How to resolve the algorithm Constrained random points on a circle step by step in the Prolog programming language

Published on 12 May 2024 09:40 PM
#Prolog

How to resolve the algorithm Constrained random points on a circle step by step in the Prolog programming language

Table of Contents

Problem Statement

Generate 100 <x,y> coordinate pairs such that x and y are integers sampled from the uniform distribution with the condition that

10 ≤

x

2

y

2

≤ 15

{\displaystyle 10\leq {\sqrt {x^{2}+y^{2}}}\leq 15}

. Then display/plot them. The outcome should be a "fuzzy" circle. The actual number of points plotted may be less than 100, given that some pairs may be generated more than once. There are several possible approaches to accomplish this. Here are two possible algorithms.

  1. Generate random pairs of integers and filter out those that don't satisfy this condition:
  2. Precalculate the set of all possible points (there are 404 of them) and select randomly from this set.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Constrained random points on a circle step by step in the Prolog programming language

Source code in the prolog programming language

:- use_module(library(clpfd)).

circle :-
	bagof([X,Y], init(X,Y), BL),
	length(BL, N),
	length(L, 100),
	maplist(choose(BL, N), L),
	draw_circle(L).


% point selection
choose(BL, N, V) :-
	I is random(N),
	nth0(I, BL, V).

% to find all couples of numbers verifying 
% 100 <= x^2 + y^2 <= 225
init(X1, Y1) :-
	X in -15..15,
	Y in -15..15,
	X*X + Y*Y #>= 100,
	X*X + Y*Y #=< 225,
	label([X,Y]),
	X1 is 10 * X + 200,
	Y1 is 10 * Y + 200.


draw_circle(L) :-
	new(D, window('Circle')),
	send(D, size,size(400,400)),
	forall(member([X,Y], L),
	       (   new(C, circle(4)),
		   send(C, fill_pattern, colour(@default, 0, 0, 0)),
		   send(C, center(point(X,Y))),
		   send(D, display, C))),
	send(D, open).

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