find if 4 points on a plane form a rectangle?

Question

Can somebody please show me in C-style pseudocode how to write a function (represent the points however you like) that returns true if 4-points (args to the function) form a rectangle, and false otherwise? I came up with a solution that first tries to find 2 distinct pairs of points with equal x-value, then does this for the y-axis. But the code is rather long. Just curious to see what others come up with.

Answer 1

#include <stdio.h>

#include <math.h>

#define IsPerpendicular(m1,m2) ((m1)*(m2)==(-1))

typedef struct _TPoint

{

double x;

double y;

}*TPoint;

double Distance( TPoint p1, TPoint p2)

{

double x1 = p1->x;

double y1 = p1->y;

double x2 = p2->x;

double y2 = p2->y;

return (

sqrt(

(x1-x2)*(x1-x2) + (y1-y2)*(y1-y2)

)

);

}//Distance

int Slope(TPoint p1, TPoint p2, double * mSlope)

{

double x1 = p1->x;

double y1 = p1->y;

double x2 = p2->x;

double y2 = p2->y;

double D = (x2-x1) ;

int iReturn = 0;

if (D!=0)

{

*mSlope = (y2-y1)/D;

}

else

{

iReturn = -1;

}

return(iReturn);

} //Slope

int InputPoint( char * promptMsg, TPoint P)

{

char defaultPromptMsg[25];

if (promptMsg==NULL)

{

sprintf(defaultPromptMsg,"INPUT POINT COORDINATES\n");

promptMsg = &defaultPromptMsg[0];

}

printf("********************************\n");

printf(promptMsg);

printf("\n********************************\n");

printf(" Please input x coordinate :>");

scanf(" %lf",&P->x);

printf(" Please input y coordinate :>");

scanf(" %lf",&P->y);

printf("\n");

}

int SlopeCheck(int M1, int M2, double m1, double m2)

{

int iReturn=0;

if ((M1>=0)&&(M2>=0)) //both slopes are defined

{

if (m1!=m2)

{

iReturn = -1;

}

}

else //one or both slopes are undefined

{

if ((M1==-1) && (M2==-1))

{

}

else //one slope is undefined and the other is not, so they're not equal

{

iReturn = -1;

}

}

return(iReturn);

}

int CornerCheck(int M1, int M2, double m1, double m2)

{

int iReturn=0;

printf(" CornerCheck M1=%d M2 = %d m1=%12.6lf m2 = %12.6lf \n",M1,M2,m1,m2);

if (( M1>=0) && (M2>=0)) //slopes are both defined

{

printf(" CornerCheck: both slopes are defined \n");

if (IsPerpendicular(m1,m2))

{

printf(" CornerCheck: slopes are negative reciprocals-->perpendicular \n");

}

else //the lines are not perpendicular so it is not a rectangle

{

printf(" CornerCheck: slopes are NOT perpendicular \n");

iReturn = -1;

}

}

else //one of the lines is vertical

{

printf(" One or both slopes undefined \n");

if (

(((M1>=0)&&(m1==0)) || ((M2>=0)&&(m2==0))) //slopes are negative reciprocals: one zero, the other undefined

)

{

printf(" LINES ARE PERPENDICULAR \n");

}

else //lines cannot be perpendicular

{

printf(" LINES ARE NOT PERPENDICULAR \n");

iReturn = -1;

}

} //lines are perpendicular

return(iReturn);

}

Rectangle(TPoint P)

{

int iReturn = 0;

struct _TPoint A = P[0];

struct _TPoint B = P[1];

struct _TPoint C = P[2];

struct _TPoint D = P[3];

double mAB, mBC, mCD, mDA; //slopes

double dAB, dBC, dCD, dDA; //distances

int Mab, Mbc, Mcd, Mda; // slopes are defined

Mab = Slope(&A, &B, &mAB);

Mbc = Slope(&B, &C, &mBC);

Mcd = Slope(&C, &D, &mCD);

Mda = Slope(&D, &A, &mDA);

dAB = Distance(&A,&B);

dBC = Distance(&B,&C);

dCD = Distance(&C,&D);

dDA = Distance(&D,&A);

if ((dAB==dCD) && (dBC==dDA))

{

//opposite sides are the same

printf(" DEBUG: opposite sides are the same \n");

if ((SlopeCheck(Mab,Mcd,mAB,mCD)>=0) && (SlopeCheck(Mbc,Mda,mBC,mDA)>=0))

{

//oppposite sides are parallel

printf(" DEBUG: opposite sides are parallel \n");

//checks that the corners are right angles

if ((CornerCheck(Mab,Mbc,mAB,mBC)>=0) &&

(CornerCheck(Mbc,Mcd,mBC,mCD)>=0) &&

(CornerCheck(Mcd,Mda,mCD,mDA)>=0) &&

(CornerCheck(Mda,Mab,mDA,mAB)>=0)

)

{

}

else // one or more of the corners are not right angles, so it cannot be a rectangle

{

iReturn=-1;

}

}

else //opposite sides are not parallel, so it cannot be a rectangle

{

iReturn = -1;

}

}

else // opposite sides are different, so it cannot be a rectangle

{

iReturn = -1;

}

return(iReturn);

}

int Go()

{

int iReturn;

struct _TPoint P[4];

int iLoop;

printf(" Please input the points in CLOCKWISE order starting with top left.....\n");

printf(" Point A is TOP LEFT \n Point B is TOP RIGHT \n Point C is BOTTOM RIGHT \n Point D is BOTTOM LEFT \n");

for (iLoop=0; iLoop<4; iLoop++)

{

char promptMsg[55];

switch (iLoop)

{

case 0:

{

sprintf(promptMsg,"Please input point A"); break;

}

case 1:

{

sprintf(promptMsg,"Please input point B"); break;

}

case 2:

{

sprintf(promptMsg,"Please input point C"); break;

}

case 3:

{

sprintf(promptMsg,"Please input point D"); break;

}

}

InputPoint(promptMsg,&P[iLoop]);

}

if (Rectangle(P)>=0)

{

printf(" IT IS A RECTANGLE \n");

}

else

{

printf(" IT IS NOT A RECTANGLE \n");

}

return(iReturn);

}

int main()

{

return(Go());

}