# Polygons

# Stars

Draw stars with flexible styling (size, colors, number-of-points).

enter image description here

// Usage:
drawStar(75,75,5,50,25,'mediumseagreen','gray',9);
drawStar(150,200,8,50,25,'skyblue','gray',3);
drawStar(225,75,16,50,20,'coral','transparent',0);
drawStar(300,200,16,50,40,'gold','gray',3);

// centerX, centerY: the center point of the star
// points: the number of points on the exterior of the star
// inner: the radius of the inner points of the star
// outer: the radius of the outer points of the star
// fill, stroke: the fill and stroke colors to apply
// line: the linewidth of the stroke

function drawStar(centerX, centerY, points, outer, inner, fill, stroke, line) {
    // define the star
    ctx.beginPath();
    ctx.moveTo(centerX, centerY+outer);
    for (var i=0; i < 2*points+1; i++) {
        var r = (i%2 == 0)? outer : inner;
        var a = Math.PI * i/points;
        ctx.lineTo(centerX + r*Math.sin(a), centerY + r*Math.cos(a));
    };
    ctx.closePath();
    // draw
    ctx.fillStyle=fill;
    ctx.fill();
    ctx.strokeStyle=stroke;
    ctx.lineWidth=line;
    ctx.stroke()
}

# Regular Polygon

A regular polygon has all sides equal length.

enter image description here

// Usage:
drawRegularPolygon(3,25,75,50,6,'gray','red',0);
drawRegularPolygon(5,25,150,50,6,'gray','gold',0);
drawRegularPolygon(6,25,225,50,6,'gray','lightblue',0);
drawRegularPolygon(10,25,300,50,6,'gray','lightgreen',0);

function drawRegularPolygon(sideCount,radius,centerX,centerY,strokeWidth,strokeColor,fillColor,rotationRadians){
    var angles=Math.PI*2/sideCount;
    ctx.translate(centerX,centerY);
    ctx.rotate(rotationRadians);
    ctx.beginPath();
    ctx.moveTo(radius,0);
    for(var i=1;i<sideCount;i++){
        ctx.rotate(angles);
        ctx.lineTo(radius,0);
    }
    ctx.closePath();
    ctx.fillStyle=fillColor;
    ctx.strokeStyle = strokeColor;
    ctx.lineWidth = strokeWidth;
    ctx.stroke();
    ctx.fill();
    ctx.rotate(angles*-(sideCount-1));
    ctx.rotate(-rotationRadians);
    ctx.translate(-centerX,-centerY);
}

# Render a rounded polygon.

Creates a path from a set of points [{x:?,y:?},{x:?,y:?},...,{x:?,y:?}] with rounded corners of radius. If the corner angle is too small to fit the radius or the distance between corners does not allow room the corners radius is reduced to a best fit. enter image description here

Usage Example

var triangle = [
    { x: 200, y : 50 },
    { x: 300, y : 200 },
    { x: 100, y : 200 }
];
var cornerRadius = 30;
ctx.lineWidth = 4;
ctx.fillStyle = "Green";
ctx.strokeStyle = "black";
ctx.beginPath(); // start a new path
roundedPoly(triangle, cornerRadius);
ctx.fill();
ctx.stroke();

Render function

var roundedPoly = function(points,radius){
    var i, x, y, len, p1, p2, p3, v1, v2, sinA, sinA90, radDirection, drawDirection, angle, halfAngle, cRadius, lenOut;
    var asVec = function (p, pp, v) { // convert points to a line with len and normalised
        v.x = pp.x - p.x; // x,y as vec
        v.y = pp.y - p.y;
        v.len = Math.sqrt(v.x * v.x + v.y * v.y); // length of vec
        v.nx = v.x / v.len; // normalised
        v.ny = v.y / v.len;
        v.ang = Math.atan2(v.ny, v.nx); // direction of vec
    }
    v1 = {};
    v2 = {};
    len = points.length;                         // number points
    p1 = points[len - 1];                        // start at end of path
    for (i = 0; i < len; i++) {                  // do each corner
        p2 = points[(i) % len];                  // the corner point that is being rounded
        p3 = points[(i + 1) % len];
        // get the corner as vectors out away from corner
        asVec(p2, p1, v1);                       // vec back from corner point
        asVec(p2, p3, v2);                       // vec forward from corner point
        // get corners cross product (asin of angle)
        sinA = v1.nx * v2.ny - v1.ny * v2.nx;    // cross product
        // get cross product of first line and perpendicular second line
        sinA90 = v1.nx * v2.nx - v1.ny * -v2.ny; // cross product to normal of line 2
        angle = Math.asin(sinA);                 // get the angle
        radDirection = 1;                        // may need to reverse the radius
        drawDirection = false;                   // may need to draw the arc anticlockwise
        // find the correct quadrant for circle center
        if (sinA90 < 0) {
            if (angle < 0) {
                angle = Math.PI + angle; // add 180 to move us to the 3 quadrant
            } else {
                angle = Math.PI - angle; // move back into the 2nd quadrant
                radDirection = -1;
                drawDirection = true;
            }
        } else {
            if (angle > 0) {
                radDirection = -1;
                drawDirection = true;
            }
        }
        halfAngle = angle / 2;
        // get distance from corner to point where round corner touches line
        lenOut = Math.abs(Math.cos(halfAngle) * radius / Math.sin(halfAngle));
        if (lenOut > Math.min(v1.len / 2, v2.len / 2)) { // fix if longer than half line length
            lenOut = Math.min(v1.len / 2, v2.len / 2);
            // ajust the radius of corner rounding to fit
            cRadius = Math.abs(lenOut * Math.sin(halfAngle) / Math.cos(halfAngle));
        } else {
            cRadius = radius;
        }
        x = p2.x + v2.nx * lenOut; // move out from corner along second line to point where rounded circle touches
        y = p2.y + v2.ny * lenOut;
        x += -v2.ny * cRadius * radDirection; // move away from line to circle center
        y += v2.nx * cRadius * radDirection;
        // x,y is the rounded corner circle center
        ctx.arc(x, y, cRadius, v1.ang + Math.PI / 2 * radDirection, v2.ang - Math.PI / 2 * radDirection, drawDirection); // draw the arc clockwise
        p1 = p2;
        p2 = p3;
    }
    ctx.closePath();
}