent :
*Approximate unit tangents at endpoints and "center" of digitized curve
*/
static Vector2d ComputeLeftTangent(Point[] d, int end)
{
Vector2d tHat1=new Vector2d(PointE.getPoint2d(d[end+1]));
tHat1.sub(PointE.getPoint2d(d[end]));
tHat1.normalize();
return tHat1;
}
static Vector2d ComputeRightTangent(Point[] d, int end)
{
//tHat2 = V2SubII(d[end-1], d[end]); tHat2 = *V2Normalize(&tHat2);
Vector2d tHat2=new Vector2d(PointE.getPoint2d(d[end-1]));
tHat2.sub(PointE.getPoint2d(d[end]));
tHat2.normalize();
return tHat2;
}
static Vector2d ComputeCenterTangent(Point[] d ,int center)
{
//V1 = V2SubII(d[center-1], d[center]);
Vector2d V1=new Vector2d(PointE.getPoint2d(d[center-1]));
V1.sub(new PointE(d[center]).getPoint2d());
//V2 = V2SubII(d[center], d[center+1]);
Vector2d V2=new Vector2d(PointE.getPoint2d(d[center]));
V2.sub(PointE.getPoint2d(d[center+1]));
//tHatCenter.x = (V1.x + V2.x)/2.0;
//tHatCenter.y = (V1.y + V2.y)/2.0;
//tHatCenter = *V2Normalize(&tHatCenter);
Vector2d tHatCenter=new Vector2d((V1.x + V2.x)/2.0, (V1.y + V2.y)/2.0);
tHatCenter.normalize();
return tHatCenter;
}
/*
* ChordLengthParameterize :
* Assign parameter values to digitized points
* using relative distances between points.
*/
static double[] ChordLengthParameterize(Point[] d,int first,int last)
{
int i;
double[] u = new double[last-first+1]; /* Parameterization */
u[0] = 0.0;
for (i = first+1; i <= last; i++) {
u[i-first] = u[i-first-1] + d[i-1].distance(d[i]);
}
for (i = first + 1; i <= last; i++) {
u[i-first] = u[i-first] / u[last-first];
}
return u;
}
/*
* ComputeMaxError :
* Find the maximum squared distance of digitized points
* to fitted curve.
*/
static double ComputeMaxError(Point2D[] d, int first, int last, Point2D[] bezCurve, double[] u, AtomicInteger splitPoint)
{
int i;
double maxDist; /* Maximum error */
double dist; /* Current error */
Point2D P; /* Point on curve */
Vector2d v; /* Vector from point to curve */
int tmpSplitPoint=(last - first + 1)/2;
maxDist = 0.0;
for (i = first + 1; i < last; i++) {
P = BezierII(3, bezCurve, u[i-first]);
v = new Vector2d(P.getX() - d[i].getX(), P.getY() - d[i].getY()); //P - d[i];
dist = v.lengthSquared();
if (dist >= maxDist) {
maxDist = dist;
tmpSplitPoint=i;
}
}
splitPoint.set(tmpSplitPoint);
return maxDist;
}
/**
* This is kind of a bridge between javax.vecmath and java.util.Point2D
* @author Ruben
* @since 1.24
*/
public static class PointE extends Point2D.Double {
private static final long serialVersionUID = -1482403817370130793L;
public PointE(Tuple2d tup) {
super(tup.x, tup.y);
}
public PointE(Point2D p) {
super(p.getX(), p.getY());
}
public PointE(double x, double y) {
super(x, y);
}
public PointE scale(double dist) {
return new PointE(getX()*dist, getY()*dist);
}
public PointE scaleAdd(double dist, Point2D sum) {
return new PointE(getX()*dist + sum.getX(), getY()*dist + sum.getY());
}
public PointE substract(Point2D p) {
return new PointE(getX() - p.getX(), getY() - p.getY());
}
public Point2d getPoint2d() {
return getPoint2d(this);
}
public static Point2d getPoint2d(Point2D p) {
return new Point2d(p.getX(), p.getY());
}
}
这是后者工作的图像，白色是线条，红色是贝塞尔曲线：
使用这种方法，我们使用的控制点更少，而且更准确。
线条创建的敏感度可以通过 lineSensitivity 属性进行调整。如果您根本不想使用线条，只需将其设置为无限。
我相信这可以改进。随意贡献:)
算法没有做任何减少，由于我的帖子中解释的第一个，我们必须运行一个。这是一个 DouglasPeuckerReduction 实现，对我来说，在某些情况下它比额外的 FitCurves 更有效（存储的点更少，渲染的速度更快）
import java.awt.Point;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
public class DouglasPeuckerReduction {
public static List<Point> reduce(Point[] points, double tolerance)
{
if (points == null || points.length < 3) return Arrays.asList(points);
int firstPoint = 0;
int lastPoint = points.length - 1;
SortedList<Integer> pointIndexsToKeep;
try {
pointIndexsToKeep = new SortedList<Integer>(LinkedList.class);
} catch (Throwable t) {
t.printStackTrace(System.out);
ErrorReport.process(t);
return null;
}
//Add the first and last index to the keepers
pointIndexsToKeep.add(firstPoint);
pointIndexsToKeep.add(lastPoint);
//The first and the last point cannot be the same
while (points[firstPoint].equals(points[lastPoint])) {
lastPoint--;
}
reduce(points, firstPoint, lastPoint, tolerance, pointIndexsToKeep);
List<Point> returnPoints = new ArrayList<Point>(pointIndexsToKeep.size());
for (int pIndex : pointIndexsToKeep) {
returnPoints.add(points[pIndex]);
}
return returnPoints;
}
private static void reduce(Point[] points, int firstPoint, int lastPoint, double tolerance, List<Integer> pointIndexsToKeep) {
double maxDistance = 0;
int indexFarthest = 0;
Line tmpLine=new Line(points[firstPoint], points[lastPoint]);
for (int index = firstPoint; index < lastPoint; index++) {
double distance = tmpLine.getDistanceFrom(points[index]);
if (distance > maxDistance) {
maxDistance = distance;
indexFarthest = index;
}
}
if (maxDistance > tolerance && indexFarthest != 0) {
//Add the largest point that exceeds the tolerance
pointIndexsToKeep.add(indexFarthest);
reduce(points, firstPoint, indexFarthest, tolerance, pointIndexsToKeep);
reduce(points, indexFarthest, lastPoint, tolerance, pointIndexsToKeep);
}
}
}
我在这里使用我自己的 SortedList 和 Line 实现。对不起，你必须自己做。