Month: October 2021

// This program displays a grid of Epitrochoid curves with increasing nPoints and cusps.
// The canvas sets up with a 5x5 grid; 
// When the mouse is pressed, more curves are drawn.
// Pressing the spacebar deletes one row and column. 

var c;				// color 
var density = 5;	// number of curves in each row and column
var nPoints;		// number of points used to draw each curve
var cusp;			// number of cusps on each curve
var mode = 0		// default mode uses Epitrochoid formula, other mode uses an edited Epitrochoid-like formula

function setup() {
    createCanvas(480, 480);
}

function draw() {
	background(200, 200, 255);
	// draw a grid of curves based on density value:
	for (var k=0; k<density; k++) {
		cusp = k+1;							// number of cusps increases from left to right
		for (var j=0; j<density; j++) {
			push();
			translate(k*width/density+240/density, 	// keeps grid centered regardless of density changes
					  j*height/density+240/density);	
			nPoints = (j+1)*density			// number of nPoints increases from top to bottom
		
        	//color based on grid and mouse location:
			let r = map(j, 0, density, 0, 255);
			let g = map(k, 0, density, 0, 255);
			let b = map(mouseX, 0, width, 0, 255);
			c = color(r, g, b);
			
			// check which mode we are in and draw curves:
			if (mode == 0) {drawEpitrochoidCurve(nPoints, cusp, c)}
			else {drawEpitrochoidyCurve(nPoints, cusp, c)}
			pop();
		}
	}
	// labeling for easier understanding of the grid pattern:
	textFont('monospace');
	text('click mouse for more curves,	press spacebar for fewer curves', 20, height-12);
	text('press "w" for weird curves,	press "r" for default curves', 20, height-3);
	text('n u m b e r		o f		c u s p s   ----- >', 5, 10);
	text('n P o i n t s', 5, 30, 1, 150);
	push(); 
	rotate(radians(90));
	text('----- >', 140, -5);
	pop();
	

}

// code adapted from sample in project description:
function drawEpitrochoidCurve(nPoints, cusp, color) {
    // Epitrochoid:
	//https://mathworld.wolfram.com/Epitrochoid.html
	
    var x;
    var y;

	var a = 15;
    var b = a / cusp;
    var h = map(mouseY/8, 0, height, 0, a*5);
    var ph = -mouseX / 40;
    
    fill(color);

	// shape of curve:
    beginShape();
    for (var i = 0; i < nPoints; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);
        
        x = (a + b) * cos(t) - h * cos(ph + t * (a + b) / b);
        y = (a + b) * sin(t) - h * sin(ph + t * (a + b) / b);
        vertex(x, y);
    }
    endShape(CLOSE);
}

// code adapted from sample in project description and edited further:
// these curves do not interact with mouseY:
function drawEpitrochoidyCurve(nPoints, cusp, color) {
    // Epitrochoidy: not quite an Epitrochoid, but follows a very similar formula
	
    var x;
    var y;

	var a = 15;
    var b = a / cusp;
    var ph = -mouseX / 40;
    
    fill(color);

	// shape of curve:
    beginShape();
    for (var i = 0; i < nPoints; i++) {
        var t = map(i, 0, nPoints, 0, TWO_PI);
        
        x = (a + b) * cos(t) * cos(ph + t * (a + b) / b);
        y = (a + b) * sin(t) * sin(ph + t * (a + b) / b);
        vertex(x, y);
    }
    endShape(CLOSE);
}

// add one more row and column each time the mouse is pressed:
function mousePressed() {
	density +=1;
}

//delete a row and column when the SPACEBAR is pressed:
function keyPressed() {
	if (keyCode == 32) { 
		if (density == 0) {density = density }		// dont let density variable go below 0
		else {density -= 1 }
	}
	if (keyCode == 87) { 
		if (mode == 0) {mode = 1}		// pressing 'w' switches to 'weird' mode
	}
	if (keyCode == 82) { 
		if (mode == 1) {mode = 0}		// pressing 'r' switches back to default 'regular' mode
	}
}