使用以下功能,可以在输入点P上拟合三次样条:
def plotCurve(P): pts = np.vstack([P, P[0]]) x, y = pts.T i = np.arange(len(pts)) interp_i = np.linspace(0, i.max(), 100000 * i.max()) xi = interp1d(i, x, kind='cubic')(interp_i) yi = interp1d(i, y, kind='cubic')(interp_i) fig, ax = plt.subplots() fig,ax=plt.subplots() ax.plot(xi, yi) ax.plot(x, y, 'ko') #plt.show() return xi,yi
输入点P可以采用以下形式:
P=[(921,1181),(951,1230),(993,1243),(1035,1230), (1065,1181),(1045,1130),(993,1130),(945,1130)]
现在,我希望使P的这些点可拖动,以便当我们更改任何点的位置时,样条线将重新拟合到新点上。
以此为参考:https : //matplotlib.org/1.4.3/examples/event_handling/poly_editor.html(matplotlib中的事件处理),我有以下代码:
""" This is an example to show how to build cross-GUI applications using matplotlib event handling to interact with objects on the canvas """ import numpy as np from matplotlib.lines import Line2D from matplotlib.artist import Artist from matplotlib.mlab import dist_point_to_segment class PolygonInteractor: """ An polygon editor. Key-bindings 't' toggle vertex markers on and off. When vertex markers are on, you can move them, delete them 'd' delete the vertex under point 'i' insert a vertex at point. You must be within epsilon of the line connecting two existing vertices """ showverts = True epsilon = 5 # max pixel distance to count as a vertex hit def __init__(self, ax, poly): if poly.figure is None: raise RuntimeError('You must first add the polygon to a figure or canvas before defining the interactor') self.ax = ax canvas = poly.figure.canvas self.poly = poly x, y = zip(*self.poly.xy) self.line = Line2D(x, y, marker='o', markerfacecolor='r', animated=True) self.ax.add_line(self.line) #self._update_line(poly) cid = self.poly.add_callback(self.poly_changed) self._ind = None # the active vert canvas.mpl_connect('draw_event', self.draw_callback) canvas.mpl_connect('button_press_event', self.button_press_callback) canvas.mpl_connect('key_press_event', self.key_press_callback) canvas.mpl_connect('button_release_event', self.button_release_callback) canvas.mpl_connect('motion_notify_event', self.motion_notify_callback) self.canvas = canvas def draw_callback(self, event): self.background = self.canvas.copy_from_bbox(self.ax.bbox) self.ax.draw_artist(self.poly) self.ax.draw_artist(self.line) self.canvas.blit(self.ax.bbox) def poly_changed(self, poly): 'this method is called whenever the polygon object is called' # only copy the artist props to the line (except visibility) vis = self.line.get_visible() Artist.update_from(self.line, poly) self.line.set_visible(vis) # don't use the poly visibility state def get_ind_under_point(self, event): 'get the index of the vertex under point if within epsilon tolerance' # display coords xy = np.asarray(self.poly.xy) xyt = self.poly.get_transform().transform(xy) xt, yt = xyt[:, 0], xyt[:, 1] d = np.sqrt((xt-event.x)**2 + (yt-event.y)**2) indseq = np.nonzero(np.equal(d, np.amin(d)))[0] ind = indseq[0] if d[ind]>=self.epsilon: ind = None return ind def button_press_callback(self, event): 'whenever a mouse button is pressed' if not self.showverts: return if event.inaxes==None: return if event.button != 1: return self._ind = self.get_ind_under_point(event) def button_release_callback(self, event): 'whenever a mouse button is released' if not self.showverts: return if event.button != 1: return self._ind = None def key_press_callback(self, event): 'whenever a key is pressed' if not event.inaxes: return if event.key=='t': self.showverts = not self.showverts self.line.set_visible(self.showverts) if not self.showverts: self._ind = None elif event.key=='d': ind = self.get_ind_under_point(event) if ind is not None: self.poly.xy = [tup for i,tup in enumerate(self.poly.xy) if i!