检查给定点是否位于矩形内
给定一个矩形的四个点，还有一个点 P。编写一个函数来检查 P 是否位于给定的矩形内。 例:
Input : R = [(10, 10), (10, -10),
(-10, -10), (-10, 10)]
P = (0, 0)
Output : yes
Illustration :
Input : R = [(10, 10), (10, -10),
(-10, -10), (-10, 10)],
P = (20, 20)
Output : no
Illustration :
先决条件: 检查给定点是否位于三角形内 逼近:让四个角的坐标为 A(x1，y1)、B(x2，y2)、C(x3，y3)和 D(x4，y4)。且给定点 P 的坐标为(x，y) 1)计算给定矩形的面积，即矩形 ABCD 的面积为三角形 ABC 的面积+三角形 ACD 的面积。 面积 A =[x1(y2–y3)+x2(y3–y1)+x3(y1-y2)]/2+[x1(y4–y3)+x4(y3–y1)+x3(y1-y4)]/2 将三角形 PAB 的面积计算为 A1。 3)将三角形 PBC 的面积计算为 A2。 4)将三角形 PCD 的面积计算为 A3。 5)将三角形 PAD 的面积计算为 A4。 6)如果 P 位于三角形内部，那么 A1 + A2 + A3 + A4 必须等于 a。
C++
#include <bits/stdc++.h>
using namespace std;
/* A utility function to calculate area of
triangle formed by (x1, y1), (x2, y2) and
(x3, y3) */
float area(int x1, int y1, int x2, int y2,
int x3, int y3)
{
return abs((x1 * (y2 - y3) + x2 * (y3 - y1) +
x3 * (y1 - y2)) / 2.0);
}
/* A function to check whether point P(x, y)
lies inside the rectangle formed by A(x1, y1),
B(x2, y2), C(x3, y3) and D(x4, y4) */
bool check(int x1, int y1, int x2, int y2, int x3,
int y3, int x4, int y4, int x, int y)
{
/* Calculate area of rectangle ABCD */
float A = area(x1, y1, x2, y2, x3, y3) +
area(x1, y1, x4, y4, x3, y3);
/* Calculate area of triangle PAB */
float A1 = area(x, y, x1, y1, x2, y2);
/* Calculate area of triangle PBC */
float A2 = area(x, y, x2, y2, x3, y3);
/* Calculate area of triangle PCD */
float A3 = area(x, y, x3, y3, x4, y4);
/* Calculate area of triangle PAD */
float A4 = area(x, y, x1, y1, x4, y4);
/* Check if sum of A1, A2, A3 and A4
is same as A */
return (A == A1 + A2 + A3 + A4);
}
/* Driver program to test above function */
int main()
{
/* Let us check whether the point P(10, 15)
lies inside the rectangle formed by A(0, 10),
B(10, 0) C(0, -10) D(-10, 0) */
if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
cout << "yes";
else
cout << "no";
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
class GFG
{
/* A utility function to calculate area of
triangle formed by (x1, y1), (x2, y2) and
(x3, y3) */
static float area(int x1, int y1, int x2,
int y2, int x3, int y3)
{
return (float)Math.abs((x1 * (y2 - y3) +
x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
}
/* A function to check whether point P(x, y)
lies inside the rectangle formed by A(x1, y1),
B(x2, y2), C(x3, y3) and D(x4, y4) */
static boolean check(int x1, int y1, int x2, int y2,
int x3, int y3, int x4, int y4, int x, int y)
{
/* Calculate area of rectangle ABCD */
float A = area(x1, y1, x2, y2, x3, y3)+
area(x1, y1, x4, y4, x3, y3);
/* Calculate area of triangle PAB */
float A1 = area(x, y, x1, y1, x2, y2);
/* Calculate area of triangle PBC */
float A2 = area(x, y, x2, y2, x3, y3);
/* Calculate area of triangle PCD */
float A3 = area(x, y, x3, y3, x4, y4);
/* Calculate area of triangle PAD */
float A4 = area(x, y, x1, y1, x4, y4);
/* Check if sum of A1, A2, A3 and A4
is same as A */
return (A == A1 + A2 + A3 + A4);
}
// Driver code
public static void main (String[] args)
{
/* Let us check whether the point P(10, 15)
lies inside the rectangle formed by A(0, 10),
B(10, 0) C(0, -10) D(-10, 0) */
if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
System.out.print("yes");
else
System.out.print("no");
}
}
// This code is contributed by Anant Agarwal.
