项目链接
github ：
https://github.com/leo19920823/phptools.git
composer :
composer require "leo1992/tools:^0"
```
## 问题描述
> 已知一个任意多边形的各顶点坐标，任意给一点坐标，判断是否在该多边形内部或边线上
## 解决思路及基础
1. 任意凸多边形中，经过任一顶点连接各个顶点，可以把多边形分割为多个三角形
2. 任意三角形中一点，和三条边上面各两个顶点的夹角共六个，如果该点在三角形内部，六个角之和等于180度，否则在三角形外部
3. 任意凹多边形都可以转化为，任一凸多边形减去N个三角形
4. 在上一条件下，如果一个点在这个大的凸多边形中（包括边），但不在去掉的N个三角形中（不包括边界），则该点在该凹多边形中
5. 一个点如果和线段的两个顶点连接形成的两个夹角和等于180°，则该点在线段上
6. 把凹多边形的问题细化到点和三角形以及点和线段的位置关系
## 实现部分
1. 设计了六个类，点、线段、角、三角形、凸多边形、多边形
2. 其中三角形继承凸多边形，凸多边形继承多边形类
### 1.Point（点类）
> 这个类主要保存点信息，没有任何操作
```
// 点类
class Point extends Base
{
private $x; // x坐标
private $y; // y 坐标
public function __construct($x, $y)
{
try {
$this->setX($x);
$this->setY($y);
unset($x, $y);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setX($x)
{
try {
$this->x = (float)$x;
unset($x);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getX()
{
try {
return $this->x;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setY($y)
{
try {
$this->y = (float)$y;
unset($y);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getY()
{
try {
return $this->y;
} catch (\Exception $e) {
throw $e;
}
}
public function __toString()
{
try {
return "({$this->getX()},{$this->getY()})";
} catch (\Exception $e) {
throw $e;
}
}
}
```
### 2.Line(线段)
> 这个类由两个点构成，提供一个操作来判断某点是否在线段上
```
class Line extends Base
{
private $p1; // 线段第一个点
private $p2; // 线段的第二个点
private $tilt; // 倾斜角，距x轴正方向的逆时针角度
private $length; // 线段的长度
public function __construct(Point $p1, Point $p2)
{
try {
// 两个端点不能重合，没长度
if ($p1 == $p2) {
throw new TwoPointOverlapException('两个端点不能重合');
}
$this->setP1($p1);
$this->setP2($p2);
unset($p1, $p2);
} catch (\Exception $e) {
throw $e;
}
}
// 生成线段的长度
private function generateLength()
{
try {
// 利用勾股定理
$length = sqrt(pow($this->getP1()->getX() - $this->getP2()->getX(), 2) +
pow($this->getP1()->getY() - $this->getP2()->getY(), 2));
$this->setLength(abs($length));
unset($length);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
// 生成倾斜角
private function generateTilt()
{
try {
$dy = $this->getP2()->getY() - $this->getP1()->getY();
$dx = $this->getP2()->getX() - $this->getP1()->getX();
// 不同的象限不同处理，dx为零的情况单独处理
if ($dx > 0 && $dy >= 0) {
$ang = (rad2deg(atan($dy/$dx)));
$ext = 0;
} elseif ($dx <= 0 && $dy >= 0) {
if (0 == $dx) {
$ang = 0;
$ext = 90;
} else {
$ang = (rad2deg(atan($dy/$dx)));
$ext = 180;
}
} elseif ($dx < 0 && $dy <= 0) {
$ang = (rad2deg(atan($dy/$dx)));
$ext = 180;
} elseif ($dx >= 0 && $dy < 0) {
if (0 == $dx) {
$ang = 0;
$ext = 270;
} else {
$ang = (rad2deg(atan($dy/$dx)));
$ext = 360;
}
}
$ang = $ang + $ext;
$this->setTilt($ang);
unset($dx, $dy, $ang, $ext);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
// 判断点是否在线上
public function inLine(Point $p)
{
try {
$l1 = new Line($p, $this->getP1());
$l2 = new Line($p, $this->getP2());
$is = false;
// 这个点和这条线段的两个端点生成的两条线的倾斜角要互补
if (180 == abs($l1->getTilt() - $l2->getTilt())) {
$is = true;
} else {
$is = false;
}
unset($l1, $l2);
return $is;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP1(Point $p1)
{
try {
$this->p1 = $p1;
unset($p1);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getP1()
{
try {
return $this->p1;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP2(Point $p2)
{
try {
$this->p2 = $p2;
unset($p2);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getP2()
{
try {
return $this->p2;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setTilt($tilt)
{
try {
$this->tilt = (float)$tilt;
unset($tilt);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getTilt()
{
try {
if (empty($this->generateTilt)) {
$this->generateTilt();
}
return $this->tilt;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setLength($length)
{
try {
$this->length = (float)$length;
unset($length);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getLength()
{
try {
if (empty($this->length)) {
$this->generateLength();
}
return $this->length;
} catch (\Exception $e) {
