diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4b6e661..f80784f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -49,6 +49,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   of drawing a NaN population and returning a NaN point with no
   error.
 
+**Signal and plots.**
+
+- `WriteSVG` keeps extreme but finite data and axis ranges drawable:
+  the padding, projection and tick arithmetic fall back to forms whose
+  terms stay in range, so the file never carries a NaN coordinate.
+
 ## [1.0.0] - 2026-09-03
 
 The initial release of Tensor, a scientific computing library in pure
diff --git a/plot/plot.go b/plot/plot.go
index 4602aee..85c4110 100644
--- a/plot/plot.go
+++ b/plot/plot.go
@@ -119,11 +119,37 @@ func (c Chart) WriteSVG(path string) error {
 	if !(yr[0] < yr[1]) || math.IsInf(yr[0], 0) || math.IsInf(yr[1], 0) {
 		yr = bounds(all, false)
 	}
+	// project maps a value of the range [r0, r1] onto the plot span
+	// starting at plotLo. The normal form is the arithmetic the chart
+	// has always run; a span, or an offset from the range's start, that
+	// overflows float64 falls back to the halved form, whose every term
+	// a finite input keeps finite, so a range the data spans but the
+	// arithmetic cannot still draws instead of carrying a coordinate no
+	// renderer displays.
+	project := func(v, r0, r1, plotLo, plotSpan float64) float64 {
+		u := (v - r0) / (r1 - r0)
+		if math.IsNaN(u) || math.IsInf(u, 0) {
+			u = (v/2 - r0/2) / (r1/2 - r0/2)
+		}
+		return plotLo + u*plotSpan
+	}
 	px := func(x float64) float64 {
-		return left + (x-xr[0])/(xr[1]-xr[0])*(float64(w)-left-right)
+		return project(x, xr[0], xr[1], left, float64(w)-left-right)
 	}
 	py := func(y float64) float64 {
-		return float64(h) - bottom - (y-yr[0])/(yr[1]-yr[0])*(float64(h)-top-bottom)
+		return float64(h) - bottom - project(y, yr[0], yr[1], 0, float64(h)-top-bottom)
+	}
+	// tickValue places the k-th of the five ticks. A span that overflows
+	// float64 makes the affine form NaN or Inf, so the tick falls back to
+	// the convex combination, which stays between the range's own finite
+	// ends.
+	tickValue := func(r0, r1 float64, k int) float64 {
+		t := r0 + (r1-r0)*float64(k)/4
+		if math.IsNaN(t) || math.IsInf(t, 0) {
+			f := float64(k) / 4
+			t = r0*(1-f) + r1*f
+		}
+		return t
 	}
 	var b strings.Builder
 	b.WriteString(xmlHeader)
@@ -133,7 +159,7 @@ func (c Chart) WriteSVG(path string) error {
 		left, esc(c.Title))
 	// Axes with five ticks each.
 	for k := range 5 {
-		t := xr[0] + (xr[1]-xr[0])*float64(k)/4
+		t := tickValue(xr[0], xr[1], k)
 		x := px(t)
 		fmt.Fprintf(&b, "<line x1=\"%g\" y1=\"%g\" x2=\"%g\" y2=\"%g\" stroke=\"#ccc\" stroke-width=\"1\"/>\n",
 			x, top, x, float64(h)-bottom)
@@ -141,7 +167,7 @@ func (c Chart) WriteSVG(path string) error {
 			x, float64(h)-bottom+16, tick(t))
 	}
 	for k := range 5 {
-		t := yr[0] + (yr[1]-yr[0])*float64(k)/4
+		t := tickValue(yr[0], yr[1], k)
 		y := py(t)
 		fmt.Fprintf(&b, "<line x1=\"%g\" y1=\"%g\" x2=\"%g\" y2=\"%g\" stroke=\"#ccc\" stroke-width=\"1\"/>\n",
 			left, y, float64(w)-right, y)
@@ -195,8 +221,14 @@ func bounds(pts []Point, xAxis bool) [2]float64 {
 	if hi == lo {
 		hi = lo + 1
 	}
-	pad := 0.05 * (hi - lo)
-	return [2]float64{lo - pad, hi + pad}
+	padLo, padHi := lo-0.05*(hi-lo), hi+0.05*(hi-lo)
+	if math.IsInf(padLo, 0) || math.IsInf(padHi, 0) {
+		// The padding, or the span it scales, overflows the range the
+		// finite data itself fits; the unpadded bounds keep every
+		// projection finite.
+		return [2]float64{lo, hi}
+	}
+	return [2]float64{padLo, padHi}
 }
 
 func tick(v float64) string {
diff --git a/plot/plot_test.go b/plot/plot_test.go
index 94c207a..8818c20 100644
--- a/plot/plot_test.go
+++ b/plot/plot_test.go
@@ -103,6 +103,39 @@ func TestWriteSVGErrors(t *testing.T) {
 	}
 }
 
+// TestWriteSVGExtremeFiniteValuesStayFinite pins the renderer against
+// the extreme-but-finite corner: data, or an explicit axis range, whose
+// span overflows float64 must not leak NaN or Inf coordinates into the
+// drawing, because no renderer displays them and the non-finite
+// refusal at the door guarantees every input point is finite.
+func TestWriteSVGExtremeFiniteValuesStayFinite(t *testing.T) {
+	dir := t.TempDir()
+	padded := sampleChart()
+	padded.XRange = [2]float64{-1e308, 1e308}
+	padded.YRange = [2]float64{-1e308, 1e308}
+	charts := []struct {
+		name  string
+		chart Chart
+	}{
+		{"wide-data.svg", Chart{Series: []Series{{Name: "wide",
+			Points: []Point{{X: 0, Y: -1e308}, {X: 1, Y: 1e308}}}}}},
+		{"wide-range.svg", padded},
+	}
+	for _, tc := range charts {
+		path := filepath.Join(dir, tc.name)
+		if err := tc.chart.WriteSVG(path); err != nil {
+			t.Fatalf("%s: %v", tc.name, err)
+		}
+		body, err := os.ReadFile(path)
+		if err != nil {
+			t.Fatalf("%s: %v", tc.name, err)
+		}
+		if s := string(body); strings.Contains(s, "NaN") || strings.Contains(s, "Inf") {
+			t.Fatalf("%s: the rendering leaked a non-finite coordinate: %s", tc.name, s)
+		}
+	}
+}
+
 func mustFromFloats(t *testing.T, values []float64, shape ...int) *core.Array {
 	t.Helper()
 	a, err := core.FromFloats(values, shape...)