Python 3
# A utility function to calculate
# area of triangle formed by (x1, y1),
# (x2, y2) and (x3, y3)
def area(x1, y1, x2, y2, x3, y3):
return abs((x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2)) / 2.0)
# A function to check whether point
# P(x, y) lies inside the rectangle
# formed by A(x1, y1), B(x2, y2),
# C(x3, y3) and D(x4, y4)
def check(x1, y1, x2, y2, x3,
y3, x4, y4, x, y):
# Calculate area of rectangle ABCD
A = (area(x1, y1, x2, y2, x3, y3) +
area(x1, y1, x4, y4, x3, y3))
# Calculate area of triangle PAB
A1 = area(x, y, x1, y1, x2, y2)
# Calculate area of triangle PBC
A2 = area(x, y, x2, y2, x3, y3)
# Calculate area of triangle PCD
A3 = area(x, y, x3, y3, x4, y4)
# Calculate area of triangle PAD
A4 = area(x, y, x1, y1, x4, y4);
# Check if sum of A1, A2, A3
# and A4 is same as A
return (A == A1 + A2 + A3 + A4)
# Driver Code
if __name__ == '__main__':
# Let us check whether the point
# P(10, 15) lies inside the
# rectangle formed by A(0, 10),
# B(10, 0) C(0, -10) D(-10, 0)
if (check(0, 10, 10, 0, 0, -10,
-10, 0, 10, 15)):
print("yes")
else:
print("no")
# This code is contributed by
# Surendra_Gangwar
C
// C# program to Check whether a given
// point lies inside a rectangle or not
using System;
class GFG {
// A utility function to calculate area
// of triangle formed by (x1, y1),
// (x2, y2) and (x3, y3)
static float area(int x1, int y1, int x2,
int y2, int x3, int y3)
{
return (float)Math.Abs((x1 * (y2 - y3) +
x2 * (y3 - y1) +
x3 * (y1 - y2)) / 2.0);
}
// A function to check whether point P(x, y)
// lies inside the rectangle formed by A(x1, y1),
// B(x2, y2), C(x3, y3) and D(x4, y4)
static bool check(int x1, int y1, int x2,
int y2, int x3, int y3,
int x4, int y4, int x, int y)
{
// Calculate area of rectangle ABCD
float A = area(x1, y1, x2, y2, x3, y3) +
area(x1, y1, x4, y4, x3, y3);
// Calculate area of triangle PAB
float A1 = area(x, y, x1, y1, x2, y2);
// Calculate area of triangle PBC
float A2 = area(x, y, x2, y2, x3, y3);
// Calculate area of triangle PCD
float A3 = area(x, y, x3, y3, x4, y4);
// Calculate area of triangle PAD
float A4 = area(x, y, x1, y1, x4, y4);
// Check if sum of A1, A2, A3
// and A4is same as A
return (A == A1 + A2 + A3 + A4);
}
// Driver code
public static void Main ()
{
// Let us check whether the point
// P(10, 15) lies inside the rectangle
// formed by A(0, 10), B(10, 0),
// C(0, -10), D(-10, 0)
if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
Console.Write("yes");
else
Console.Write("no");
}
}
// This code is contributed by Nitin Mittal.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to check whether a
// given point lies inside a
// rectangle or not
