line: add bezier/bezier_precision properties

examples/canvas/lines_extended.py

@@ -83,6 +83,20 @@ Builder.load_string('''
     Label:
         center: root.center
         text: 'Rectangle'
+
+
+<LineBezier>:
+    canvas:
+        Color:
+            rgba: .1, .1, 1, .9
+        Line:
+            width: 2.
+            bezier: (self.x, self.y, self.center_x - 40, self.y + 100, self.center_x + 40, self.y - 100, self.right, self.y) 
+    Label:
+        center: root.center
+        text: 'Bezier'
+
+
 ''')
 
 
@@ -107,6 +121,9 @@ class LineCircle3(Widget):
 class LineRectangle(Widget):
     pass
 
+class LineBezier(Widget):
+    pass
+
 class LineExtendedApp(App):
     def build(self):
         root = GridLayout(cols=2, padding=50, spacing=50)
@@ -117,6 +134,7 @@ class LineExtendedApp(App):
         root.add_widget(LineCircle2())
         root.add_widget(LineCircle3())
         root.add_widget(LineRectangle())
+        root.add_widget(LineBezier())
         return root
 
 if __name__ == '__main__':

kivy/graphics/vertex_instructions_line.pxi

@@ -11,6 +11,7 @@ DEF LINE_MODE_POINTS = 0
 DEF LINE_MODE_ELLIPSE = 1
 DEF LINE_MODE_CIRCLE = 2
 DEF LINE_MODE_RECTANGLE = 3
+DEF LINE_MODE_BEZIER = 4
 
 from kivy.graphics.stencil_instructions cimport StencilUse, StencilUnUse, StencilPush, StencilPop
 
@@ -77,6 +78,11 @@ cdef class Line(VertexInstruction):
         `rectangle`: list
             If set, the :data:`points` will be set to build a rectangle. Check
             :data:`rectangle` for more information.
+        `bezier`: list
+            If set, the :data:`points` will be set to build a bezier line. Check
+            :data:`bezier` for more information.
+        `bezier_precision`: int, default to 180
+            Precision of the Bezier drawing.
 
     .. versionadded:: 1.0.8
         `dash_offset` and `dash_length` have been added
@@ -84,10 +90,14 @@ cdef class Line(VertexInstruction):
     .. versionadded:: 1.4.1
         `width`, `cap`, `joint`, `cap_precision`, `joint_precision`, `close`,
         `ellipse`, `rectangle` have been added.
+
+    .. versionadded:: 1.4.1
+        `bezier`, `bezier_precision` have been added.
     '''
     cdef int _cap
     cdef int _cap_precision
     cdef int _joint_precision
+    cdef int _bezier_precision
     cdef int _joint
     cdef list _points
     cdef float _width
@@ -115,6 +125,7 @@ cdef class Line(VertexInstruction):
         self.cap = kwargs.get('cap') or 'round'
         self._cap_precision = kwargs.get('cap_precision') or 10
         self._joint_precision = kwargs.get('joint_precision') or 10
+        self._bezier_precision = kwargs.get('bezier_precision') or 180
         self._close = int(bool(kwargs.get('close', 0)))
         self._stencil_rect = None
         self._stencil_push = None
@@ -130,6 +141,8 @@ cdef class Line(VertexInstruction):
             self.prebuild_circle()
         elif self._mode == LINE_MODE_RECTANGLE:
             self.prebuild_rectangle()
+        elif self._mode == LINE_MODE_BEZIER:
+            self.prebuild_bezier()
         if self._width == 1.0:
             self.build_legacy()
         else:
@@ -767,7 +780,7 @@ cdef class Line(VertexInstruction):
 
         def __set__(self, value):
             if value < 1:
-                raise GraphicException('Invalid cap_precision value, must be >= 1')
+                raise GraphicException('Invalid joint_precision value, must be >= 1')
             self._joint_precision = int(value)
             self.flag_update()
 
@@ -987,3 +1000,71 @@ cdef class Line(VertexInstruction):
 
         self._points = [x, y, x + width, y, x + width, y + height, x, y + height]
         self._close = 1
+
+    property bezier:
+        '''Use this property to build a rectangle, without calculate the
+        :data:`points`. You can only set this property, not get it.
+
+        The argument must be a tuple of (x, y, width, height)
+        angle_end, segments):
+
+        * x and y represent the bottom-left position of the rectangle
+        * width and height represent the size
+
+        The line is automatically closed.
+
+        Usage::
+
+            Line(rectangle=(0, 0, 200, 200))
+
+        .. versionadded:: 1.4.2
+        '''
+
+        def __set__(self, args):
+            if args == None:
+                raise GraphicException(
+                        'Invalid rectangle value: {0!r}'.format(args))
+            self._mode_args = tuple(args)
+            self._mode = LINE_MODE_BEZIER
+            self.flag_update()
+
+    cdef void prebuild_bezier(self):
+        cdef double x, y, l
+        cdef int segments = self._bezier_precision
+        cdef list T = list(self._mode_args)[:]
+
+        self._points = []
+        for x in xrange(segments):
+            l = x / (1.0 * segments)
+            # http://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm
+            # as the list is in the form of (x1, y1, x2, y2...) iteration is
+            # done on each item and the current item (xn or yn) in the list is
+            # replaced with a calculation of "xn + x(n+1) - xn" x(n+1) is
+            # placed at n+2. each iteration makes the list one item shorter
+            for i in range(1, len(T)):
+                for j in xrange(len(T) - 2*i):
+                    T[j] = T[j] + (T[j+2] - T[j]) * l
+
+            # we got the coordinates of the point in T[0] and T[1]
+            self._points.append(T[0])
+            self._points.append(T[1])
+
+        # add one last point to join the curve to the end
+        self._points.append(T[-2])
+        self._points.append(T[-1])
+
+    property bezier_precision:
+        '''Number of iteration for drawing the bezier between 2 segments,
+        default to 180. The bezier_precision must be at least 1.
+
+        .. versionadded:: 1.4.2
+        '''
+
+        def __get__(self):
+            return self._bezier_precision
+
+        def __set__(self, value):
+            if value < 1:
+                raise GraphicException('Invalid bezier_precision value, must be >= 1')
+            self._bezier_precision = int(value)
+            self.flag_update()