=ind] self.line.set_data(zip(*self.poly.xy)) elif event.key=='i': xys = self.poly.get_transform().transform(self.poly.xy) p = event.x, event.y # display coords for i in range(len(xys)-1): s0 = xys[i] s1 = xys[i+1] d = dist_point_to_segment(p, s0, s1) if d<=self.epsilon: self.poly.xy = np.array( list(self.poly.xy[:i]) + [(event.xdata, event.ydata)] + list(self.poly.xy[i:])) self.line.set_data(zip(*self.poly.xy)) break self.canvas.draw() def motion_notify_callback(self, event): 'on mouse movement' if not self.showverts: return if self._ind is None: return if event.inaxes is None: return if event.button != 1: return x,y = event.xdata, event.ydata self.poly.xy[self._ind] = x,y self.line.set_data(zip(*self.poly.xy)) self.canvas.restore_region(self.background) self.ax.draw_artist(self.poly) self.ax.draw_artist(self.line) self.canvas.blit(self.ax.bbox) if __name__ == '__main__': import matplotlib.pyplot as plt from matplotlib.patches import Polygon #theta = np.arange(0, 2*np.pi, 0.1) #r = 1.5 #xs = r*np.cos(theta) #ys = r*np.sin(theta) xs = (921, 951, 993, 1035, 1065, 1045, 993, 945) ys = (1181, 1230, 1243, 1230, 1181, 1130, 1130, 1130) poly = Polygon(list(zip(xs, ys)), animated=True) fig, ax = plt.subplots() ax.add_patch(poly) p = PolygonInteractor(ax, poly) #ax.add_line(p.line) ax.set_title('Click and drag a point to move it') #ax.set_xlim((-2,2)) #ax.set_ylim((-2,2)) ax.set_xlim((800, 1300)) ax.set_ylim((1000, 1300)) plt.show()
现在,我要做的是用样条曲线拟合功能替换多边形拟合。由于我是新手,所以我不知道该怎么做。有什么方法可以保持所有相同的功能,而只能使样条曲线适合于给定点而不是多边形,从而使其具有交互性并根据点移动来重新拟合样条曲线?
我的样条线看起来像这样:
我应该怎么做呢?
或者,如果还有其他合适的方法可以达到相同的效果,请推荐。
也欢迎使用MATLAB提出建议。
当然,您需要将功能添加到中PolygonInteractor。但是不要让它自己绘制任何东西。然后在类中添加新行,self.line2这将是要更新的行。
PolygonInteractor
self.line2
最后,让全班同学也为您画一条新线。并使用插值函数的结果更新它。
为了方便起见,您可以将“多边形(self.poly)”设置为不可见,也可以从中删除该线,self.line并且仅显示点可能有意义。
self.poly
self.line
import numpy as np from scipy.interpolate import interp1d from matplotlib.lines import Line2D from matplotlib.artist import Artist from matplotlib.mlab import dist_point_to_segment class PolygonInteractor(object): """ A polygon editor. https://matplotlib.org/gallery/event_handling/poly_editor.html Key-bindings 't' toggle vertex markers on and off. When vertex markers are on, you can move them, delete them 'd' delete the vertex under point 'i' insert a vertex at point. You must be within epsilon of the line connecting two existing vertices """ showverts = True epsilon = 5 # max pixel distance to count as a vertex hit def __init__(self, ax, poly, visible=False): if poly.figure is None: raise RuntimeError('You must first add the polygon to a figure ' 'or canvas before defining the interactor') self.ax = ax canvas = poly.figure.canvas self.poly = poly self.poly.set_visible(visible) x, y = zip(*self.poly.xy) self.line = Line2D(x, y, ls="", marker='o', markerfacecolor='r', animated=True) self.ax.add_line(self.line) self.cid = self.poly.add_callback(self.poly_changed) self._ind = None # the active vert canvas.mpl_connect('draw_event', self.draw_callback) canvas.mpl_connect('button_press_event', self.button_press_callback) canvas.mpl_connect('key_press_event', self.key_press_callback) canvas.mpl_connect('button_release_event', self.button_release_callback) canvas.mpl_connect('motion_notify_event', self.motion_notify_callback) self.canvas = canvas x,y = self.interpolate() self.line2 = Line2D(x, y, animated=True) self.ax.add_line(self.line2) def