移动图形的一条线增大或缩小图形，但是保持形状不变，求移动后移动线与另外两条相交线的新交点（或者说图形的新坐标）。如图所示：将直线①移动到虚线②处，求虚线处的E、F两个新坐标。
思路：
已经AC点求出直线①的斜率，当①移动到②处时，直线②的斜率和①是相同的，同时可知②线上的一个已经点（即鼠标抬起时ACTION_UP事件中的点）这样就可以求出直线②的方程。直线③和④方程分别由BC和AB求得，求新的相交点让方程相等即可。
注：
这里的斜率是按照数学中的第一象限求得的，但是在Android中整个屏幕所处的象限与数学中是不一样的，整个屏幕以左上角为（0,0）点向右X增大向下Y增大，但是并不影响求得直线方程求出相交点。
TIM截图20170727151205.png
/**
* 计算直线斜率
*/
public static float calSlope(Point point, Point point1) {
float k = (point1.getY() - point.getY()) / (point1.getX() - point.getX());
return k;
}
/**
* 根据 不同直线上的两个点 求两条直线的相交点x坐标
* @param moveLineK 移动线斜率
* @param crossLineK 相交线斜率
* @param movePoint 移动线抬起时鼠标点坐标
* @param inwardPoint 相交线的两个坐标中任意一个
* @return
*/
public static float calCrosspointX(float moveLineK, float crossLineK, Point movePoint, Point inwardPoint) {
float x, temp;
float movePointX = movePoint.getX();
float movePointY = movePoint.getY();
float inwardPointX = inwardPoint.getX();
float inwardPointY = inwardPoint.getY();
temp = moveLineK * movePointX - crossLineK * inwardPointX + inwardPointY - movePointY;
x = temp / (moveLineK - crossLineK);
return x;
}
/**
* 根据相交点x坐标求已经方程经过该点的y坐标
*/
public static float calBeelineEquation(float k, float x, Point point) {
float y;
y = k * (x - point.getX()) + point.getY();
return y;
}
public class FirstActivity extends AppCompatActivity implements View.OnClickListener {
private DrawPolygonView2 drawPloygonView2;
private Button clear;
private TextView textView;
private List<Point> list;
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_first);
drawPloygonView2 = (DrawPolygonView2) findViewById(R.id.drawPloygonView2);
clear = (Button) findViewById(R.id.clear);
textView = (TextView) findViewById(R.id.textView);
clear.setOnClickListener(this);
setOrderPointList();
Point movePoint = new Point(0, 1); //移动线抬起时的鼠标的点坐标
// Point movePoint = new Point(6, 7); //移动线抬起时的鼠标的点坐标
getPoint(list, movePoint);
}
/**
* 该集合点必须是顺序的 （顺时针），
* 第0个为移动线的坐标
* 第1个为移动线的坐标
* 第2个为第一条相交线另一个坐标
* 第3个为第二条相交线另一个坐标
*/
public void setOrderPointList() {
list = new ArrayList<>(); //顺时针添加
// Point point = new Point(5, 6); //移动线的坐标 ：集合中第0个
// Point point1 = new Point(8, 7); //移动线的坐标
// Point point2 = new Point(10, 0); //第一条相交线另一个坐标
// Point point3 = new Point(2, 1); //第二条相交线另一个坐标
// list.add(point);
// list.add(point1);
// list.add(point2);
// list.add(point3);
Point point = new Point(0, 0); //移动线的坐标 ：集合中第0个
Point point1 = new Point(2, 2); //移动线的坐标
Point point2 = new Point(1, 0); //第一条相交线另一个坐标
Point point3 = new Point(1, 0); //第二条相交线另一个坐标
list.add(point);
list.add(point1);
list.add(point2);
list.add(point3);
}
public List<Point> getPoint(List<Point> list, Point movePoint) {
List<Point> moveinwardPoint = new ArrayList<>();
float moveLineK = DrawUtils.calSlope(list.get(0), list.get(1)); //移动线的斜率
float crossLineK = DrawUtils.calSlope(list.get(1), list.get(2)); //与移动线相交的其他两条线的斜率
float crosspointX = DrawUtils.calCrosspointX(moveLineK, crossLineK, movePoint, list.get(1));
float crosspointY = DrawUtils.calBeelineEquation(moveLineK, crosspointX, movePoint);
float crossLineK1 = DrawUtils.calSlope(list.get(0), list.get(3)); //与移动线相交的其他两条线的斜率
