# HG changeset patch # User Emily Kirkman <> # Date 1242874073 25200 # Node ID ef8c792c47412e9cd9e3c328790bfebf94d0c4c5 # Parent ca1f31d6f6bf7b1f8da0cb8973c838ab19921c29 3d bezier path implementation diff -r ca1f31d6f6bf -r ef8c792c4741 sage/plot/bezier_path.py --- a/sage/plot/bezier_path.py Thu Jul 09 15:14:36 2009 -0700 +++ b/sage/plot/bezier_path.py Wed May 20 19:47:53 2009 -0700 @@ -15,11 +15,11 @@ # # http://www.gnu.org/licenses/ #***************************************************************************** -from sage.plot.primitive import GraphicPrimitive +from sage.plot.primitive import GraphicPrimitive_xydata from sage.plot.misc import options, rename_keyword from sage.plot.colors import to_mpl_color -class BezierPath(GraphicPrimitive): +class BezierPath(GraphicPrimitive_xydata): """ Path of Bezier Curves graphics primitive. """ @@ -41,7 +41,7 @@ codes += (len(curve))*[len(curve)+1] self.codes = codes self.vertices = np.array(vertices, np.float) - GraphicPrimitive.__init__(self, options) + GraphicPrimitive_xydata.__init__(self, options) def _allowed_options(self): """ @@ -63,8 +63,58 @@ 'thickness':'How thick the border of the polygon is.', 'rgbcolor':'The color as an rgb tuple.', 'zorder':'The layer level in which to draw', - 'linestyle':"The style of the line, which is one of 'dashed', 'dotted', 'solid', 'dashdot'."} - + 'linestyle':"The style of the line, which is one of 'dashed', 'dotted', 'solid', 'dashdot'."} + + def _plot3d_options(self, options=None): + """ + Updates BezierPath options to those allowed by 3d implementation. + + EXAMPLES: + + 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._plot3d_options() + Traceback (most recent call last): + ... + NotImplementedError: Invalid 3d line style: dashed + sage: B = BezierPath([[(0,0),(.5,.5),(1,0)],[(.5,1),(0,0)]],{'fill':False, 'thickness':2}) + sage: B._plot3d_options() + {'thickness': 2} + """ + if options == None: + options = dict(self.options()) + options_3d = {} + if 'thickness' in options: + options_3d['thickness'] = options['thickness'] + del options['thickness'] + if 'fill' in options: + if options['fill']: + raise NotImplementedError, "Invalid 3d fill style. Must set fill to False." + del options['fill'] + if 'linestyle' in options: + if options['linestyle'] != 'solid': + raise NotImplementedError, "Invalid 3d line style: %s" % options['linestyle'] + del options['linestyle'] + options_3d.update(GraphicPrimitive_xydata._plot3d_options(self, options)) + return options_3d + + def plot3d(self, **kwds): + """ + Returns a 3d plot (Jmol) of the bezier path. Since a BezierPath primitive contains + only x,y coordinates, the path will be drawn in the z=0 plane. To create a bezier path + with nonzero z coordinates in the path and control points, use the constructor bezier3d + instead of bezier_path. + + EXAMPLES: + sage: b = bezier_path([[(0,0),(0,1),(1,0)]]) + sage: b.plot3d() + sage: bezier3d([[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]]) + """ + from sage.plot.plot3d.shapes2 import bezier3d + options = self._plot3d_options() + options.update(kwds) + return bezier3d([[(x,y,0) for x,y in self.path[i]] for i in range(len(self.path))], **options) + def _repr_(self): return "Bezier path from %s to %s"%(self.path[0][0],self.path[-1][-1]) diff -r ca1f31d6f6bf -r ef8c792c4741 sage/plot/plot3d/all.py --- a/sage/plot/plot3d/all.py Thu Jul 09 15:14:36 2009 -0700 +++ b/sage/plot/plot3d/all.py Wed May 20 19:47:53 2009 -0700 @@ -6,7 +6,7 @@ from platonic import tetrahedron, cube, octahedron, dodecahedron, icosahedron -from shapes2 import sphere, line3d, polygon3d, point3d, text3d +from shapes2 import sphere, line3d, polygon3d, point3d, text3d, bezier3d from shapes import arrow3d diff -r ca1f31d6f6bf -r ef8c792c4741 sage/plot/plot3d/shapes2.py --- a/sage/plot/plot3d/shapes2.py Thu Jul 09 15:14:36 2009 -0700 +++ b/sage/plot/plot3d/shapes2.py Wed May 20 19:47:53 2009 -0700 @@ -104,6 +104,89 @@ w._set_extra_kwds(kwds) return w +@options(opacity=1, color="red", aspect_ratio=[1,1,1], thickness=2) +def