Performance enhancement of the turtle module

Feature or enhancement

Proposal:

The original implementation of turtle.RawTurtle._goto:

    def _goto(self, end):
        """Move the pen to the point end, thereby drawing a line
        if pen is down. All other methods for turtle movement depend
        on this one.
        """
        ## Version with undo-stuff
        go_modes = ( self._drawing,
                     self._pencolor,
                     self._pensize,
                     isinstance(self._fillpath, list))
        screen = self.screen
        undo_entry = ("go", self._position, end, go_modes,
                      (self.currentLineItem,
                      self.currentLine[:],
                      screen._pointlist(self.currentLineItem),
                      self.items[:])
                      )
        if self.undobuffer:
            self.undobuffer.push(undo_entry)
        start = self._position
        if self._speed and screen._tracing == 1:
            diff = (end-start)
            diffsq = (diff[0]*screen.xscale)**2 + (diff[1]*screen.yscale)**2
            nhops = 1+int((diffsq**0.5)/(3*(1.1**self._speed)*self._speed))
            delta = diff * (1.0/nhops)
            for n in range(1, nhops):
                if n == 1:
                    top = True
                else:
                    top = False
                self._position = start + delta * n
                if self._drawing:
                    screen._drawline(self.drawingLineItem,
                                     (start, self._position),
                                     self._pencolor, self._pensize, top)
                self._update()
            if self._drawing:
                screen._drawline(self.drawingLineItem, ((0, 0), (0, 0)),
                                               fill="", width=self._pensize) # ---- calls _drawline(), causing the time complexity to be O(n**2) ----
        # Turtle now at end,
        if self._drawing: # now update currentLine
            self.currentLine.append(end)
        if isinstance(self._fillpath, list):
            self._fillpath.append(end)
        ######    vererbung!!!!!!!!!!!!!!!!!!!!!!
        self._position = end
        if self._creatingPoly:
            self._poly.append(end)
        if len(self.currentLine) > 42: # ---- hard-coded ----
            self._newLine()
        self._update() #count=True)

The hard-coded number 42 performs well on my Ubuntu, but it seriously lowers the frame rate of complicated turtle programs on Windows. According to my own FPS test, the number 320 performs best on Windows.

On the other hand, the TurtleScreenBase._drawline method:

    def _drawline(self, lineitem, coordlist=None,
                  fill=None, width=None, top=False):
        """Configure lineitem according to provided arguments:
        coordlist is sequence of coordinates
        fill is drawing color
        width is width of drawn line.
        top is a boolean value, which specifies if polyitem
        will be put on top of the canvas' displaylist so it
        will not be covered by other items.
        """
        if coordlist is not None:
            cl = []
            for x, y in coordlist: # ---- Repeats converting data ----
                cl.append(x * self.xscale)
                cl.append(-y * self.yscale)
            self.cv.coords(lineitem, *cl)
        if fill is not None:
            self.cv.itemconfigure(lineitem, fill=fill)
        if width is not None:
            self.cv.itemconfigure(lineitem, width=width)
        if top:
            self.cv.tag_raise(lineitem)

The current time complexity is O(n**2). With some data preprocessed in _goto method, the performance can be further optimized.
From my perspective, the turtle module could be an excellent substitute for original tkinter.Canvas if it were optimized significantly.

Additionally, this proposal originally comes from my own project's source code.

Has this already been discussed elsewhere?

No response given

Links to previous discussion of this feature:

No response

Review turtle.RawTurtle._goto and TurtleScreenBase._drawline, focusing on the repeated line updates and coordinate conversion described in the proposal. Establish a representative FPS benchmark across platforms and verify that any optimization preserves drawing, undo, and turtle behavior. Done means measurable performance improvement without regressions.