throw $e;
}
}
public function __toString()
{
try {
return '[' . (string)$this->getP1() . '->' . (string)$this->getP2() . ']';
} catch (\Exception $e) {
throw $e;
}
}
}
```
### 3.Angle（角）
> 角类由两条线段构成，提供返回夹角的操作
```
// 角度类
class Angle extends Base
{
private $l1;
private $l2;
private $angle;
public function __construct(Line $l1, Line $l2)
{
try {
if ($l1->getP2() != $l2->getP1()) {
throw new \Exception('两条线段不是首尾相连');
}
// 会引起错误
// if (360 == ($l1->getTilt() + $l2->getTilt())) {
// throw new LineOverlapException('两条线段不能重叠');
// }
$this->setL1($l1);
$this->setL2($l2);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
private function generateAngle()
{
try {
$angle = $this->getL1()->getTilt() - $this->getL2()->getTilt() + 180;
$angle = fmod(($angle + 360),360);
$this->setAngle($angle);
return 0;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
public function setL1(Line $l1)
{
try {
$this->l1 = $l1;
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getL1()
{
try {
return $this->l1;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
public function setP(Point $p)
{
try {
$this->p = $p;
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getP()
{
try {
return $this->p;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
public function setL2(Line $l2)
{
try {
$this->l2 = $l2;
return 0;
} catch (\Exception $e) {
throw $e;
}
}
public function getL2()
{
try {
return $this->l2;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setAngle($angle)
{
try {
$this->angle = $angle;
} catch (\Exception $e) {
throw $e;
}
}
public function getAngle()
{
try {
if (empty($this->angle)) {
$this->generateAngle();
}
return $this->angle;
} catch (\Exception $e) {
throw $e;
}
}
public function __toString()
{
try {
return '{' . (string)$this->getL1() . '=>' . (string)$this->getL2() . '}';
} catch (\Exception $e) {
throw $e;
}
}
}
```
### 4.Polygon（多边形）
> 由一组相邻不重复的点构成，提供一个操作用来判断点是否在多边形内部
如果是凹多边形，把多边形中内角为优角的点去掉一个，用剩下的点构成一个多边形，记录下由此补上的三角形
如果依然是凹多边形，继续去掉一个凹点，把补上的三角形记录下来
最后会得到一个凸多边形和一组补上的三角形，
对凸多边形和三角形集合分别求解，
在凸多边形内而不在三角形集合中的点则在凹多边形内部，否则在外部
```php
// 矩形类
class Triangle extends ConvexPolygon
{
private $p1;
private $p2;
private $p3;
public function __construct(Point $p1, Point $p2, Point $p3)
{
try {
$this->setP1($p1);
$this->setP2($p2);
$this->setP3($p3);
$arr = [
$this->getP1(),
$this->getP2(),
$this->getP3()
];
parent::__construct($arr);
} catch (\Exception $e) {
throw $e;
}
}
// 判断一个点是否在矩形内
public function inTriangle(Point $p)
{
try {
$p1 = $this->getP1();
$p2 = $this->getP2();
$p3 = $this->getP3();
$ls = $this->getLines();
$l1 = new Line($p, $p1);
$l2 = new Line($p, $p2);
$l3 = new Line($p, $p3);
$a1 = (new Angle($l1, $ls[0]))->getAngle();
$a2 = (new Angle($l2, $ls[1]))->getAngle();
$a3 = (new Angle($l3, $ls[2]))->getAngle();
// $t = new Angle($l3, $ls[2]);
// dump($t);
// dump($t->getAngle());
$l1 = new Line($p1, $p);
$l2 = new Line($p2, $p);
$l3 = new Line($p3, $p);
$b1 = (new Angle($ls[2], $l1))->getAngle();
$b2 = (new Angle($ls[0], $l2))->getAngle();
$b3 = (new Angle($ls[1], $l3))->getAngle();
// $as = $tri->getAngles();
// foreach ($as as $a) {
// dump($a->getAngle());
// }
// dump($this);
// dump("$a1/ $a2/ $a3/ $b1/ $b2/ $b3");
// die;
$c = $a1 + $a2 + $a3 + $b1 + $b2 + $b3;
$is = false;
if (180 >= (int)$c) {
$is = true;
} else {
$is = false;
}
return $is;
} catch (LineOverlapException $e) {
return true;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP1(Point $p1)
{
try {
$this->p1 = $p1;
} catch (\Exception $e) {
throw $e;
}
}
public function getP1()
{
try {
return $this->p1;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP2(Point $p2)
{
try {
$this->p2 = $p2;
} catch (\Exception $e) {
throw $e;
}
}
public function getP2()
{
try {
return $this->p2;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP3(Point $p3)
{
try {
$this->p3 = $p3;
} catch (\Exception $e) {
throw $e;
}
}
public function getP3()
{
try {
return $this->p3;