// A utility function to
// calculate area of
// triangle formed by
// (x1, y1), (x2, y2)
// and (x3, y3)
function area($x1, $y1, $x2,
$y2, $x3, $y3)
{
return abs(($x1 * ($y2 - $y3) +
$x2 * ($y3 - $y1) +
$x3 * ($y1 - $y2)) / 2.0);
}
/* A function to check
whether point P(x, y)
lies inside the rectangle
formed by A(x1, y1),
B(x2, y2), C(x3, y3)
and D(x4, y4) */
function check($x1, $y1, $x2, $y2, $x3,
$y3, $x4, $y4, $x, $y)
{
// Calculate area of rectangle ABCD
$A = area($x1, $y1, $x2, $y2, $x3, $y3) +
area($x1, $y1, $x4, $y4, $x3, $y3);
// Calculate area of triangle PAB
$A1 = area($x, $y, $x1, $y1, $x2, $y2);
// Calculate area of triangle PBC
$A2 = area($x, $y, $x2, $y2, $x3, $y3);
// Calculate area of triangle PCD
$A3 = area($x, $y, $x3, $y3, $x4, $y4);
// Calculate area of triangle PAD
$A4 = area($x, $y, $x1, $y1, $x4, $y4);
// Check if sum of A1, A2,
// A3 and A4 is same as A
return ($A == $A1 + $A2 + $A3 + $A4);
}
// Driver Code
// Let us check whether
// the point P(10, 15)
// lies inside the rectangle
// formed by A(0, 10),
// B(10, 0) C(0, -10)
// D(-10, 0)
if (check(0, 10, 10, 0, 0, -10,
-10, 0, 10, 15))
echo "yes";
else
echo "no";
// This code is contributed by vt_m.
?>
java 描述语言
<script>
/* A utility function to calculate area of
triangle formed by (x1, y1), (x2, y2) and
(x3, y3) */
function area(x1, y1, x2, y2,
x3, y3)
{
return Math.abs((x1 * (y2 - y3) + x2 * (y3 - y1) +
x3 * (y1 - y2)) / 2.0);
}
/* A function to check whether point P(x, y)
lies inside the rectangle formed by A(x1, y1),
B(x2, y2), C(x3, y3) and D(x4, y4) */
function check(x1, y1, x2, y2, x3,
y3, x4, y4, x, y)
{
/* Calculate area of rectangle ABCD */
let A = area(x1, y1, x2, y2, x3, y3) +
area(x1, y1, x4, y4, x3, y3);
/* Calculate area of triangle PAB */
let A1 = area(x, y, x1, y1, x2, y2);
/* Calculate area of triangle PBC */
let A2 = area(x, y, x2, y2, x3, y3);
/* Calculate area of triangle PCD */
let A3 = area(x, y, x3, y3, x4, y4);
/* Calculate area of triangle PAD */
let A4 = area(x, y, x1, y1, x4, y4);
/* Check if sum of A1, A2, A3 and A4
is same as A */
return (A == A1 + A2 + A3 + A4);
}
/* Driver program to test above function */
/* Let us check whether the point P(10, 15)
lies inside the rectangle formed by A(0, 10),
B(10, 0) C(0, -10) D(-10, 0) */
if (check(0, 10, 10, 0, 0, -10, -10, 0, 10, 15))
document.write("yes");
else
document.write("no");
// This code is contributed by Mayank Tyagi
</script>
输出:
no
本文由Shivam Pradhan(anuj _ charm)供稿。如果你喜欢 GeeksforGeeks 并想投稿，你也可以使用write.geeksforgeeks.org写一篇文章或者把你的文章邮寄到 review-team@geeksforgeeks.org。看到你的文章出现在极客博客主页上，帮助其他极客。 如果发现有不正确的地方，或者想分享更多关于上述话题的信息，请写评论。
版权属于：月萌API www.moonapi.com，转载请注明出处
