How to resolve the algorithm Archimedean spiral step by step in the Lambdatalk programming language

Published on 12 May 2024 09:40 PM
#Lambdatalk

How to resolve the algorithm Archimedean spiral step by step in the Lambdatalk programming language

Table of Contents

Problem Statement

The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.

An Archimedean spiral can be described by the equation: with real numbers a and b.

Draw an Archimedean spiral.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Archimedean spiral step by step in the Lambdatalk programming language

Source code in the lambdatalk programming language

1) from polar to cartesian coordinates

x = r*cos(t) = (a+b*t)*cos(t)
y = r*sin(t) = (a+b*t)*sin(t)

2) define the curve

{def CURVE       
 {lambda {:a :b :t}    
  {* {+ :a {* :b :t}} {cos :t}}     
  {* {+ :a {* :b :t}} {sin :t}}  
}}
-> CURVE

3) and draw it using SVG

{{SVG 580}
 {g {AXES 580 580}
  {polyline {@ points="{S.map {CURVE 5 4} 
                              {S.serie 0 {* 10 {PI}} 0.1}}"  
               {stroke red 3}}
}}}

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