How to resolve the algorithm Total circles area step by step in the zkl programming language

Published on 12 May 2024 09:40 PM
#Zkl

How to resolve the algorithm Total circles area step by step in the zkl programming language

Table of Contents

Problem Statement

Given some partially overlapping circles on the plane, compute and show the total area covered by them, with four or six (or a little more) decimal digits of precision. The area covered by two or more disks needs to be counted only once. One point of this Task is also to compare and discuss the relative merits of various solution strategies, their performance, precision and simplicity. This means keeping both slower and faster solutions for a language (like C) is welcome. To allow a better comparison of the different implementations, solve the problem with this standard dataset, each line contains the x and y coordinates of the centers of the disks and their radii   (11 disks are fully contained inside other disks): The result is   21.56503660... .

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Total circles area step by step in the zkl programming language

Source code in the zkl programming language

circles:=File("circles.txt").pump(List,'wrap(line){
   line.split().apply("toFloat")  // L(x,y,r)
});
    # compute the bounding box of the circles
x_min:=(0.0).min(circles.apply(fcn([(x,y,r)]){ x - r })); // (0) not used, just the list of numbers
x_max:=(0.0).max(circles.apply(fcn([(x,y,r)]){ x + r }));
y_min:=(0.0).min(circles.apply(fcn([(x,y,r)]){ y - r }));
y_max:=(0.0).max(circles.apply(fcn([(x,y,r)]){ y + r }));

box_side:=500;
dx:=(x_max - x_min)/box_side;
dy:=(y_max - y_min)/box_side;

count:=0;
foreach r in (box_side){
   y:=y_min + dy*r;
   foreach c in (box_side){
      x:=x_min + dx*c;
      count+=circles.filter1('wrap([(cx,cy,cr)]){
         x-=cx; y-=cy;
      	 x*x + y*y <= cr*cr
      }).toBool(); // -->False|L(x,y,z), L(x,y,r).toBool()-->True, 
   }
}

println("Approximated area: ", dx*dy*count);

You may also check:How to resolve the algorithm Mutual recursion step by step in the MiniZinc programming language
You may also check:How to resolve the algorithm Exponentiation operator step by step in the BASIC programming language
You may also check:How to resolve the algorithm Box the compass step by step in the Raku programming language
You may also check:How to resolve the algorithm Man or boy test step by step in the Standard ML programming language
You may also check:How to resolve the algorithm Count in octal step by step in the APL programming language