[instancer/L4] Implement an optimization

Lib/fontTools/varLib/instancer/solver.py

@@ -153,16 +153,47 @@ def _solve(tent, axisLimit, negative=False):
             out.append((scalar1 - gain, loc1))
             out.append((scalar2 - gain, loc2))
 
+    else:
+        # Special-case if peak is at axisMax.
+        if axisMax == peak:
+            upper = peak
+
+        # Case pre3:
+        # we keep deltas as is and only scale the axis upper to achieve
+        # the desired new tent if feasible.
+        #
+        #            |           peak |
+        #  1.........|............o...|..................
+        #            |           /x\  |
+        #            |          /xxx\ |
+        #            |         /xxxxx\|
+        #            |        /xxxxxxx+
+        #            |       /xxxxxxxx|\
+        #  0---|-----|------oxxxxxxxxx|xo---------------1
+        #    axisMin |  lower         | upper
+        #            |                |
+        #          axisDef          axisMax
+        #
+        newUpper = peak + (1 - gain) * (upper - peak)
+        if axisMax <= newUpper and newUpper <= axisDef + (axisMax - axisDef) * 2:
+            upper = newUpper
+            if not negative and axisDef + (axisMax - axisDef) * MAX_F2DOT14 < upper:
+                # we clamp +2.0 to the max F2Dot14 (~1.99994) for convenience
+                upper = axisDef + (axisMax - axisDef) * MAX_F2DOT14
+                assert peak < upper
+
+            loc = (max(axisDef, lower), peak, upper)
+            scalar = 1
+
+            out.append((scalar - gain, loc))
+
         # Case 3: Outermost limit still fits within F2Dot14 bounds;
-    # we keep deltas as is and only scale the axes bounds. Deltas beyond -1.0
-    # or +1.0 will never be applied as implementations must clamp to that range.
+        # We keep axis bound as is. Deltas beyond -1.0 or +1.0 will never be
+        # applied as implementations must clamp to that range.
         #
         # A second tent is needed for cases when gain is positive, though we add it
         # unconditionally and it will be dropped because scalar ends up 0.
         #
-    # TODO: See if we can just move upper closer to adjust the slope, instead of
-    # second tent.
-    #
         #            |           peak |
         #  1.........|............o...|..................
         #            |           /x\  |
@@ -181,10 +212,6 @@ def _solve(tent, axisLimit, negative=False):
                 upper = axisDef + (axisMax - axisDef) * MAX_F2DOT14
                 assert peak < upper
 
-        # Special-case if peak is at axisMax.
-        if axisMax == peak:
-            upper = peak
-
             loc1 = (max(axisDef, lower), peak, upper)
             scalar1 = 1
 

Tests/varLib/instancer/solver_test.py

@@ -137,8 +137,7 @@ class RebaseTentTest(object):
                 (0.25, 0.25, 0.75),
                 [
                     (0.5, None),
-                    (0.5, (0, 0.5, 1.5)),
-                    (-0.5, (0.5, 1.5, 1.5)),
+                    (0.5, (0, 0.5, 1.0)),
                 ],
             ),
             # Case 1neg