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POFractally generated lines with pre-specified endpoints
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copied!<p>Here is my problem:</p> <p>I have two random points (x,y) and (x2, y2). I would like to great a 'random-step' or fractal line between the two. I have set up a situation wherein the step distance and direction are randomly generated based on a probability matrix. However, leaving it solely to the direction of this matrix, the line will have a random endpoint which is impossible to pre-determine. I have therefore attempted to set up bounds for my line where--if a point falls--the location is adjusted accordingly. These bounds are not working. </p> <p>Ideally, my boundaries would be a circle created with each random point at opposite ends of the area. I have tried the following.</p> <ol> <li><p>I have set up a loop which will iterate through each x-point of the line using a variable <strong>i</strong> which starts with the lesser of x and x2 and moves towards the greater.</p></li> <li><p>I have set up a variable <strong>j</strong> to which the random step will be added and initialised it to the equivalent y-value for the lesser x-value (if x1 is greater set to y1 else set to x).</p></li> <li><p>I have set up a variable which contains the slope of the theoretical straight line between x,y and x1,y1.</p></li> <li><p>I have set up a probability matrix which takes a variable <strong>mod</strong> and sets it to a value between 8 and -8.</p></li> <li><p>I have set up checks to disallow the formation of the line outside of the boundaries of the given plane.</p></li> <li><p>I have set up a check to determine if the variable <strong>i</strong> is one less than the greater of x and x2. If so, variable <strong>j</strong> is set to that x-value's y-value;</p></li> </ol> <p>It is at this point that I fail to find the appropriate algorithm to set up the final check. Here is what I would like the algorithm to do:</p> <p>A. I would like it to be able to, given a random x-value between x and x1, determine if the current variable <strong>j</strong> added to the current variable <strong>mod</strong> is outside of the circle generated by the two aforementioned points (see the second paragraph). If it is not, add mod to variable <strong>j</strong> and increment the loop.</p> <p>B. If this point would fall outside the bounds, I would like the step direction to be reversed (e.g. -6 to 6 and 2 to -2) and the same check to be made again.</p> <p>C. If adding in either direction would put it out of bounds (which will most likely happen near the far end of the circle where the boundaries constrict the most), I would like to be able to run through a loop which checks each value and its inverse beginning at 0 and moving to consecutively larger values until a workable value is determined.</p> <p>I hope you experience mathematicians and programmers out there see this as a surmountable challenge. It has stumped me for three weeks and I have run out of ideas.</p>

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