Infinite loop with y=mx+b randomisation

Programming Questions

utherdoul

Infinite loop with y=mx+b randomisation

in Programming Questions • 8 months ago

I'm trying to write a simple program which draws a line from the centre of the screen to a randomised point within the window. Then, I want to (for now) draw an ellipse somewhere along that line, using the y-intercept formula y=mx+b to track the line's slope. So far, so good.

However, now I want to ensure that this ellipse isn't drawn too close to the centre. I used a while loop to check the distance between the ellipse's centre coordinates and the centre of the screen, but it's quite regularly, though not always, getting stuck in an infinite loop. It seems x and y are fairly often being assigned / calculated to 100.0 (i.e. the centre of the screen). Code below (beware of infinite looping if you decide to run it):

size(200, 200);
background(#13212C);
smooth();
stroke(255);
float x1 = width / 2;
float y1 = height / 2;
float x2 = random(0, width);
float y2 = random(0, height);
while(x2 > (width / 4) && x2 < ((width / 4) * 3) && x2 > (height / 4) && x2 <((height / 4) * 3))
{
x2 = random(0, width);
y2 = random(0, height);
}
line(x1, y1, x2, y2);
float m = (y2 - y1) / (x2 - x1);
float b = y1 - (m * x1);
float x = random(x1, x2);
float y = (m * x) + b;
float nodeProx = dist(x, y, x1, y1);
println("nodeProx" + nodeProx);
println("x" + x + ", y" + y);
while(nodeProx <= 20.0)
{
x = random(x1, x2);
y = (m * x) + b;
nodeProx = dist(x, y, x1, y1);
println("x" + x + ", y" + y);
println(nodeProx);
}
println("m = " + m);
println("b = " + b);
noStroke();
fill(255);
ellipse((width / 2), (height / 2), 20, 20); // central ellipse
fill(255, 0, 0);
ellipse(x, y, 5, 5); // 'node' ellipse

I thought I'd allowed for the infinite loop by randomising x within the while loop, re-calculating y, then reassigning nodeProx to the new distance, however, it spits out 0.0 for nodeProx and can't change despite the reassignment within the while loop.

I'm relatively new to Processing and my maths is extremely rusty. I suspect it's a maths problem over a programming problem, but after managing to get to this point, I'm a little stuck.

Can anyone see the error of my ways? Is there a simpler solution for drawing a random point along a randomly-generated line?

Many thanks in advance!

Replies(3)

quarks

Re: Infinite loop with y=mx+b randomisation

8 months ago

Several problems here the first is using the formula y = mx + b to represent a line. Although this is ok when doing geometry it has a number of problems when it comes to programming. The reasom is that m becomes infinity when the line is vertical and computers don't handle infinite values very well.

In programming we use parametric equations so if we want to define the line between two points [x1,y1] and [x2,y2] then we use two parametric formulae

x(t) = x1 + (x2-x1)*t
y(t) = y1 + (y2-y1)*t

where t is a value in the range >=0 and <=1

When t = 0 then
x(t) = x1
y(t) = y1

and when t = 1 then
x(t) = x2
y(t) = y2

The mid point will be when t = 0.5

The other prolem is the while statement in line 11 in that it tests X2 againt both width and height so I suspect you meant

while(x2 > (width / 4) && x2 < ((width / 4) * 3) && y2 > (height / 4) && y2 <((height / 4) * 3))

Even this is seems wrong in that only values near x1,y1 or near the display border are acceptable? I suspect that you meant the opposite.

The other problem with this is that there is only 1 in 4 chance of this expression returning true. It would be better to calculate valid values for x2 and y2 by changing lines 8 and 9 to

float x2 = random(0.25*width, 0.75*width);
float y2 = random(0.25*height, 0.75*height);

I strongly recommend that you look at parametric equations as they are used extensively in programming.

HTH

utherdoul

Re: Re: Infinite loop with y=mx+b randomisation

8 months ago

Thank you, quarks. The parametric equations (or lack thereof) is clearly where I was going wrong; I'll look into that.

The while loop with highlighted sections you pointed out was in fact a typo setting the loop back after some trial-and-error tests, so that's not a major issue (though thanks for pointing it out). However, what that loop is supposed to do is force (x2, y2) to be near the edges within a (0.25 * width) or (0.25 * height) border. As (x1, y1) is in the centre, it forces the line to extend a minimum of (0.5 * width) or (0.5 * height). There's probably a simpler way of doing this too.

quarks

Re: Infinite loop with y=mx+b randomisation

8 months ago

supposed to do is force (x2, y2) to be near the edges within a (0.25 * width) or (0.25 * height) border

This would do that for you.

float x2 = random(0, 0.25 * width);
if(random(1) < 0.5)
x2 = width - x2;
float y2 = random(0, 0.25 * height);
if(random(1) < 0.5)
y2 = height - y2;

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