Python中的交互式BSpline拟合(Interactive BSpline fitting in Python)

Python中的交互式BSpline拟合(Interactive BSpline fitting in Python)

使用以下函数，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可以是以下形式：

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，这样当我们改变任何点的位置时，样条曲线将被重新拟合到新的点上。

使用它作为参考： 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，我想做的是用我的样条拟合函数替换多边形拟合。 由于我是新手，我无法弄清楚如何做到这一点。 有没有办法保持所有相同的功能，但只是通过给定点拟合样条而不是多边形，使其交互并根据点移动重新调整样条线？

我的样条曲线看起来有点像这样：

我应该怎么做呢？

或者，如果有任何其他合适的方法来实现相同的，请善意推荐。

使用MATLAB也欢迎提出建议。

Using the following function, one can fit a cubic spline on input points P:

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

The input points P can be of the following form:

P=[(921,1181),(951,1230),(993,1243),(1035,1230), (1065,1181),(1045,1130),(993,1130),(945,1130)]

Now, I wish to make these points of P draggable, such that as and when we change the position of any point, the spline gets refitted on the new points.

Using this as a reference: https://matplotlib.org/1.4.3/examples/event_handling/poly_editor.html (event handling in matplotlib), I have the following code:

""" 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()

Now, what I wish to do is to replace the polygon fitting with my spline fitting function. As I am new to this I am not able to figure out how to do it. Is there any way to keep all the same functionalities, but only to fit the spline instead of polygon through the given points, making it interactive and refitting the spline as per point movement?

My spline would look somewhat like this :

How should I go about doing it?

Or, if there is any other suitable method to achieve the same, kindly recommend.

Suggestions are also welcome using MATLAB.

最满意答案

当然，您需要将您的函数添加到PolygonInteractor 。 不要让它自己画任何东西。 然后在类中添加一个新行self.line2 ，它将是要更新的行。

最后，让班级也画出你的新行。 并使用插值函数的结果更新它。

为方便起见，您可以将Polygon（ self.poly ） self.poly不可见，同时从self.line删除该行，只显示这些点可能有意义。

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，曲线不是很平滑。 这可以通过使用一组真正循环的贝塞尔曲线来规避，如使用matplotlib创建随机形状/轮廓所示。

Of course you need to add your function to the PolygonInteractor. Don't let it draw anything itself though. Then add a new line to the class, self.line2 which will be the line to update.

Finally, let the class draw your new line as well. And update it with the result from your interpolation function.

For convenience you may turn the Polygon (self.poly) invisible, also removing the line from the self.line and only showing the points may make sense.

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()

Note that the curve created here is not truely cyclic. It has a start point where the curve is not really smooth. This can be circumvented by using a truely cyclic set of bezier curves as shown in Create random shape/contour using matplotlib.