interpolate(self): x, y = self.poly.xy[:].T i = np.arange(len(x)) interp_i = np.linspace(0, i.max(), 100 * i.max()) xi = interp1d(i, x, kind='cubic')(interp_i) yi = interp1d(i, y, kind='cubic')(interp_i) return xi,yi def draw_callback(self, event): self.background = self.canvas.copy_from_bbox(self.ax.bbox) self.ax.draw_artist(self.poly) self.ax.draw_artist(self.line) self.ax.draw_artist(self.line2) # do not need to blit here, this will fire before the screen is # updated def poly_changed(self, poly): 'this method is called whenever the polygon object is called' # only copy the artist props to the line (except visibility) vis = self.line.get_visible() Artist.update_from(self.line, poly) self.line.set_visible(vis) # don't use the poly visibility state def get_ind_under_point(self, event): 'get the index of the vertex under point if within epsilon tolerance' # display coords xy = np.asarray(self.poly.xy) xyt = self.poly.get_transform().transform(xy) xt, yt = xyt[:, 0], xyt[:, 1] d = np.hypot(xt - event.x, yt - event.y) indseq, = np.nonzero(d == d.min()) ind = indseq[0] if d[ind] >= self.epsilon: ind = None return ind def button_press_callback(self, event): 'whenever a mouse button is pressed' if not self.showverts: return if event.inaxes is None: return if event.button != 1: return self._ind = self.get_ind_under_point(event) def button_release_callback(self, event): 'whenever a mouse button is released' if not self.showverts: return if event.button != 1: return self._ind = None def key_press_callback(self, event): 'whenever a key is pressed' if not event.inaxes: return if event.key == 't': self.showverts = not self.showverts self.line.set_visible(self.showverts) if not self.showverts: self._ind = None elif event.key == 'd': ind = self.get_ind_under_point(event) if ind is not None: self.poly.xy = np.delete(self.poly.xy, ind, axis=0) self.line.set_data(zip(*self.poly.xy)) elif event.key == 'i': xys = self.poly.get_transform().transform(self.poly.xy) p = event.x, event.y # display coords for i in range(len(xys) - 1): s0 = xys[i] s1 = xys[i + 1] d = dist_point_to_segment(p, s0, s1) if d <= self.epsilon: self.poly.xy = np.insert( self.poly.xy, i+1, [event.xdata, event.ydata], axis=0) self.line.set_data(zip(*self.poly.xy)) break if self.line.stale: self.canvas.draw_idle() def motion_notify_callback(self, event): 'on mouse movement' if not self.showverts: return if self._ind is None: return if event.inaxes is None: return if event.button != 1: return x, y = event.xdata, event.ydata self.poly.xy[self._ind] = x, y if self._ind == 0: self.poly.xy[-1] = x, y elif self._ind == len(self.poly.xy) - 1: self.poly.xy[0] = x, y self.line.set_data(zip(*self.poly.xy)) x,y = self.interpolate() self.line2.set_data(x,y) self.canvas.restore_region(self.background) self.ax.draw_artist(self.poly) self.ax.draw_artist(self.line) self.ax.draw_artist(self.line2) self.canvas.blit(self.ax.bbox) if __name__ == '__main__': import matplotlib.pyplot as plt from matplotlib.patches import Polygon #theta = np.arange(0, 2*np.pi, 0.1) #r = 1.5 #xs = r*np.cos(theta) #ys = r*np.sin(theta) xs = (921, 951, 993, 1035, 1065, 1045, 993, 945) ys = (1181, 1230, 1243, 1230, 1181, 1130, 1130, 1130) poly = Polygon(list(zip(xs, ys)), animated=True) fig, ax = plt.subplots() ax.add_patch(poly) p = PolygonInteractor(ax, poly, visible=False) ax.set_title('Click and drag a point to move it') ax.set_xlim((800, 1300)) ax.set_ylim((1000, 1300)) plt.show()
请注意,此处创建的曲线不是真正的循环。它有一个起点,曲线并不真正平滑。