} catch (\Exception $e) {
throw $e;
}
}
}
```
### 5. ConvexPolygon（凸多边形）
> 因为凸多边形可以被分割成N个三角形，所有只要判断是否在三角形集合内就可以确定是否在凸多边形内
```
// 凸多边形类
class ConvexPolygon extends Polygon
{
private $triangles;
public function __construct(array $arr_point)
{
try {
parent::__construct($arr_point);
} catch (\Exception $e) {
throw $e;
}
}
// 判断是否在凸多边形内
public function inConvexPolygon(Point $p)
{
try {
$arr_tri = $this->getTriangles();
$is = false;
foreach ($arr_tri as $tri) {
if ($tri->inTriangle($p)) {
$is = true;
break;
}
// // dump("判断凸多边形".(int)$is);
// $as = $tri->getAngles();
// foreach ($as as $a) {
// dump($a->getAngle());
// }
}
return $is;
} catch (\Exception $e) {
throw $e;
}
}
// 生成三角形集合
private function generateTriangles()
{
try {
$num = $this->getNumber();
$ps = $this->getPoints();
$p0 = $ps[0];
unset($ps[0]);
for ($i = 1; $i < $num - 1; $i++) {
$arr[] = new Triangle($p0, $ps[$i], $ps[$i+1]);
}
$this->setTriangles($arr);
unset($num);
unset($ps);
unset($p0);
unset($arr);
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setTriangles($arr)
{
try {
$this->triangles= $arr;
} catch (\Exception $e) {
throw $e;
}
}
public function getTriangles()
{
try {
if ('Leo\Figure\Triangle' != get_class($this)) {
if (empty($this->triangles)) {
$this->generateTriangles();
}
}
return $this->triangles;
} catch (\Exception $e) {
throw $e;
}
}
}
```
### 6.Triangle(三角形)
> 由三个点构成， 提供一个操作来判断点是否在三角形内部
通过该点连接三角形三个顶点，会把原本的三个夹角变成六个夹角，如果六个夹角和等于180°，则在三角形内部
```
// 矩形类
class Triangle extends ConvexPolygon
{
private $p1;
private $p2;
private $p3;
public function __construct(Point $p1, Point $p2, Point $p3)
{
try {
$this->setP1($p1);
$this->setP2($p2);
$this->setP3($p3);
$arr = [
$this->getP1(),
$this->getP2(),
$this->getP3()
];
parent::__construct($arr);
} catch (\Exception $e) {
throw $e;
}
}
// 判断一个点是否在矩形内
public function inTriangle(Point $p)
{
try {
$p1 = $this->getP1();
$p2 = $this->getP2();
$p3 = $this->getP3();
$ls = $this->getLines();
$l1 = new Line($p, $p1);
$l2 = new Line($p, $p2);
$l3 = new Line($p, $p3);
$a1 = (new Angle($l1, $ls[0]))->getAngle();
$a2 = (new Angle($l2, $ls[1]))->getAngle();
$a3 = (new Angle($l3, $ls[2]))->getAngle();
// $t = new Angle($l3, $ls[2]);
// dump($t);
// dump($t->getAngle());
$l1 = new Line($p1, $p);
$l2 = new Line($p2, $p);
$l3 = new Line($p3, $p);
$b1 = (new Angle($ls[2], $l1))->getAngle();
$b2 = (new Angle($ls[0], $l2))->getAngle();
$b3 = (new Angle($ls[1], $l3))->getAngle();
// $as = $tri->getAngles();
// foreach ($as as $a) {
// dump($a->getAngle());
// }
// dump($this);
// dump("$a1/ $a2/ $a3/ $b1/ $b2/ $b3");
// die;
$c = $a1 + $a2 + $a3 + $b1 + $b2 + $b3;
$is = false;
if (180 >= (int)$c) {
$is = true;
} else {
$is = false;
}
return $is;
} catch (LineOverlapException $e) {
return true;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP1(Point $p1)
{
try {
$this->p1 = $p1;
} catch (\Exception $e) {
throw $e;
}
}
public function getP1()
{
try {
return $this->p1;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP2(Point $p2)
{
try {
$this->p2 = $p2;
} catch (\Exception $e) {
throw $e;
}
}
public function getP2()
{
try {
return $this->p2;
} catch (\Exception $e) {
throw $e;
}
}
// setting and getting
private function setP3(Point $p3)
{
try {
$this->p3 = $p3;
} catch (\Exception $e) {
throw $e;
}
}
public function getP3()
{
try {
return $this->p3;
} catch (\Exception $e) {
throw $e;
}
}
}
```
## 使用示例
```
$drawing = [
['x' => 0, 'y' => 0],
['x' => 10, 'y' => 0],
['x' => 10, 'y' => 10],
['x' => 7, 'y' => 10],
['x' => 7, 'y' => 5],
['x' => 3, 'y' => 5],
['x' => 3, 'y' => 10],
['x' => 0, 'y' => 10],
['x' => 0, 'y' => 0]
];
$p = new Point(5, 10);
$arr_p_pol = [];
for($i = count($drawing)-1; $i > 0;$i--) {
if ($drawing[$i]['x'] == $drawing[$i-1]['y'] &&
$drawing[$i]['x'] == $drawing[$i-1]['y']
) {
continue;
}
$arr_p_pol[] = new Point($drawing[$i]['x], $drawing[$i]['y']);
}
$pol = new Polygon($arr_p_pol);
$is_1 = $pol->inPolygon($p);
```