bezier3d(path, **options): + """ + Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each + point in the path and each control point is required to have 3 coordinates. + + INPUT: + + - ``path`` - a list of curves, which each is a list of points. See further + detail below. + + - ``thickness`` - (default: 2) + + - ``color`` - a word that describes a color + + - ``opacity`` - (default: 1) if less than 1 then is + transparent + + - ``aspect_ratio`` - (default:[1,1,1]) + + The path is a list of curves, and each curve is a list of points. + Each point is a tuple (x,y,z). + + The first curve contains the endpoints as the first and last point + in the list. All other curves assume a starting point given by the + last entry in the preceding list, and take the last point in the list + as their opposite endpoint. A curve can have 0, 1 or 2 control points + listed between the endpoints. In the input example for path below, + the first and second curves have 2 control points, the third has one, + and the fourth has no control points: + + path = [[p1, c1, c2, p2], [c3, c4, p3], [c5, p4], [p5], ...] + + In the case of no control points, a striaght line will be drawn + between the two endpoints. If one control point is supplied, then + the curve at each of the endpoints will be tangent to the line from + that endpoint to the control point. Similarly, in the case of two + control points, at each endpoint the curve will be tangent to the line + connecting that endpoint with the control point immediately after or + immediately preceding it in the list. + + So in our example above, the curve between p1 and p2 is tangent to the + line through p1 and c1 at p1, and tangent to the line through p2 and c2 + at p2. Similarly, the curve between p2 and p3 is tangent to line(p2,c3) + at p2 and tangent to line(p3,c4) at p3. Curve(p3,p4) is tangent to + line(p3,c5) at p3 and tangent to line(p4,c5) at p4. Curve(p4,p5) is a + straight line. + + EXAMPLES: + sage: path = [[(0,0,0),(.5,.1,.2),(.75,3,-1),(1,1,0)],[(.5,1,.2),(1,.5,0)],[(.7,.2,.5)]] + sage: b = bezier3d(path, color='green') + sage: b + + To construct a simple curve, create a list containing a single list: + + sage: path = [[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]] + sage: curve = bezier3d(path, thickness=5, color='blue') + sage: curve + """ + import parametric_plot3d as P3D + from sage.modules.free_module_element import vector + from sage.calculus.calculus import var + + p0 = vector(path[0][-1]) + t = var('t') + if len(path[0]) > 2: + B = (1-t)**3*vector(path[0][0])+3*t*(1-t)**2*vector(path[0][1])+3*t**2*(1-t)*vector(path[0][-2])+t**3*p0 + G = P3D.parametric_plot3d(list(B), (0, 1), color=options['color'], aspect_ratio=options['aspect_ratio'], thickness=options['thickness'], opacity=options['opacity']) + else: + G = line3d([path[0][0], p0], color=options['color'], thickness=options['thickness'], opacity=options['opacity']) + + for curve in path[1:]: + if len(curve) > 1: + p1 = vector(curve[0]) + p2 = vector(curve[-2]) + p3 = vector(curve[-1]) + B = (1-t)**3*p0+3*t*(1-t)**2*p1+3*t**2*(1-t)*p2+t**3*p3 + G += P3D.parametric_plot3d(list(B), (0, 1), color=options['color'], aspect_ratio=options['aspect_ratio'], thickness=options['thickness'], opacity=options['opacity']) + else: + G += line3d([p0,curve[0]], color=options['color'], thickness=options['thickness'], opacity=options['opacity']) + p0 = curve[-1] + return G + @rename_keyword(alpha='opacity') @options(opacity=1, color=(0,0,1)) def polygon3d(points, **options): diff -r ca1f31d6f6bf -r ef8c792c4741 sage/plot/primitive.py --- a/sage/plot/primitive.py Thu Jul 09 15:14:36 2009 -0700 +++ b/sage/plot/primitive.py Wed May 20 19:47:53 2009 -0700 @@ -106,6 +106,8 @@ if 'alpha' in options: options_3d['opacity'] = options['alpha'] del options['alpha'] + if 'zorder' in options: + del options['zorder'] if len(options) != 0: raise NotImplementedError, "Unknown plot3d equivalent for %s" % ", ".join(options.keys()) return options_3d