How to resolve the algorithm Pentagram step by step in the Nim programming language

Published on 12 May 2024 09:40 PM
#Nim

How to resolve the algorithm Pentagram step by step in the Nim programming language

Table of Contents

Problem Statement

A pentagram is a star polygon, consisting of a central pentagon of which each side forms the base of an isosceles triangle. The vertex of each triangle, a point of the star, is 36 degrees.

Draw (or print) a regular pentagram, in any orientation. Use a different color (or token) for stroke and fill, and background. For the fill it should be assumed that all points inside the triangles and the pentagon are inside the pentagram.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pentagram step by step in the Nim programming language

Source code in the nim programming language

import libgd
from math import sin, cos, degToRad

const
  width = 500
  height = width
  outerRadius = 200

proc main() =

  proc calcPosition(x: int, y: int, radius: int, posAngle: float): (cint, cint) =
    var width = int(radius.float * sin(degToRad(posAngle)))
    var height = int(radius.float * cos(degToRad(posAngle)))
    return (cast[cint](x + width), cast[cint](y - height))

  proc getPentagonPoints(startAngle = 0, radius: int): array[5, array[2, int]] =
    let spacingAngle = 360 / 5

    var posAngle = (90 - startAngle).float

    var n = 0
    var points: array[5, array[2, int]]
    while n < 5:
      (points[n][0], points[n][1]) = calcPosition(250, 250, radius, posAngle)
      n += 1
      posAngle -= spacingAngle

    return points

  let outerPentagon = getPentagonPoints(18, outerRadius) # rotate 18 degrees
  let innerPentagon = getPentagonPoints(54, int((cos(degToRad(72.0))/cos(degToRad(36.0))) * outerRadius)) # rotate 54 degrees

  var pentagram: array[10, array[2, int]]
  var n = 0
  for i in countup(0, 4):
    pentagram[n] = outerPentagon[i]
    inc(n)
    pentagram[n] = innerPentagon[i]
    inc(n)

  withGd imageCreate(width, height) as img:
    discard img.setColor(255, 255, 255)

    let black = img.setColor(0x404040)
    let blue = img.setColor(0x6495ed)

    img.drawPolygon(
      points=pentagram,
      color=blue,
      fill=true,
      open=false)

    img.setThickness(4)

    img.drawPolygon(
      points=pentagram,
      color=black,
      fill=false,
      open=false)

    img.drawPolygon(
      points=innerPentagon,
      color=black,
      fill=false,
      open=false)

    let png_out = open("pentagram.png", fmWrite)
    img.writePng(png_out)

    png_out.close()

main()

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