Polygons

// 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()
}

// 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);
}

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();

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();
}