Nous avons un cercle centré à l'origine (0 0). En entrée, nous recevons l'angle de départ du secteur du cercle et la taille du secteur du cercle en pourcentage.
Exemples :
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
fenêtre.ouvrir javascript
Source : Wikibook.org
Dans cette image, l'angle de départ est de 0 degré de rayon r et supposons que le pourcentage de zone colorée est de 12 %, nous calculons alors l'angle de fin comme suit : 360/pourcentage + angle de départ .
Pour savoir si un point (x y) existe ou non dans un secteur de cercle (centré à l'origine), nous trouvons les coordonnées polaires de ce point, puis suivons les étapes suivantes :
- Convertissez x y en coordonnées polaires en utilisant ceci
Angle = absence (y/x); Rayon = sqrt(x * y y y y y y); - Ensuite, l'angle doit être compris entre StartingAngle et EndingAngle et Radius entre 0 et votre rayon.
// C++ program to check if a point lies inside a circle // sector. #include
// 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 sectorn'); else System.out.print('Point'+'('+x+''+y+')'+ ' exist in the circle sectorn'); } // Driver Program to test above function public 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 program to check if a point # lies inside a circle sector. import math def 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 code radius x y = 8 3 4 percent startAngle = 12 0 checkPoint(radius x y percent startAngle) # This code is contributed by # Smitha Dinesh Semwal
// 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
<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 sectorn'); else document.write('Point' + '(' + x + '' + y + ')' + ' exist in the circle sectorn'); } // 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>
Sortir :
Point(3 4) exists in the circle sector
Complexité temporelle : O(1)
Espace auxiliaire : O(1)