generate random points on a line

[Marc Dansereau]

Hi all,

I wonder what is the most efficient way to generate random point on a line
defined by 2 double points (x0,y0) and (x1,y1).

Here is the pseudocode of my method :

for each point {
dx=x1-x0
dy=y1-y1

if dx != 0 {
m=dy/dx
b = y0-m*x0
x = (rand()%(int)dx)+x0
y = m* x + b
printf("(%f, %f) is a random point on the line", x, y);
} else {
x = x0
y = (rand() %(int)dy)+y0
}
}

There is probably a problem with the rounding of dy and dx ... There is
probably a better way to do this, but I can't figure which ?

Thank you

 

[Rouben Rostamian]

I wonder what is the most efficient way to generate random point on a line
defined by 2 double points (x0,y0) and (x1,y1).

Generate a random number t in the interval [0,1]. Then let:

x = (1-t)*x0 + t*x1;
y = (1-t)*y0 + t*y1;

 

[Martin Ambuhl]

Hi all,

I wonder what is the most efficient way to generate random point on a line
defined by 2 double points (x0,y0) and (x1,y1).

Here is the pseudocode of my method :

for each point {
dx=x1-x0
dy=y1-y1

if dx != 0 {
m=dy/dx
b = y0-m*x0
x = (rand()%(int)dx)+x0
y = m* x + b
printf("(%f, %f) is a random point on the line", x, y);
} else {
x = x0
y = (rand() %(int)dy)+y0
}
}

There is probably a problem with the rounding of dy and dx ... There is
probably a better way to do this, but I can't figure which ?

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

typedef struct
{
double x, y;
} pt;

pt randompt(pt a, pt b)
{
pt c;
c.x = a.x + (b.x - a.x) * rand() / (1. + RAND_MAX);
c.y = a.y + (c.x - a.x) * (a.y - b.y) / (a.x - b.x);
return c;
}

int main(void)
{
pt p1 = { 1, 1 }, p2 = { 2, 3 }, p3;
int i;
const int npts = 10;
srand((unsigned) time(0));
printf("Here are %d randomly chosen points on the line\n"
"from (%g,%g) to (%g,%g)\n", npts, p1.x, p1.y, p2.x, p2.y);
for (i = 0; i < npts; i++) {
p3 = randompt(p1, p2);
printf("%2d: (%g,%g)\n", i + 1, p3.x, p3.y);
}
return 0;
}



Here are 10 randomly chosen points on the line
from (1,1) to (2,3)
1: (1.38438,1.76876)
2: (1.46981,1.93962)
3: (1.96502,2.93003)
4: (1.68285,2.3657)
5: (1.91771,2.83543)
6: (1.77233,2.54467)
7: (1.88148,2.76296)
8: (1.26106,1.52211)
9: (1.77445,2.5489)
10: (1.43061,1.86122)

 

[CBFalconer]

I wonder what is the most efficient way to generate random point
on a line defined by 2 double points (x0,y0) and (x1,y1).

Generate a random number t in the interval [0,1]. Then let:

x = (1-t)*x0 + t*x1;
y = (1-t)*y0 + t*y1;

Which, off hand, I think is the same as converting to polar based
on (x0,y0) and adjusting the magnitude of the polar coordinates of
(x1,y1). At any rate this is off-topic for c.l.c and is better
suited for comp.programming. Cross-posted and f'ups set.

 

[Chris Croughton]

I wonder what is the most efficient way to generate random point on a line
defined by 2 double points (x0,y0) and (x1,y1).

Generate a random number t in the interval [0,1]. Then let:

x = (1-t)*x0 + t*x1;
y = (1-t)*y0 + t*y1;

I would write it as:

x = x0 + t * (x1 - x0);
y = y0 + t * (y1 - y0);

which only does one multiply per expression. It also reflects the way I
think about lines (translate the start of the line to be the origin,
scale and then translate back).

Incidentally, using the interval [0,1] assumes that the endpoints of
the line are inclusive. This may be a problem, since a lot of random
number generators are in the (usually more useful) range [0,1) which
would exclude the end of the line (I've fallen into that trap before).
I've had to resort to using two generator functions:

double randf(void)
{
return rand() / (double)(RAND_MAX + 1);
}

double randfinc(void)
{
return rand() / (double)RAND_MAX;
}

Similarly for (0,1) and (0,1] if needed (I've needed the former but not
the latter).

(Actually I use a more consistent but non-Standard RNG instead of
rand(), see other threads about RNGs...)

Chris C