update to use curveMonotoneX alg for smothing curves

go/webui/chart_geom.go

@@ -170,26 +170,66 @@ func linePathD(pts [][2]float64) string {
 	return b.String()
 }
 
-// smoothPathD: Catmull-Rom → cubic bezier through every point.
+func monoSign(x float64) float64 {
+	if x < 0 {
+		return -1
+	}
+	return 1
+}
+
+// monoTangent is the interior tangent for monotone-cubic interpolation (d3's
+// curveMonotoneX): the lesser of the two neighbouring secant slopes, and zero at a local
+// extremum. Capping the tangent is what stops a segment bulging past its endpoints, so an
+// area fill can't dip below a value-0 point into negative space the way a Catmull-Rom
+// overshoot does.
+func monoTangent(x0, y0, x1, y1, x2, y2 float64) float64 {
+	h0, h1 := x1-x0, x2-x1
+	var s0, s1 float64
+	if h0 != 0 {
+		s0 = (y1 - y0) / h0
+	}
+	if h1 != 0 {
+		s1 = (y2 - y1) / h1
+	}
+	p := (s0*h1 + s1*h0) / (h0 + h1)
+	m := (monoSign(s0) + monoSign(s1)) * math.Min(math.Min(math.Abs(s0), math.Abs(s1)), 0.5*math.Abs(p))
+	if math.IsNaN(m) || math.IsInf(m, 0) {
+		return 0
+	}
+	return m
+}
+
+// monoEndTangent is the endpoint tangent (d3 slope2): a parabola-end estimate constrained
+// by the adjacent interior tangent t, so the boundary segments don't overshoot either.
+func monoEndTangent(x0, y0, x1, y1, t float64) float64 {
+	h := x1 - x0
+	if h == 0 {
+		return t
+	}
+	return (3*(y1-y0)/h - t) / 2
+}
+
+// smoothPathD: monotone cubic through every point, emitted as cubic beziers. A monotone
+// interpolant never overshoots its data, so the smoothed curve stays within the value
+// range of each pair of adjacent points.
 func smoothPathD(pts [][2]float64) string {
-	if len(pts) < 3 {
+	n := len(pts)
+	if n < 3 {
 		return linePathD(pts)
 	}
+	m := make([]float64, n)
+	for i := 1; i < n-1; i++ {
+		m[i] = monoTangent(pts[i-1][0], pts[i-1][1], pts[i][0], pts[i][1], pts[i+1][0], pts[i+1][1])
+	}
+	m[0] = monoEndTangent(pts[0][0], pts[0][1], pts[1][0], pts[1][1], m[1])
+	m[n-1] = monoEndTangent(pts[n-2][0], pts[n-2][1], pts[n-1][0], pts[n-1][1], m[n-2])
 	var b strings.Builder
 	b.WriteString("M" + num(pts[0][0]) + "," + num(pts[0][1]))
-	for i := 0; i < len(pts)-1; i++ {
-		p0 := pts[i]
-		if i > 0 {
-			p0 = pts[i-1]
-		}
-		p1, p2 := pts[i], pts[i+1]
-		p3 := p2
-		if i+2 < len(pts) {
-			p3 = pts[i+2]
-		}
-		c1x, c1y := p1[0]+(p2[0]-p0[0])/6, p1[1]+(p2[1]-p0[1])/6
-		c2x, c2y := p2[0]-(p3[0]-p1[0])/6, p2[1]-(p3[1]-p1[1])/6
-		b.WriteString(" C" + num(c1x) + "," + num(c1y) + " " + num(c2x) + "," + num(c2y) + " " + num(p2[0]) + "," + num(p2[1]))
+	for i := 0; i < n-1; i++ {
+		dx := (pts[i+1][0] - pts[i][0]) / 3
+		c1x, c1y := pts[i][0]+dx, pts[i][1]+dx*m[i]
+		c2x, c2y := pts[i+1][0]-dx, pts[i+1][1]-dx*m[i+1]
+		b.WriteString(" C" + num(c1x) + "," + num(c1y) + " " + num(c2x) + "," + num(c2y) + " " + num(pts[i+1][0]) + "," + num(pts[i+1][1]))
 	}
 	return b.String()
 }