algorithm.md

arcLandscape/algorithm.md

arcLandscape

Tool to convert text or hexadecimal sequence into generative art based on arc system.
GitHub: https://github.com/YujiSODE/arcLandscape
Wiki: https://github.com/YujiSODE/arcLandscape/wiki

Copyright (c) 2022 Yuji SODE <yuji.sode@gmail.com>
This software is released under the MIT License.
See LICENSE or http://opensource.org/licenses/mit-license.php

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arcLandscape is tool to convert text or hexadecimal sequence into generative art based on arc system.
Arc system is a system, where every object is regarded as structure on a spherical surface.

Figure 1. Chart showing algorithm of arc system.
Result paths (blue) derives from given circle (dashed line) and value changes along y axis (red).

Value in a sequence

A hexadecimal sequence: seq.
Length of this hexadecimal sequence: L.
An index for a value in this hexadecimal sequence: I := i%L, where i = 0,1,2, ....

A value in this sequence hex is expressed as follows:
hex = seq[I] = seq[i%L]

Global constants

• midX = (target canvas width)*0.5
• midY = (target canvas height)*0.5
• R0 = max(midX,midY)*SQRT(2)
• dT = π/100

Function: arc(I)

arc(I) := {
	x=xO+r0*cos(t);
	y=yO+r0*sin(t)+r;
	draw(t = from T0 to T0 +2*π);
}

Local values in arc(I)

Color

Fill color: #rrggbbaa = #{seq[I]}{seq[(I+1)%L]}{seq[(I+2)%L]}{seq[(I+3)%L]}{seq[(I+4)%L]}{seq[(I+5)%L]}ff,
where (r,g,b,a) = 0,1, ...,e,f.

Values

1. Direction and Radius for O := (xO, yO)

   • direction: direction = π*seq[I]/8 = 2*π*hex/16
   • radius: R = R0*(1.0+seq[(I+1)%L]/16)

2. x and y

   • xO = midX +R*cos(direction)
   • yO = midY +R*sin(direction)
   • x = (target canvas width)*seq[(I+2)%L]/16
   • y = (target canvas height)*seq[(I+3)%L]/16

3. Radius for arc(I) and T0

   • T0: initial angle between the positive x-axis and a vector (x-xO, y-yO)
   • radius: r0 = SQRT((x-xO)^2+(y-yO)^2)

Changes of r in arc(I)

• r = 0.0
• T = dT
• t = T0 +T
• j = 1

while(T<2*π){
	idx = I+seq[I]*j;

	a0 = seq[idx%L];
	a1 = seq[(idx+1)%L];
	a2 = seq[(idx+2)%L];
	a3 = seq[(idx+3)%L];

	r += (a1-a0)*(a3-a2);

	x=xO+r0*cos(t);
	y=yO+r0*sin(t)+r;

	j += 1;
	T = j*dT;
	t = T0+T;
}

Normal order

i = from 0 to L-1

i = 0;
while(i<L){
	arc(i);
	i+=1;
}

Reverse order

i = from L-1 to 0

i = L-1;
while(!(i<0)){
	arc(i);
	i+=-1;
}