I have to write an algorithm in C and Python to know if a point belongs to a polygon or not (all entered by the user).
My algorithm works in python but the C one doesn't work and I can't find my errors since my debugger code blocks refuse to work.
So if someone could tell me where my error is, I would be very grateful...
The user is asked for the number of vertices of the polygon n≥3 (while).
We ask for their coordinates (For) which we store in 2 arrays (CoordX/CoordY).
The coordinates of the point to be tested are requested (TestX/TestY).
We find the equations of lines connecting the points that follow each other (For).
General case: we look for a and b of y = ax + b.
a= (y(i+1) - y(i))/(x(i+1) -x(i)); b=y-ax
Special case:
if the point at x, (i+1) - i = 0 then we have a line of equation y = x = k (constant) with b = 0; Line = True.
if the point at y, (i+1) - i = 0 then we have a line with equation y = b with a = 0.
We determine if the point is between the bounds y(i) and y(i+1) (For) in order to know which line will cross the point to be tested: Bound = True/False, which we store in an array of Booleans, TabBorne.
We count the number of lines that the point to be tested will cross if we tend x towards infinity (For); we increment k (we take care to use only the lines that we will cross (If)).
y=ax+b<=>x= (y-b)/a,a≠0
Special case: if a point lies on a vertex, Vertex = True and the point lies in the figure.
We count the number of lines touched % 2 : If = 1, it is inside the polygon; Otherwise, it is outside.
In Python:
n=0
NbCroise = 0
k = 0
CoordX = [0]*100
CoordY = [0]*100
TabA=[0]*100
TabB=[0]*100
Ligne=[0]*100
TabBorne = [0]*100
Droite = [0]*100
while n<3:
n = int(input("Entrer le nombre de sommets >=3 : "))
for i in range (n):
CoordX[i] = float(input("Valeur de x : "))
CoordY[i] = float(input("Valeur de y : "))
TestX = float (input("Valeur x du point à tester : "))
TestY = float (input("Valeur y du point à tester : "))
for i in range (n-1):
if CoordX[i+1]-CoordX[i]==0 or CoordY[i+1]-CoordY[i]==0:
if CoordX[i+1]-CoordX[i]==0 :
TabA[i] = CoordX[i]
TabB[i] = 0
Ligne[i] = True
else :
TabA[i] = 0
TabB[i] = CoordY[i]
Ligne[i] = False
else :
TabA[i] = (CoordY[i+1]-CoordY[i])/(CoordX[i+1]-CoordX[i])
TabB[i] = (CoordY[i]-TabA[i]*CoordX[i])
Ligne[i] = False
if CoordX[n-1]-CoordX[0]==0 or CoordY[n-1]-CoordY[0]==0:
if CoordX[n-1]-CoordX[0]==0 :
TabA[n-1] = CoordX[0]
TabB[n-1] = 0
Ligne[n-1] = True
else :
TabA[n-1] = 0
TabB[n-1] = CoordY[0]
Ligne[n-1] = False
else :
TabA[n-1] = (CoordY[n-1]-CoordY[0])/(CoordX[n-1]-CoordX[0])
TabB[n-1] = (CoordY[0]-TabA[n-1]*CoordX[0])
Ligne[n-1] = False
for i in range (n-1) :
Borne = False
if (CoordY[i]<=TestY and CoordY[i+1]>=TestY) or (CoordY[i]>=TestY and CoordY[i+1]<=TestY):
Borne = True
TabBorne[i] = Borne
Borne = False
if (CoordY[n-1]<=TestY and CoordY[0]>=TestY) or (CoordY[n-1]>=TestY and CoordY[0]<=TestY):
Borne = True
TabBorne[n-1] = Borne
for i in range (n):
if TabBorne[i] == True:
if Ligne[i] == True:
Droite[k] = TabA[i]
elif TabA[i] != 0 :
Droite[k] = ((TestY-TabB[i])/TabA[i])
k = k + 1
for i in range (k):
if TestX<=Droite[i]:
NbCroise = NbCroise+1
Sommet = False
for i in range(n):
if TestX == CoordX[i] and TestY == CoordY[i]:
Sommet = True
if Sommet == True:
print ("Le point est dans la figure.")
elif NbCroise % 2 == 0:
print ("Le point n'est pas dans la figure.")
else:
print ("Le point est dans la figure.")
