<svg>
  <path id='star'/>
	<path id='heart'/>
</svg>
body {
	display: flex;
	margin: 0;
	height: 100vh
}

svg { flex: 1 }

path {
	fill: none;
	stroke-width: 5
}

#star { stroke: #f90 }

#heart { stroke: #b53 }
const _SVG = document.querySelector('svg'), 
			_STAR = document.getElementById('star'), 
			_HEART = document.getElementById('heart'), 
			D = 1000 /* viewBox size */,
			O = {} /* data object */,
			/* number of cubic curves/ polygon vertices */
			P = 5;

function getStarPoints(f = .5) {
	const RCO = f*D /* outer (pentagram) circumradius*/, 
				BAS = 2*(2*Math.PI/P) /* base angle for star poly */, 
				BAC = 2*Math.PI/P /* base angle for convex poly */, 
				RI = RCO*Math.cos(.5*BAS) /*pentagram/ inner pentagon inradius */, 
				RCI = RI/Math.cos(.5*BAC) /* inner pentagon circumradius */, 
				ND = 2*P /* total number of distinct points we need to get */, 
				BAD = 2*Math.PI/ND /* base angle for point distribution */, 
				PTS = [] /* array we fill with point coordinates */;

	for(let i = 0; i < ND; i++) {
		let /* radius at end point (inner)/ control point (outer) */
				cr = i%2 ? RCI : RCO, 
				/* angle of radial segment from origin to current point */
				ca = i*BAD + .5*Math.PI, 
				x = Math.round(cr*Math.cos(ca)), 
				y = Math.round(cr*Math.sin(ca));

		PTS.push([x, y]);
		/* for even indices double it, control points coincide here */
		if(!(i%2)) PTS.push([x, y]);
	}

	return PTS
};

function getHeartPoints(f = .25) {
	const R = f*D /* helper circle radius  */, 
				RC = Math.round(R/Math.SQRT2) /* circumradius of square of edge R */, 
				XT = 0, YT = -RC /* coords of point T */, 
				XA = 2*RC, YA = -RC /* coords of A points (x in abs value) */, 
				XB = 2*RC, YB = RC /* coords of B points (x in abs value) */, 
				XC = 0, YC = 3*RC /* coords of point C */, 
				XD = RC, YD = -2*RC /* coords of D points (x in abs value) */, 
				XE = 3*RC, YE = 0 /* coords of E points (x in abs value) */, 
				/* const for cubic curve approx of quarter circle */
				C = .551915, 
        CC = 1 - C, 
        /* coords of ctrl points on TD segs */
				XTD = Math.round(CC*XT + C*XD), YTD = Math.round(CC*YT + C*YD), 
        /* coords of ctrl points on AD segs */
				XAD = Math.round(CC*XA + C*XD), YAD = Math.round(CC*YA + C*YD), 
        /* coords of ctrl points on AE segs */
				XAE = Math.round(CC*XA + C*XE), YAE = Math.round(CC*YA + C*YE), 
        /* coords of ctrl points on BE segs */
				XBE = Math.round(CC*XB + C*XE), YBE = Math.round(CC*YB + C*YE);
	
	return [
		[XC, YC], [XC, YC], [-XB, YB], 
		[-XBE, YBE], [-XAE, YAE], [-XA, YA], 
		[-XAD, YAD], [-XTD, YTD], [XT, YT], 
		[XTD, YTD], [XAD, YAD], [XA, YA], 
		[XAE, YAE], [XBE, YBE], [XB, YB]
	];
};

function fnStr(fname, farg) { return `${fname}(${farg})` }

(function init() {	
	_SVG.setAttribute('viewBox', [-.5*D, -.5*D, D, D].join(' '));
	
	O.d = {
		ini: getStarPoints(), 
		fin: getHeartPoints(), 
		afn: function(pts) {
			return pts.reduce((a, c, i) => {
				return a + (i%3 ? ' ' : 'C') + c
			}, `M${pts[pts.length - 1]}`)
		}
	};
	
	for(let p in O) {
		_STAR.setAttribute(p, O[p].afn(O[p].ini));
		_HEART.setAttribute(p, O[p].afn(O[p].fin));
	}
})();
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