Switched interpolation of stroke width into monotonic cubic interpolation

support/monotonic-interpolate.js

@@ -0,0 +1,72 @@
+exports.createInterpolant = function(xs, ys) {
+	var i, length = xs.length;
+	
+	// Deal with length issues
+	if (length != ys.length) { throw 'Need an equal count of xs and ys.'; }
+	if (length === 0) { return function(x) { return 0; }; }
+	if (length === 1) {
+		// Impl: Precomputing the result prevents problems if ys is mutated later and allows garbage collection of ys
+		// Impl: Unary plus properly converts values to numbers
+		var result = +ys[0];
+		return function(x) { return result; };
+	}
+	
+	// Rearrange xs and ys so that xs is sorted
+	var indexes = [];
+	for (i = 0; i < length; i++) { indexes.push(i); }
+	indexes.sort(function(a, b) { return xs[a] < xs[b] ? -1 : 1; });
+	var oldXs = xs, oldYs = ys;
+	// Impl: Creating new arrays also prevents problems if the input arrays are mutated later
+	xs = []; ys = [];
+	// Impl: Unary plus properly converts values to numbers
+	for (i = 0; i < length; i++) { xs.push(+oldXs[indexes[i]]); ys.push(+oldYs[indexes[i]]); }
+	
+	// Get consecutive differences and slopes
+	var dys = [], dxs = [], ms = [];
+	for (i = 0; i < length - 1; i++) {
+		var dx = xs[i + 1] - xs[i], dy = ys[i + 1] - ys[i];
+		dxs.push(dx); dys.push(dy); ms.push(dy/dx);
+	}
+	
+	// Get degree-1 coefficients
+	var c1s = [ms[0]];
+	for (i = 0; i < dxs.length - 1; i++) {
+		var m = ms[i], mNext = ms[i + 1];
+		if (m*mNext <= 0) {
+			c1s.push(0);
+		} else {
+			var dx = dxs[i], dxNext = dxs[i + 1], common = dx + dxNext;
+			c1s.push(3*common/((common + dxNext)/m + (common + dx)/mNext));
+		}
+	}
+	c1s.push(ms[ms.length - 1]);
+	
+	// Get degree-2 and degree-3 coefficients
+	var c2s = [], c3s = [];
+	for (i = 0; i < c1s.length - 1; i++) {
+		var c1 = c1s[i], m = ms[i], invDx = 1/dxs[i], common = c1 + c1s[i + 1] - m - m;
+		c2s.push((m - c1 - common)*invDx); c3s.push(common*invDx*invDx);
+	}
+	
+	// Return interpolant function
+	return function(x) {
+		// The rightmost point in the dataset should give an exact result
+		var i = xs.length - 1;
+		if (x == xs[i]) { return ys[i]; }
+		
+		// Search for the interval x is in, returning the corresponding y if x is one of the original xs
+		var low = 0, mid, high = c3s.length - 1;
+		while (low <= high) {
+			mid = Math.floor(0.5*(low + high));
+			var xHere = xs[mid];
+			if (xHere < x) { low = mid + 1; }
+			else if (xHere > x) { high = mid - 1; }
+			else { return ys[mid]; }
+		}
+		i = Math.max(0, high);
+		
+		// Interpolate
+		var diff = x - xs[i], diffSq = diff*diff;
+		return ys[i] + c1s[i]*diff + c2s[i]*diffSq + c3s[i]*diff*diffSq;
+	};
+};