Description
/*
* ◯⟷△ №.04
* Interpolation From a Circle to an Equilateral Triangle (#04)
* "By considering it as a set of alternating straight lines
* and arcs, in which the arcs shrink while the lines grow."
* Page Four of a 14-Page Pedagogical Sketchbook
* By Golan Levin (@golan), 2017-2021.
* https://link.medium.com/bn3sesXYOkb
*
* Animated GIF, 1024x1024, 720 frames @50fps, made with p5.js;
* Presented October 25, 2017 on the Coding Train episode,
* "Guest Tutorial #7: Circle Morphing with Golan Levin"
* (https://www.youtube.com/watch?v=mvgcNOX8JGQ&t=25m02s).
* NFT created in 2021 for #Sketch4Processing, and minted by
* KT1TaPfAuhmnyo6Le6zKe17opvFCsTxk1VN7 (golan_x_processingorg).
* Per contract, 20% of all sales are donated to @ProcessingOrg.
*
* References:
* - Joseph Choma, "Morphing: A Guide to Mathematical
* Transformations for Architects and Designers", 2015.
* - Guus Craenen and Adrian Häne, "Fruit Salad", 1970.
* - CTG Japan (Masao Kohmura, Koji Fujino, Makoto Ohtake),
* "Running Cola is Africa!", 1968.
* - Wassily Kandinsky, "Point and Line to Plane", 1926.
* - William Kolomyjec, "Banana Cone", 1970-1975.
* - Jürg Lehni and Wilm Thoben, "Footnotes from the History
* of Two Cultures: Mitsuo Katsui", 2015.
* - Manfred Mohr, "P-112 / Lady Quark", 1972.
* - Bruno Munari, "Square Circle Triangle", 1960-1976.
* - Charles Philipon, "Les Poires", 1831.
* - Troika, "Squaring the Circle"; "Dark Matter", 2013-2014.
* - Wucius Wong, "Principles of Two-Dimensional Design", 1972.
* - Yuki Yoshida, "A Book of drawCircle()", 2014.
*/
var radius;
var trianglePoints = [];
var bShowDebug;
var nFrames = 360;
var nLoops = 2;
var theta;
var strokeCol1;
var backgrCol;
function setup() {
createCanvas(1024, 1024);
pixelDensity(1);
frameRate(60);
strokeCol1 = color(24, 14, 6, 255);
backgrCol = color(253, 247, 241);
radius = (width / 2) * 0.75;
for (var i = 0; i < 3; i++) {
var x = radius * cos((i * TWO_PI) / 3.0 - HALF_PI);
var y = radius * sin((i * TWO_PI) / 3.0 - HALF_PI);
trianglePoints[i] = { x, y };
}
}
function draw() {
background(backgrCol);
noFill();
var t = ((frameCount / nLoops) % nFrames) / nFrames;
theta = TWO_PI * t;
push();
translate(width / 2, height / 2);
rotate(PI);
var currentRadii01 = 0.5 + 0.5 * sin(theta);
var rad = currentRadii01 * radius;
if (cos(theta) > 0) scale(-1, 1);
var nPointsInArc = 60;
strokeJoin(currentRadii01 < 0.002 ? ROUND : MITER);
stroke(strokeCol1);
strokeWeight(ceil(width * 0.01));
beginShape();
for (var i = 0; i < 3; i++) {
var px = 0 - map(currentRadii01, 0, 1, trianglePoints[i].x, 0);
var py = 0 - map(currentRadii01, 0, 1, trianglePoints[i].y, 0);
var ang1 = ((i + 1) * TWO_PI) / 3 + HALF_PI / 3 + PI;
var ang2 = ((i + 2) * TWO_PI) / 3 + HALF_PI / 3 + PI;
for (var j = 0; j <= nPointsInArc; j++) {
var t = map(j, 0, nPointsInArc, ang1, ang2);
var ax = px + rad * cos(t);
var ay = py + rad * sin(t);
vertex(ax, ay);
}
}
endShape(CLOSE);
bShowDebug = theta <= TWO_PI * 0.25 || theta >= TWO_PI * 0.75;
if (bShowDebug) {
var t2 = (theta + PI * 1.5) % TWO_PI;
var alph = 0.5 - 0.5 * cos(t2);
stroke(24, 14, 6, 128 * pow(alph, 0.333));
strokeWeight(width / 1024.0);
for (var i = 0; i < 3; i++) {
var px = 0 - map(currentRadii01, 0, 1, trianglePoints[i].x, 0);
var py = 0 - map(currentRadii01, 0, 1, trianglePoints[i].y, 0);
var qx = 0 - map(currentRadii01, 0, 1, trianglePoints[(i + 1) % 3].x, 0);
var qy = 0 - map(currentRadii01, 0, 1, trianglePoints[(i + 1) % 3].y, 0);
line(px, py, qx, qy);
var ang1 = ((i + 1) * TWO_PI) / 3 + HALF_PI / 3 + PI;
var ang2 = ((i + 2) * TWO_PI) / 3 + HALF_PI / 3 + PI;
var ax = px + rad * cos(ang1);
var ay = py + rad * sin(ang1);
line(ax, ay, px, py);
var bx = px + rad * cos(ang2);
var by = py + rad * sin(ang2);
line(bx, by, px, py);
}
}
pop();
}