diff --git a/web/app.py b/web/app.py
index d6d5419..d9ae546 100644
--- a/web/app.py
+++ b/web/app.py
@@ -344,6 +344,95 @@ def generate_svg(unit, min_val, max_val, left_label, right_label, big_ticks, sma
                  label_size=5.1126, font_key=None):
     fd = _FONTS.get(font_key) or _FONTS.get(_DEFAULT_FONT) or next(iter(_FONTS.values()))
 
+    if scale_type == 'log':
+        if min_val <= 0 or max_val <= 0:
+            raise ValueError("Logarithmic scale requires min and max values greater than 0.")
+        lmin, lmax = math.log(min_val), math.log(max_val)
+        lspan = lmax - lmin
+        if lspan == 0:
+            raise ValueError("Logarithmic scale requires min and max values to differ.")
+
+        def value_to_angle(v):
+            return ANGLE_MIN + (ANGLE_MAX - ANGLE_MIN) * (math.log(v) - lmin) / lspan
+
+        def major_value(i):
+            return min_val * (max_val / min_val) ** (i / big_ticks)
+
+    elif scale_type == 'sqrt':
+        if min_val < 0:
+            raise ValueError("Square-root scale requires min value ≥ 0.")
+        span = max_val - min_val
+        if span <= 0:
+            raise ValueError("Square-root scale requires max value greater than min.")
+
+        def value_to_angle(v):
+            return ANGLE_MIN + (ANGLE_MAX - ANGLE_MIN) * math.sqrt((v - min_val) / span)
+
+        def major_value(i):
+            return min_val + span * (i / big_ticks) ** 2
+
+    elif scale_type == 'reciprocal':
+        if min_val <= 0:
+            raise ValueError("Reciprocal scale requires min and max values greater than 0.")
+        if not math.isinf(max_val) and max_val <= min_val:
+            raise ValueError("Reciprocal scale requires max value greater than min.")
+        if math.isinf(max_val):
+            def value_to_angle(v):
+                if math.isinf(v):
+                    return ANGLE_MIN
+                return ANGLE_MIN + (ANGLE_MAX - ANGLE_MIN) * min_val / v
+
+            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
+
+            def value_to_angle(v):
+                return ANGLE_MIN + (ANGLE_MAX - ANGLE_MIN) * (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
+
+        def value_to_angle(v):
+            if span == 0:
+                return ANGLE_MIN
+            return ANGLE_MIN + (ANGLE_MAX - ANGLE_MIN) * (v - min_val) / span
+
+        def major_value(i):
+            return min_val + span * i / big_ticks
+
+    big_interval_angle = (ANGLE_MAX - ANGLE_MIN) / big_ticks
+    big_angles = [ANGLE_MIN + i * big_interval_angle for i in range(big_ticks + 1)]
+    big_vals = [major_value(i) for i in range(big_ticks + 1)]
+
+    if custom_labels:
+        label_count = max(1, min(len(custom_labels), big_ticks + 1))
+        custom_labels = custom_labels[:label_count]
+    else:
+        label_count = max(2, min(label_count, big_ticks + 1))
+
+    if label_count == 1:
+        label_indices = [0]
+    else:
+        label_indices = [round(k * big_ticks / (label_count - 1)) for k in range(label_count)]
+
+    def _tick_line(angle_deg, length, width):
+        x = PIVOT_X
+        y1 = PIVOT_Y - R0
+        y2 = PIVOT_Y - R0 - length
+        return (
+            f'    <line x1="{x:.5f}" y1="{y1:.5f}" x2="{x:.5f}" y2="{y2:.5f}"'
+            f' style="stroke:#1a1a1a;stroke-width:{width:.5f};stroke-linecap:butt"'
+            f' transform="rotate({angle_deg:.5f},{PIVOT_X:.5f},{PIVOT_Y:.5f})" />'
+        )
+
     font_face = (
         '<defs><style>'
         f'@font-face {{font-family:"{fd.label}";'
@@ -384,6 +473,24 @@ def generate_svg(unit, min_val, max_val, left_label, right_label, big_ticks, sma
         f' cx="{PIVOT_X:.5f}" cy="{PIVOT_Y:.5f}" r="{PIVOT_CIRCLE_R}" />'
     )
 
+    for angle in big_angles:
+        parts.append(_tick_line(angle, MAJOR_LEN, MAJOR_W))
+
+    if small_ticks > 0:
+        sub = small_ticks + 1
+        medium_j = sub // 2 if small_ticks % 2 == 1 else None
+        for i in range(big_ticks):
+            for j in range(1, small_ticks + 1):
+                if scale_type == 'sqrt':
+                    angle = big_angles[i] + (j / sub) ** 2 * (big_angles[i + 1] - big_angles[i])
+                elif scale_type == 'reciprocal' or math.isinf(big_vals[i]):
+                    angle = big_angles[i] + (j / sub) * (big_angles[i + 1] - big_angles[i])
+                else:
+                    v = big_vals[i] + j * (big_vals[i + 1] - big_vals[i]) / sub
+                    angle = value_to_angle(v)
+                length, width = (MEDIUM_LEN, MEDIUM_W) if j == medium_j else (SMALL_LEN, SMALL_W)
+                parts.append(_tick_line(angle, length, width))
+
     parts += ['  </g>', '</svg>']
     return '\n'.join(parts)