Android使用Catmull_Rom插值算法画光滑曲线图

一、算法核心思想

1、每次插值需要四个基础点（暂假设为A、B、C、D）。

2、根据已知的四个基础点，插值算法每次只能实现在中间两个点间画出光滑的曲线（此处就是B点和C点）。

二、工程代码

1、“Catmull_Rom插值算法”画光滑曲线的类（Catmull_Rom.java）

</pre><pre name="code" class="java">package com.example.test;

import java.util.ArrayList;

import android.content.Context;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Paint.Style;
import android.graphics.Path;
import android.util.AttributeSet;
import android.view.View;

public class Catmull_Rom extends View {
  private final Paint mGesturePaint = new Paint();
  private final Path mPath = new Path();

  private ArrayList<Point> point = new ArrayList<Point>();
  private ArrayList<Point> save = new ArrayList<Point>();

  public Catmull_Rom(Context context) {
    super(context);
  }

  public Catmull_Rom(Context context, AttributeSet attrs) {
    super(context, attrs);
    mGesturePaint.setAntiAlias(true);
    mGesturePaint.setStyle(Style.STROKE);
    mGesturePaint.setStrokeWidth(5);
    mGesturePaint.setColor(Color.WHITE);
  }

  public Catmull_Rom(Context context, AttributeSet attrs, int defStyle) {
    super(context, attrs, defStyle);
  }

  @Override
  protected void onDraw(Canvas canvas) {
    // TODO Auto-generated method stub
    super.onDraw(canvas);
    point.add(new Point(0, 0));
    point.add(new Point(1, 1));
    point.add(new Point(80, 100));
    point.add(new Point(160, 60));
    point.add(new Point(240, 120));
    point.add(new Point(320, 30));
    point.add(new Point(400, 200));
    point.add(new Point(401, 201));

    function_Catmull_Rom(point, 1000, save, mPath);
    canvas.drawPath(mPath, mGesturePaint);
  }

  public void function_Catmull_Rom(ArrayList<Point> point, int cha, ArrayList<Point> save, Path path) {
    if (point.size() < 4) {
      return;
    }
    path.moveTo(point.get(0).x, point.get(0).y);
    save.add(point.get(0));
    for (int index = 1; index < point.size() - 2; index++) {
      Point p0 = point.get(index - 1);
      Point p1 = point.get(index);
      Point p2 = point.get(index + 1);
      Point p3 = point.get(index + 2);

      for (int i = 1; i <= cha; i++) {
        float t = i * (1.0f / cha);
        float tt = t * t;
        float ttt = tt * t;

        Point pi = new Point(); // intermediate point
        pi.x = (float) (0.5 * (2 * p1.x + (p2.x - p0.x) * t + (2 * p0.x - 5 * p1.x + 4 * p2.x - p3.x) * tt + (3 * p1.x - p0.x - 3 * p2.x + p3.x)
            * ttt));
        pi.y = (float) (0.5 * (2 * p1.y + (p2.y - p0.y) * t + (2 * p0.y - 5 * p1.y + 4 * p2.y - p3.y) * tt + (3 * p1.y - p0.y - 3 * p2.y + p3.y)
            * ttt));
        path.lineTo(pi.x, pi.y);
        save.add(pi);
        pi = null;
      }
    }
    path.lineTo(point.get(point.size() - 1).x, point.get(point.size() - 1).y);
    save.add(point.get(point.size() - 1));
  }
}

2、主活动（MainActivity.java）

package com.example.test;

import android.app.Activity;
import android.os.Bundle;

public class MainActivity extends Activity {

  @Override
  protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
  }

}

3、主布局

<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="com.example.test.MainActivity" >

    <com.example.test.Catmull_Rom
        android:id="@+id/path"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content" />

</RelativeLayout>

4、坐标类（Point.java）

package com.example.test;

public class Point {
  public float x;
  public float y;

  public Point() {
  }

  public Point(float x, float y) {
    super();
    this.x = x;
    this.y = y;
  }

  public float getX() {
    return x;
  }

  public void setX(float x) {
    this.x = x;
  }

  public float getY() {
    return y;
  }

  public void setY(float y) {
    this.y = y;
  }

}

三、实现效果图如下：