In C:
#include <stdio.h>
#include <stdlib.h>
int main()
{
int i, n, k, NbCroise, Borne, Sommet, TabBorne[100], Ligne[100];
float TestX, TestY, CoordX[100], CoordY[100], TabA[100], TabB[100], Droite[100];
Sommet = 0;
NbCroise = 0;
k = 0;
n = 0;
while (n<3)
{printf("Entrer le nombre de sommets >=3 \n");
scanf ("%d", &n) ;}
for (i=0;i<n;i=i+1)
{printf("Valeur de x :\n");
scanf ("%f", &CoordX[i]);
printf("Valeur de y :\n");
scanf ("%f", &CoordY[i]);}
printf("Valeur x du point a tester :\n");
scanf ("%f", &TestX);
printf("Valeur y du point a tester :\n");
scanf ("%f", &TestY);
for (i=0;i<(n-1);i=i+1)
{if (((CoordX[i+1]-CoordX[i])==0) || ((CoordY[i+1]-CoordY[i])==0))
{if ((CoordX[i+1]-CoordX[i])==0)
{TabA[i] = CoordX[i];
TabB[i] = 0;
Ligne[i] = 1;}
else
{TabA[i] = 0;
TabB[i] = CoordY[i];
Ligne[i] = 0;}}
else
{TabA[i] = ((CoordY[i+1]-CoordY[i])/(CoordX[i+1]-CoordX[i]));
TabB[i] = (CoordY[i]-(TabA[i]*CoordX[i]));
Ligne[i] = 0;}
}
if (((CoordX[n-1]-CoordX[0])==0) || ((CoordY[n-1]-CoordY[0])==0))
{if ((CoordX[n-1]-CoordX[0])==0)
{TabA[n-1] = CoordX[0];
TabB[n-1] = 0;
Ligne[n-1] = 1;}
else
{TabA[n-1] = 0;
TabB[n-1] = CoordY[0];
Ligne[n-1] = 0;}}
else
{TabA[n-1] = ((CoordY[n-1]-CoordY[0])/(CoordX[n-1]-CoordX[0]));
TabB[n-1] = (CoordY[0]-(TabA[n-1]*CoordX[0]));
Ligne[n-1] = 0;}
for (i=0;i<(n-1);i=i+1)
{Borne = 0;
if (((CoordY[i]<=TestY) && (CoordY[i+1]>=TestY)) || ((CoordY[i]>=TestY) && (CoordY[i+1]<=TestY)))
{Borne = 1;
TabBorne[i] = Borne;}}
Borne = 0;
if (((CoordY[n-1]<=TestY) && (CoordY[0]>=TestY)) || ((CoordY[n-1]>=TestY) && (CoordY[0]<=TestY)))
{Borne = 1;
TabBorne[n-1] = Borne;}
for (i=0;i<n;i=i+1)
{if (TabBorne[i] == 1)
{if (Ligne[i] == 1)
{Droite[k] = TabA[i];}
k = (k+1);}
else if (TabA[i] != 0)
{Droite[k] = ((TestY-TabB[i])/TabA[i]);
k = (k+1);}}
for (i=0;i<k;i=i+1)
{if (TestX <= Droite[i])
NbCroise = (NbCroise + 1);}
for (i=0;i<n;i=i+1)
{if ((TestX == CoordX[i]) && (TestY == CoordY[i]))
Sommet = 1;}
if (Sommet == 1)
{printf("Le point est dans la figure.\n");}
else if (NbCroise % 2 == 0)
{printf("Le point n'est pas dans la figure.\n");}
else
{printf("Le point est dans la figure.\n");}
return 0;
}
