Description
/*
* ◯⟷△ №.07
* Interpolation From a Circle to an Equilateral Triangle (#07)
* "By gradually shrinking the circle's radius,
* revealing triangular corners within."
* Page Seven of a 14-Page Pedagogical Sketchbook
* By Golan Levin (@golan), 2017-2021.
* https://link.medium.com/bn3sesXYOkb
*
* Animated GIF, 1024x1024, 360 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=24m10s).
* 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 cx, cy;
var trianglePoints = [];
var nFrames = 360;
var third;
var theta;
var strokeCol;
var backgrCol;
function setup() {
createCanvas(1024, 1024);
pixelDensity(1);
frameRate(60);
strokeCol = color(24, 14, 6, 255);
backgrCol = color(253, 247, 241);
radius = width / 2 * 0.75;
cx = width / 2;
cy = height / 2;
third = TWO_PI / 3.0;
for (var i = 0; i < 3; i++) {
var x = cx + radius * cos(i * third - HALF_PI);
var y = cy + radius * sin(i * third - HALF_PI);
trianglePoints[i] = { x, y };
}
}
function draw() {
background(backgrCol);
noFill();
stroke(strokeCol);
strokeJoin(ROUND);
strokeCap(ROUND);
strokeWeight(ceil(width * 0.01));
theta = TWO_PI * (frameCount % nFrames) / nFrames;
var amount = 0.745 + 0.255 * cos(theta); // Magic numbers
var rad = amount * radius;
var nPts = 30;
for (var i = 0; i < 3; i++) {
var x1 = trianglePoints[(i + 0) % 3].x - cx;
var y1 = trianglePoints[(i + 0) % 3].y - cy;
var x2 = trianglePoints[(i + 1) % 3].x - cx;
var y2 = trianglePoints[(i + 1) % 3].y - cy;
var dx = x2 - x1;
var dy = y2 - y1;
var dr = sqrt(dx * dx + dy * dy);
var D = (x1 * y2) - (x2 * y1);
// See http://mathworld.wolfram.com/Circle-LineIntersection.html
var discriminant = rad * rad * dr * dr - D * D;
if (discriminant <= 0) {
line(x1 + cx, y1 + cy, x2 + cx, y2 + cy);
} else {
var dysign = ((dy < 0) ? -1 : 1);
var px = cx + (D * dy + dysign * dx * sqrt(discriminant)) / (dr * dr);
var py = cy + (-D * dx + abs(dy) * sqrt(discriminant)) / (dr * dr);
var qx = cx + (D * dy - dysign * dx * sqrt(discriminant)) / (dr * dr);
var qy = cy + (-D * dx - abs(dy) * sqrt(discriminant)) / (dr * dr);
var pAng = atan2(py - cy, px - cx);
var qAng = atan2(qy - cy, qx - cx);
if (i == 2) {
var tmp = pAng;
pAng = qAng;
qAng = tmp;
if (py > cy) {
qAng -= TWO_PI;
}
}
beginShape();
vertex(x2 + cx, y2 + cy);
for (var j = 0; j <= nPts; j++) {
var t = map(j, 0, nPts, pAng, qAng);
var tx = cx + rad * cos(t);
var ty = cy + rad * sin(t);
vertex(tx, ty);
}
vertex(x1 + cx, y1 + cy);
endShape();
}
}
}