Trac #31646: clean BezierPath constructor

From http://ask.sagemath.org/question/56608/possible-problem-in-
bezier_pathpy/

URL: https://trac.sagemath.org/31646
Reported by: vdelecroix
Ticket author(s): Vincent Delecroix
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/plot/bezier_path.py

@@ -18,7 +18,6 @@
 #
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-from copy import deepcopy
 from sage.plot.primitive import GraphicPrimitive_xydata
 from sage.misc.decorators import options, rename_keyword
 from sage.plot.colors import to_mpl_color
@@ -35,7 +34,7 @@ class BezierPath(GraphicPrimitive_xydata):
 
         sage: from sage.plot.bezier_path import BezierPath
         sage: BezierPath([[(0,0), (.5,.5),(1,0)],[(.5,1),(0,0)]], {'linestyle':'dashed'})
-        Bezier path from (0, 0) to (0, 0)
+        Bezier path from (0.0, 0.0) to (0.0, 0.0)
 
     We use :func:`bezier_path` to actually plot Bezier curves::
 
@@ -56,17 +55,44 @@ def __init__(self, path, options):
 
             sage: from sage.plot.bezier_path import BezierPath
             sage: BezierPath([[(0,0),(.5,.5),(1,0)],[(.5,1),(0,0)]], {'linestyle':'dashed'})
-            Bezier path from (0, 0) to (0, 0)
+            Bezier path from (0.0, 0.0) to (0.0, 0.0)
+
+            sage: BezierPath([[(0,0), (1,2), (3,6), (2,-1), (3,3)]], {})
+            Traceback (most recent call last):
+            ...
+            ValueError: invalid input for BezierPath
+
+        TESTS:
+
+        Check :trac:`31646`::
+
+            sage: from sage.plot.bezier_path import BezierPath
+            sage: p2d = [[(3,0),(4,1),(2,1),(3,0)], [(2,2),(3,1),(2,1)]]
+            sage: P = BezierPath(p2d, {})
+            sage: P.path
+            [array([[3., 0.], [4., 1.], [2., 1.], [3., 0.]]),
+             array([[2., 2.], [3., 1.], [2., 1.]])]
         """
         import numpy as np
-        self.path = deepcopy(path)
-        codes = [1] + (len(self.path[0])-1)*[len(self.path[0])]
-        vertices = self.path[0]
-        for curve in self.path[1:]:
-            vertices += curve
-            codes += (len(curve)) * [len(curve)+1]
+
+        self.path = [np.array(l, float) for l in path]
+
+        # In oder to feed later to matplotlib.path.Path we convert in the following form
+        # - vertices: an Nx2 float array of vertices
+        # - codes: an N-length uint8 array of vertex types, or None
+        #   where each code could be MOVETO (=1), LINETO (=2), CURVE3 (=3), CURVE4 (=4)
+        self.vertices = np.concatenate(self.path)
+        N, _ = self.vertices.shape
+        codes = np.zeros((N,), np.uint8)
+        k = 0
+        for i, curve in enumerate(self.path):
+            code = len(curve) + (i > 0)
+            if code < 2 or code > 4:
+                raise ValueError('invalid input for BezierPath')
+            codes[k:k+len(curve)] = code
+            k += len(curve)
+        codes[0] = 1 # MOVETO
         self.codes = codes
-        self.vertices = np.array(vertices, float)
         GraphicPrimitive_xydata.__init__(self, options)
 
     def _allowed_options(self):
@@ -178,9 +204,11 @@ def _repr_(self):
             sage: from sage.plot.bezier_path import BezierPath
             sage: B = BezierPath([[(0,0),(.5,.5),(1,0)],[(.5,1),(0,0)]], {'linestyle':'dashed'})
             sage: B._repr_()
-            'Bezier path from (0, 0) to (0, 0)'
+            'Bezier path from (0.0, 0.0) to (0.0, 0.0)'
         """
-        return "Bezier path from %s to %s" % (self.path[0][0], self.path[-1][-1])
+        x0, y0 = self.vertices[0]
+        x1, y1 = self.vertices[-1]
+        return "Bezier path from (%s, %s) to (%s, %s)" % (x0, y0, x1, y1)
 
     def _render_on_subplot(self, subplot):
         """