Improve cone rendering plus some lint...

mathics/builtin/drawing/graphics3d.py

@@ -195,20 +195,24 @@ class Sphere(Builtin):
 
 class Cone(Builtin):
     """
-    <url>:WMA link:https://reference.wolfram.com/language/ref/Cone.html</url>
+    <url>:Cone:https://en.wikipedia.org/wiki/Cone</url> (<url>
+    :WMA:https://reference.wolfram.com/language/ref/Cone.html</url>)
 
     <dl>
-      <dt>'Cone'[{{$x1$, $y1$, $z1$}, {$x2$, $y2$, $z2$}}]
-      <dd>represents a cone of radius 1.
+      <dt>'Cone'[]
+      <dd>is a cone of radius 1 and height 2 oriented in the upward $z$ direction.
 
-      <dt>'Cone'[{{$x1$, $y1$, $z1$}, {$x2$, $y2$, $z2$}}, $r$]
-      <dd>is a cone of radius $r$ starting at ($x1$, $y1$, $z1$) and ending at \
-          ($x2$, $y2$, $z2$).
+      <dt>'Cone'[{{$x_1$, $y_1$, $z_1$}, {$x_2$, $y_2$, $z_2$}}, $r$]
+      <dd>is a cone of radius $r$ starting at ($x_1$, $y_1$, $z_1$) and ending at \
+          ($x2$, $y_2$, $z_2$).
 
-      <dt>'Cone'[{{$x1$, $y1$, $z1$}, {$x2$, $y2$, $z2$}, ... }, $r$]
+      <dt>'Cone'[{{$x_1$, $y_1$, $z_1$}, {$x_2$, $y_2$, $z_2$}, ... }, $r$]
       <dd>is a collection cones of radius $r$.
     </dl>
 
+    >> Graphics3D[Cone[]]
+     = -Graphics3D-
+
     >> Graphics3D[Cone[{{0, 0, 0}, {1, 1, 1}}, 1]]
      = -Graphics3D-
 
@@ -223,7 +227,7 @@ class Cone(Builtin):
     }
 
     rules = {
-        "Cone[]": "Cone[{{0, 0, 0}, {1, 1, 1}}, 1]",
+        "Cone[]": "Cone[{{0, 0, 0}, {0, 0, 2}}, 1]",
         "Cone[positions_List]": "Cone[positions, 1]",
     }
 

mathics/builtin/drawing/graphics_internals.py

@@ -26,7 +26,7 @@ def create_as_style(klass, graphics, item):
 
 
 class _GraphicsElementBox(BoxExpression, ABC):
-    def init(self, graphics, item=None, style=None, opacity=1.0):
+    def init(self, graphics, item=None, style={}, opacity=1.0):
         if item is not None and not item.has_form(self.get_name(), None):
             raise BoxExpressionError
         self.graphics = graphics

mathics/format/asy.py

@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
 """
-Lower-level format of Mathics objects as Asymptote strings.
+Lower-level format of Mathics objects as Asymptote Vector graphics strings.
 """
 
 import re
@@ -36,10 +36,6 @@
     PointSize,
     RGBColor,
 )
-
-INVERSE_POINT_FACTOR = 1 / DEFAULT_POINT_FACTOR
-
-
 from mathics.core.formatter import add_conversion_fn, lookup_method
 from mathics.format.asy_fns import (
     asy_add_bezier_fn,
@@ -50,6 +46,8 @@
     asy_number,
 )
 
+INVERSE_POINT_FACTOR = 1 / DEFAULT_POINT_FACTOR
+
 
 class _ASYTransform:
     _template = """
@@ -97,7 +95,7 @@ def arcbox(self: _ArcBox, **options) -> str:
         # It is an empty circle
         return _roundbox(self)
 
-    x, y, rx, ry, sx, sy, ex, ey, large_arc = self._arc_params()
+    x, y, rx, ry, sx, sy, ex, ey, _ = self._arc_params()
 
     ry = max(ry, 0.1)  # Avoid division by 0
     yscale = ry / rx
@@ -137,7 +135,7 @@ def create_arc_path(is_closed: bool, yscale: float) -> str:
         edge_opacity=edge_opacity_value,
         face_opacity=face_opacity_value,
         stroke_width=stroke_width,
-        is_face_element=self.face_element,
+        is_face_element=bool(self.face_element),
     )
     command = "filldraw" if self.face_element else "draw"
     arc_path = create_arc_path(self.face_element or False, yscale)
@@ -254,27 +252,34 @@ def cone3dbox(self: Cone3DBox, **options) -> str:
     opacity = self.face_opacity
     color_str = build_3d_pen_color(face_color, opacity)
 
-    # FIXME: currently always drawing around the axis X+Y
-    axes_point = (1, 1, 0)
-
     asy = "// Cone3DBox\n"
     i = 0
     while i < len(self.points) / 2:
         try:
-            point1 = self.points[i * 2].pos()[0]
-            point2 = self.points[i * 2 + 1].pos()[0]
-
-            # Compute distance between start point and end point.
-            distance = (
-                (point1[0] - point2[0]) ** 2
-                + (point1[1] - point2[1]) ** 2
-                + (point1[2] - point2[2]) ** 2
+            # See https://tex.stackexchange.com/questions/736116/how-to-draw-the-base-geometrical-face-of-a-cone-surface-by-asymptote/736120#736120
+            cone_center = self.points[i * 2].pos()[0]
+            cone_tip = self.points[i * 2 + 1].pos()[0]
+            if cone_center is None or cone_tip is None:
+                continue
+
+            # Compute the cone's height : the distance between the center of the cone's base and the
+            # cone's tip.
+            cone_height = (
+                (cone_center[0] - cone_tip[0]) ** 2
+                + (cone_center[1] - cone_tip[1]) ** 2
+                + (cone_center[2] - cone_tip[2]) ** 2
             ) ** 0.5
 
-            asy += (
-                f"draw(surface(cone({tuple(point1)}, {self.radius}, {distance}, {axes_point})), {color_str});"
-                + "\n"
-            )
+            asy += f"""
+                   triple cone_center = {tuple(cone_center)};
+                   triple cone_tip = {tuple(cone_tip)};
+                   real cone_radius = {self.radius};
+                   real cone_height = {cone_height};
+
+                   path3 cone_circle = circle(cone_center, cone_radius, cone_tip);
+                   draw(surface(cone_circle), {color_str});
+                   draw(surface(cone(cone_center, cone_radius, cone_height, cone_tip)), {color_str});
+                   """
         except:  # noqa
             pass
 
@@ -299,6 +304,9 @@ def cuboid3dbox(self: Cuboid3DBox, **options) -> str:
             point1 = self.points[i * 2].pos()[0]
             point2 = self.points[i * 2 + 1].pos()[0]
 
+            if point1 is None or point2 is None:
+                continue
+
             asy += f"""
                 draw(shift({point1[0]}, {point1[1]}, {point1[2]}) * scale(
                     {point2[0] - point1[0]},
@@ -334,6 +342,10 @@ def cylinder3dbox(self: Cylinder3DBox, **options) -> str:
         try:
             point1 = self.points[i * 2].pos()[0]
             point2 = self.points[i * 2 + 1].pos()[0]
+
+            if point1 is None or point2 is None:
+                continue
+
             asy += f"real r={self.radius};\n"
             asy += f"triple A={tuple(point1)}, B={tuple(point2)};\n"
             asy += "real h=abs(A-B);\n"