Bent surface for crown face

nhf/touhou/shiki_eiki/crown.py

@@ -61,6 +61,7 @@ class Crown(Model):
 
         assert self.front_wing_angle < 180 / self.facets
         assert self.front_wing_dh + self.front_wing_height < self.height
+        assert self.slot_phi < 2 * math.pi / self.facets
 
     @property
     def facet_width_lower(self):
@@ -88,21 +89,79 @@ class Crown(Model):
     def radius_upper_front(self):
         return self.radius_lower_front + (self.radius_upper - self.radius_lower)
 
-    def profile_base(self) -> Cq.Sketch:
-        # Generate the pentagonal shape
+    @property
+    def slot_r0(self):
+        return self.radius_lower + self.thickness / 2
+    @property
+    def slot_r1(self):
+        return self.radius_upper + self.thickness / 2
+
+    @property
+    def slot_h0(self) -> float:
+        """
+        Phantom height formed by similar triangle, i.e. h0 in
+
+        (h0 + h) / r2 = h0 / r1
+        """
+        rat = self.slot_r0  / (self.slot_r1 - self.slot_r0)
+        return self.height * rat
+    @property
+    def slot_theta(self) -> float:
+        """
+        Cone tilt, related to other quantities by
+        h0 = r1 * cot theta
+        """
+        h = self.height
+        return math.atan(self.slot_r0 / (self.height + self.slot_h0))
+    @property
+    def slot_phi(self) -> float:
+        """
+        When a slice of the crown is expanded (via Gauss's Theorema Egregium),
+        it does not form a full circle. phi is the angle of one of the slices.
+
+        Note that on the cone itself, the angular slice is `2 pi / n` which `n`
+        is the number of sides.
+        """
+        arc = self.slot_r0 * math.pi * 2 / self.facets
+        rho = self.slot_h0 / math.cos(self.slot_theta)
+        return arc / rho
+
+
+    def profile_base(self) -> Cq.Sketch:
+        # Generate a conical pentagonal shape
+
+        y0 = self.slot_h0 / math.cos(self.slot_theta)
+        yh = (self.height/2 + self.slot_h0) / math.cos(self.slot_theta)
+        yq = (self.height*3/4 + self.slot_h0) / math.cos(self.slot_theta)
+        y1 = (self.height + self.slot_h0) / math.cos(self.slot_theta)
+        phi2 = self.slot_phi / 2
 
-        dx_l = self.facet_width_lower
-        dx_u = self.facet_width_upper
-        dy = self.height
         return (
             Cq.Sketch()
-            .polygon([
-                (dx_l/2, 0),
-                (dx_u/2, dy/2),
-                (0, dy),
-                (-dx_u/2, dy/2),
-                (-dx_l/2, 0),
-            ])
+            .segment(
+                (y0 * math.sin(phi2), y0 * (-1 + math.cos(phi2))),
+                (yh * math.sin(phi2), -y0 + yh * math.cos(phi2)),
+            )
+            .arc(
+                (yh * math.sin(phi2), -y0 + yh * math.cos(phi2)),
+                (yq * math.sin(phi2/2), -y0 + yq * math.cos(phi2/2)),
+                (0, y1 - y0),
+            )
+            .arc(
+                (-yh * math.sin(phi2), -y0 + yh * math.cos(phi2)),
+                (-yq * math.sin(phi2/2), -y0 + yq * math.cos(phi2/2)),
+                (0, y1 - y0),
+            )
+            .segment(
+                (-y0 * math.sin(phi2), y0 * (-1 + math.cos(phi2))),
+                (-yh * math.sin(phi2), -y0 + yh * math.cos(phi2)),
+            )
+            .arc(
+                (y0 * math.sin(phi2), -y0 + y0 * math.cos(phi2)),
+                (0, 0),
+                (-y0 * math.sin(phi2), y0 * (-1 + math.cos(phi2))),
+            )
+            .assemble()
         )
 
     @target(name="side", kind=TargetKind.DXF)