float crosspointX1 = DrawUtils.calCrosspointX(moveLineK, crossLineK1, movePoint, list.get(3));
float crosspointY1 = DrawUtils.calBeelineEquation(moveLineK, crosspointX1, movePoint);
Log.e("FirstActivity", "moveLineK:" + moveLineK + "/" + "crossLineK:" + crossLineK + "/" +
"crosspointX:" + crosspointX + "/" + "crosspointY:" + crosspointY);
Log.e("FirstActivity", "moveLineK:" + moveLineK + "/" + "crossLineK1:" + crossLineK1 + "/" +
"crosspointX1:" + crosspointX1 + "/" + "crosspointY1:" + crosspointY1);
moveinwardPoint.add(new Point(crosspointX, crosspointY));
moveinwardPoint.add(new Point(crosspointX1, crosspointY1));
return moveinwardPoint;
}
@Override
public void onClick(View v) {
switch (v.getId()) {
case R.id.clear:
drawPloygonView2.cleanDraw();
break;
default:
break;
}
}
}
另附一份自定义View中关于计算方便的常用方法
public class DrawUtils {
/**
* 判断点击的点是否在图形内
*/
static Region re = new Region();
public static boolean isInside(Path path, MotionEvent event) {
//构造一个区域对象，左闭右开的。
RectF r = new RectF();
//计算控制点的边界
path.computeBounds(r, true);
//设置区域路径和剪辑描述的区域
re.setPath(path, new Region((int) r.left, (int) r.top, (int) r.right, (int) r.bottom));
//在封闭的path内返回true 不在返回false
return re.contains((int) event.getX(), (int) event.getY());
}
/**
* 标点是否落在指定的多边形区域内
* 判断坐
*/
public static int PtInRegion(Point p0, List<Point> plg) {
int nowValue, lastValue, dValue, sumValue = 0;
double tempMult;
double eps = 0.0000000000000001;
Point l1, l2;
if (plg.get(0).getY() > p0.getY()) {
lastValue = 1;
} else if (plg.get(0).getY() < p0.getY()) {
lastValue = -1;
} else {
lastValue = 0;
}
for (int i = 1; i < plg.size(); i++) {
//计算矢量积
l1 = plg.get(i - 1);
l2 = plg.get(i);
tempMult = xmult(l1, l2, p0);
//判断点是否在边上
if (Math.abs(tempMult) < eps && (l1.getX() - p0.getX()) * (l2.getX() - p0.getX()) < eps && (l1.getY() -
p0.getY()) * (l2.getY() - p0.getY()) < eps) {
return 0;
}
//判断是否跨射线
if (l2.getY() > p0.getY()) {
nowValue = 1;
} else if (l2.getY() < p0.getY()) {
nowValue = -1;
} else {
nowValue = 0;
}
dValue = nowValue - lastValue;
//判断是否与射线相交,相交则累加
if (dValue != 0) {
if (dValue > 0 && tempMult > 0) {
sumValue += dValue;
} else if (dValue < 0 && tempMult < 0) {
sumValue += dValue;
}
}
lastValue = nowValue;
}
//判断最终结果，如和为0，则在多边形外，否则在多边形内
if (sumValue == 0) {
return -1;
} else {
return 1;
}
}
public static double xmult(Point p1, Point p2, Point p0) {
return (p1.getX() - p0.getX()) * (p2.getY() - p0.getY()) - (p2.getX() - p0.getX()) * (p1.getY() - p0.getY());
}
/**
* 根据手机的分辨率从 dp 的单位 转成为 px(像素)
*/
public static int dip2px(Context context, float dpValue) {
final float scale = context.getResources().getDisplayMetrics().density;
return (int) (dpValue * scale + 0.5f);
}
/**
* 根据手机的分辨率从 px(像素) 的单位 转成为 dp
*/
public static int px2dip(Context context, float pxValue) {
final float scale = context.getResources().getDisplayMetrics().density;
return (int) (pxValue / scale + 0.5f);
}
/**
* @param str 字符是否为空
*/
public static boolean isEmpty(String str) {
if (null == str || str.trim().length() == 0
|| str.trim().equals("null")) {
return true;
}
return false;
}
/**
* 保留指定位数
*
* @param num 保留位数
*/
public static String formatString(Object obj, int num) {
try {
BigDecimal bd = new BigDecimal(obj + "");
