We have a circle centered at origin (0, 0). As input we are given with starting angle of the circle sector and the size of the circle sector in percentage.
Examples:
Input : Radius = 8
StartAngle = 0
Percentage = 12
x = 3 y = 4
Output : Point (3, 4) exists in the circle
sector
Input : Radius = 12
Startangle = 45
Percentage = 25
x = 3 y = 4
Output : Point (3, 4) does not exist in
the circle sector
Source:wikibooks.org
In this image starting angle is 0 degree, radius r and suppose that percentage of colored area is 12% then we calculate Ending Angle as 360/percentage + starting angle.
To find whether a point (x, y) exists in a circle sector (centered at origin) or not we find polar coordinates of that point and then go through the following steps:
- Convert x, y to polar coordinates using this
Angle = atan(y/x); Radius = sqrt(x * x + y * y); - Then Angle must be between StartingAngle and EndingAngle, and Radius between 0 and your Radius.
C++
// C++ program to check if a point lies inside a circle// sector.#include<bits/stdc++.h>using namespace std;void checkPoint(int radius, int x, int y, float percent, float startAngle){ // calculate endAngle float endAngle = 360/percent + startAngle; // Calculate polar co-ordinates float polarradius = sqrt(x*x+y*y); float Angle = atan(y/x); // Check whether polarradius is less then radius of circle // or not and Angle is between startAngle and endAngle // or not if (Angle>=startAngle && Angle<=endAngle && polarradius<radius) printf("Point (%d, %d) exist in the circle sector\n", x, y); else printf("Point (%d, %d) does not exist in the circle sector\n", x, y);}// Driver codeint main(){ int radius = 8, x = 3, y = 4; float percent = 12, startAngle = 0; checkPoint(radius, x, y, percent, startAngle); return 0;} |
Java
// Java program to check if// a point lies inside a circle// sector.class GFG{static void checkPoint(int radius, int x, int y, float percent, float startAngle){ // calculate endAngle float endAngle = 360/percent + startAngle; // Calculate polar co-ordinates double polarradius = Math.sqrt(x*x+y*y); double Angle = Math.atan(y/x); // Check whether polarradius is // less then radius of circle // or not and Angle is between // startAngle and endAngle // or not if (Angle>=startAngle && Angle<=endAngle && polarradius<radius) System.out.print("Point"+"("+x+","+y+")"+ " exist in the circle sector\n"); else System.out.print("Point"+"("+x+","+y+")"+ " exist in the circle sector\n");}// Driver Program to test above functionpublic static void main(String arg[]){ int radius = 8, x = 3, y = 4; float percent = 12, startAngle = 0; checkPoint(radius, x, y, percent, startAngle);}}// This code is contributed// by Anant Agarwal. |
Python3
# Python3 program to check if a point # lies inside a circle sector.import mathdef checkPoint(radius, x, y, percent, startAngle): # calculate endAngle endAngle = 360 / percent + startAngle # Calculate polar co-ordinates polarradius = math.sqrt(x * x + y * y) Angle = math.atan(y / x) # Check whether polarradius is less # then radius of circle or not and # Angle is between startAngle and # endAngle or not if (Angle >= startAngle and Angle <= endAngle and polarradius < radius): print("Point (", x, ",", y, ") " "exist in the circle sector") else: print("Point (", x, ",", y, ") " "does not exist in the circle sector")# Driver coderadius, x, y = 8, 3, 4percent, startAngle = 12, 0checkPoint(radius, x, y, percent, startAngle)# This code is contributed by# Smitha Dinesh Semwal |
C#
// C# program to check if a point lies// inside a circle sector.using System.IO;using System;class GFG { static void checkPoint(int radius, int x, int y, float percent, float startAngle) { // calculate endAngle float endAngle = 360 / percent + startAngle; // Calculate polar co-ordinates float polarradius = (float)Math.Sqrt(x * x + y * y); float Angle = (float)Math.Atan(y / x); // Check whether polarradius is less then // radius of circle or not and Angle is // between startAngle and endAngle or not if (Angle >= startAngle && Angle <= endAngle && polarradius < radius) Console.Write("Point ({0}, {1}) exist in " + "the circle sector", x, y); else Console.Write("Point ({0}, {1}) does not " + "exist in the circle sector", x, y); } // Driver code public static void Main() { int radius = 8, x = 3, y = 4; float percent = 12, startAngle = 0; checkPoint(radius, x, y, percent, startAngle); }}// This code is contributed by Smitha Dinesh Semwal |
Javascript
<script>// Javascript program to check if// a point lies inside a circle// sector.function checkPoint(radius, x, y, percent, startAngle){ // Calculate endAngle let endAngle = 360 / percent + startAngle; // Calculate polar co-ordinates let polarradius = Math.sqrt(x * x + y * y); let Angle = Math.atan(y / x); // Check whether polarradius is // less then radius of circle // or not and Angle is between // startAngle and endAngle // or not if (Angle >= startAngle && Angle <= endAngle && polarradius < radius) document.write("Point" + "(" + x + "," + y + ")" + " exist in the circle sector\n"); else document.write("Point" + "(" + x + "," + y + ")" + " exist in the circle sector\n");} // Driver code let radius = 8, x = 3, y = 4;let percent = 12, startAngle = 0;checkPoint(radius, x, y, percent, startAngle);// This code is contributed by splevel62 </script> |
Output :
Point(3, 4) exists in the circle sector
Time complexity: O(1)
Auxiliary Space: O(1)
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