Add infinity max option for reciprocal scale

web/app.py

@@ -8,7 +8,7 @@ from fontTools.pens.svgPathPen import SVGPathPen
 
 app = Flask(__name__)
 
-VERSION = "0.82"
+VERSION = "0.83"
 
 _LOGO_PATH = pathlib.Path(__file__).parent / 'static' / 'logo.png'
 _LOGO_B64 = base64.b64encode(_LOGO_PATH.read_bytes()).decode()
@@ -291,6 +291,8 @@ def _unit_font_size(unit: str) -> float:
 
 
 def _fmt(v: float) -> str:
+    if math.isinf(v):
+        return '∞'
     # Snap near-integers — log-scale geometric values accumulate FP error
     # (e.g. 9999.9999), which would otherwise miss the integer case.
     r = round(v)
@@ -363,17 +365,31 @@ def generate_svg(unit, min_val, max_val, range_label, big_ticks, small_ticks, la
             return min_val + span * (i / big_ticks) ** 2
 
     elif scale_type == 'reciprocal':
-        if min_val <= 0 or max_val <= 0:
+        if min_val <= 0:
             raise ValueError("Reciprocal scale requires min and max values greater than 0.")
-        if max_val <= min_val:
+        if not math.isinf(max_val) and max_val <= min_val:
             raise ValueError("Reciprocal scale requires max value greater than min.")
-        k = 1.0 / min_val - 1.0 / max_val   # always positive
+        if math.isinf(max_val):
+            # Simplified form when max = ∞: x = ZERO_X + SCALE_LEN * min_val / v
+            def value_to_x(v):
+                if math.isinf(v):
+                    return ZERO_X
+                return ZERO_X + SCALE_LEN * min_val / v
 
-        def value_to_x(v):
-            return ZERO_X + SCALE_LEN * (1.0 / v - 1.0 / max_val) / k
+            def major_value(i):
+                if i == 0:
+                    return math.inf
+                return min_val * big_ticks / i
+        else:
+            if max_val <= 0:
+                raise ValueError("Reciprocal scale requires min and max values greater than 0.")
+            k = 1.0 / min_val - 1.0 / max_val   # always positive
 
-        def major_value(i):
-            return 1.0 / (1.0 / max_val + i / big_ticks * k)
+            def value_to_x(v):
+                return ZERO_X + SCALE_LEN * (1.0 / v - 1.0 / max_val) / k
+
+            def major_value(i):
+                return 1.0 / (1.0 / max_val + i / big_ticks * k)
 
     else:
         span = max_val - min_val
@@ -471,6 +487,10 @@ def generate_svg(unit, min_val, max_val, range_label, big_ticks, small_ticks, la
             for j in range(1, small_ticks + 1):
                 if scale_type == 'sqrt':
                     x = big_xs[i] + (j / sub) ** 2 * (big_xs[i + 1] - big_xs[i])
+                elif math.isinf(big_vals[i]):
+                    # First interval with ∞ at the left: interpolate in position space
+                    # (linear value interpolation is undefined from ∞).
+                    x = big_xs[i] + (j / sub) * (big_xs[i + 1] - big_xs[i])
                 else:
                     v = big_vals[i] + j * (big_vals[i + 1] - big_vals[i]) / sub
                     x = value_to_x(v)
@@ -511,6 +531,8 @@ def generate():
     label_count = max(2, int(request.form.get('label_count', 6)))
     use_paths   = request.form.get('output_mode', 'paths') == 'paths'
     scale_type  = request.form.get('scale_type', 'linear')
+    if request.form.get('max_is_inf') == '1':
+        max_val = math.inf
 
     custom_labels = [s.strip() for s in request.form.get('labels', '').split(',') if s.strip()] or None
     label_size    = max(0.5, min(25.0, float(request.form.get('label_size', 9))))