bd = bd.setScale(num, BigDecimal.ROUND_DOWN);
return bd.toString();
} catch (Exception e) {
return obj.toString();
}
}
/**
* 获取屏幕宽高
*
* @return size[0]:width size[1]:height
*/
public static int[] getScreenSize(Context context) {
int[] size = new int[2];
DisplayMetrics dm = new DisplayMetrics();
WindowManager mg = (WindowManager) context
.getSystemService(Context.WINDOW_SERVICE);
mg.getDefaultDisplay().getMetrics(dm);
size[0] = dm.widthPixels;
size[1] = dm.heightPixels;
return size;
}
/**
* 获取控件左上角和右下角的点
*/
public static Point[] getPointWithView(View v) {
Point[] coordinate = new Point[2];
int left = v.getLeft();
int top = v.getTop();
int right = v.getRight();
int bottom = v.getBottom();
Point lt = new Point(left, top);
Point rb = new Point(right, bottom);
coordinate[0] = lt;
coordinate[1] = rb;
return coordinate;
}
// 点到直线的距离 ： 点（x0,y0） 到由两点组成的线段（x1,y1） ,( x2,y2 )
public static double pointToLine(float x0, float y0, Point point1, Point point2) {
float x1 = point1.getX();
float y1 = point1.getY();
float x2 = point2.getX();
float y2 = point2.getY();
double space = 0;
double a, b, c;
a = lineSpace(x1, y1, x2, y2);// 线段的长度
b = lineSpace(x1, y1, x0, y0);// (x1,y1)到点的距离
c = lineSpace(x2, y2, x0, y0);// (x2,y2)到点的距离
if (c <= 0.000001 || b <= 0.000001) {
space = 0;
return space;
}
if (a <= 0.000001) {
space = b;
return space;
}
if (c * c >= a * a + b * b) {
space = b;
return space;
}
if (b * b >= a * a + c * c) {
space = c;
return space;
}
double p = (a + b + c) / 2;// 半周长
double s = Math.sqrt(p * (p - a) * (p - b) * (p - c));// 海伦公式求面积
space = 2 * s / a;// 返回点到线的距离（利用三角形面积公式求高）
return space;
}
// 计算两点之间的距离
public static double lineSpace(float x1, float y1, float x2, float y2) {
double lineLength = 0;
lineLength = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2)
* (y1 - y2));
return lineLength;
}
/**
* 计算两点间距离
*/
public static float calTwoPointDistance(Point first, Point second) {
float firstX = first.getX();
float firstY = first.getY();
float secondX = second.getX();
float secondY = second.getY();
float lineDis = (float) Math.sqrt(Math.pow(secondX - firstX, 2) + Math.pow(secondY - firstY, 2));
return lineDis;
}
/**
* 计算直线斜率
*/
public static float calSlope(Point point, Point point1) {
float k = (point1.getY() - point.getY()) / (point1.getX() - point.getX());
return k;
}
/**
* 根据 不同直线上的两个点 求两条直线的相交点x坐标
* @param moveLineK 移动线斜率
* @param crossLineK 相交线斜率
* @param movePoint 移动线抬起时鼠标点坐标
* @param inwardPoint 相交线的两个坐标中任意一个
* @return
*/
public static float calCrosspointX(float moveLineK, float crossLineK, Point movePoint, Point inwardPoint) {
float x, temp;
float movePointX = movePoint.getX();
float movePointY = movePoint.getY();
float inwardPointX = inwardPoint.getX();
float inwardPointY = inwardPoint.getY();
temp = moveLineK * movePointX - crossLineK * inwardPointX + inwardPointY - movePointY;
x = temp / (moveLineK - crossLineK);
return x;
}
/**
* 根据相交点x坐标求已经方程经过该点的y坐标
*/
public static float calBeelineEquation(float k, float x, Point point) {
float y;
y = k * (x - point.getX()) + point.getY();
return y;
}
}
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