ncgraph.py

import curses
import math
import numpy

# Just for reference: Unicode box-drawing characters
# ─│┌┐└┘├┤┬┴┼

LEFTBORDER = 7
BOTTOMBORDER = 2

debug_file = open("debug.output", 'w')
def DEBUG(string):
    debug_file.write("%s\n" % string)

class DataSeries(object):
    def __init__(self, X, Y, label, color=0):
        assert (len(X) == len(Y))
        self.X = X.copy()
        self.Y = Y.copy()
        self.label = label
        self.length = len(X)
        self.color = color

# TODO Currently unused
class Lim(object):
    def __init__(self, lower, upper):
        self.set(lower, upper)
    def set(self, lower, upper):
        self.lower = lower
        self.upper = upper
    def range(self):
        return self.upper - self.lower

class Interval(object):
    def __init__(self, a, b):
        self.a = a
        self.b = b
    """
    Checks if the interval contains the point/value p.
    """
    def contains(self, p):
        # As an interval could be decreasing, there are two possible cases how an interval
        # could contain a value. We have to test them both here.
        return (p >= self.a and p <= self.b) or (p <= self.a and p >= self.b)
    """
    Returns a (increasing) list of all integer values between a and b plus a and b themselves.
    As the interval could be defined with a > b and the returned list here is always increasing,
    the direction could be inverted.
    """
    def arange(self):
        # The rounding operations are required for range() to work. The direction of rounding
        # is determined so that the range does NOT contain the values themselves so that they
        # can be appended afterwards.
        if self.a < self.b:
            a,b = self.a, self.b
        else:
            a,b = self.b, self.a
        return [a] + list(range(math.floor(a)+1, math.floor(b))) + [b]
        

""" 
Returns the point of intersection of the lines passing through a2,a1 and b2,b1.
a1: [x, y] a point on the first line
a2: [x, y] another point on the first line
b1: [x, y] a point on the second line
b2: [x, y] another point on the second line
"""
# Inspired by / Taken from https://stackoverflow.com/a/42727584/805673
# Returns errorcode, x, y; errorcode == 0 if successful.
# After calculating the intersection of the two lines, we additionally check
# if this is a valid intersection for the two line segments, i.e. check if the
# found point is between the two points of each line segment.
def get_intersectBak(a1, a2, b1, b2):
    s = numpy.vstack([a1,a2,b1,b2])        # s for stacked
    h = numpy.hstack((s, numpy.ones((4, 1)))) # h for homogeneous
    l1 = numpy.cross(h[0], h[1])           # get first line
    l2 = numpy.cross(h[2], h[3])           # get second line
    x, y, z = numpy.cross(l1, l2)          # point of intersection
    if z == 0:                          # lines are parallel
        return -1, None, None
    x,y = (x/z, y/z) # The points are defined as (x, y, 1)
    # Now check if the point we have found is on the two line segments
    # The following check is not safe because of numeric issues (especially for horizontal and vertical lines)
    #if Interval(a1[0], a2[0]).contains(x) \
    #        and Interval(b1[0], b2[0]).contains(x) \
    #        and Interval(a1[1], a2[1]).contains(y) \
    #        and Interval(b1[1], b2[1]).contains(y):
    #            return 0, x, y
    # Instead, let's check if we have to move something between 0% and 100% of the
    # distance between two points:
    # The point we found is the point of a line segment plus a relative amount t of the
    # connection vector to the other point of that line segment:
    # (x,y) = a1 + (a2-a1) * t
    # (x,y) - a1 = (a2-a1) * t
    b = numpy.array([x-a1[0], y-a1[1]])
    A = numpy.array([[a2[0]-a1[0]], [a2[1]-a1[1]]])
    t = numpy.linalg.lstsq(A, b, rcond=None)[0][0] # First index for return-struct-unpacking, second for solution-indexing
    if Interval(0,1).contains(t):
        return 0, x, y
    else:
        return -1, None, None

def get_intersect(a1, a2, b1, b2):
    # v = vector from p1 to p2
    # line segment = p1 + v * [0..1]
    a = numpy.array(a1).reshape(2,1)
    a2 = numpy.array(a2).reshape(2,1)
    b = numpy.array(b1).reshape(2,1)
    b2 = numpy.array(b2).reshape(2,1)
    va = a2 - a
    vb = b2 - b
    #    a + va * ta = b + vb * tb
    # => a - b = vb * tb - va * ta
    # => a - b = (vb, -va) * (tb ta)^T = A * (tb ta)^T
    A = numpy.hstack((vb, -va))
    t, residuals, rank, singularvals = numpy.linalg.lstsq(A, a-b, rcond=None)
    if rank < 2:
        return -1, None, None
    i = Interval(0,1)
    if i.contains(t[0]) and i.contains(t[1]):
        p = a + va * t[1]
        return 0, p[0,0], p[1,0] # p.shape == (2,1) (it's 2D)
    return -1, None, None

class Mapping(object):
    def __init__(self, x_from, x_to, hbin_from, hbin_to, y_from, y_to, vbin_from, vbin_to):
        self.x_from = x_from
        self.x_to = x_to
        self.y_from = y_from
        self.y_to = y_to
        self.hbin_from = hbin_from
        self.hbin_to = hbin_to
        self.vbin_from = vbin_from
        self.vbin_to = vbin_to
        self.hbins_per_x = (hbin_to - hbin_from) / (x_to - x_from)
        self.vbins_per_y = (vbin_to - vbin_from) / (y_to - y_from)

    def map(self, x, y, rounding=True):
        return self.mapx(x, rounding), self.mapy(y, rounding)
    def mapx(self, x, rounding=True):
        # The nice thing about these mappings is that if any direction is reversed, this
        # effect is automatically fixed by the quotient hbins_per_x.
        # For example, if the x-direction is reversed (i.e. x_from > x_to), the denominator of
        # hbins_per_x is negative. Then, for any valid/fitting x, (x - self.x_from) is negative,
        # too. The result of the division indicates which fraction of the whole hbin-interval we
        # have to advance. The same holds true for the bin indexes.
        # Therefore, we can ignore the directions of x, h, y and v here.
        res = (x - self.x_from) * self.hbins_per_x + self.hbin_from
        if rounding:
            res = numpy.round(res)
            res = res.astype(int)
        return res
    def mapy(self, y, rounding=True):
        res = (y - self.y_from) * self.vbins_per_y + self.vbin_from
        if rounding:
            res = numpy.round(res)
            res = res.astype(int)
        return res

    def fits(self, x, y):
        return self.fitsx(x) and self.fitsy(y)
    def fitsx(self, x):
        return Interval(self.x_from, self.x_to).contains(x)
    def fitsy(self, y):
        return Interval(self.y_from, self.y_to).contains(y)

    def nofit(self, x, y):
        # Ensure that we are working on arrays
        x = numpy.array(x)
        y = numpy.array(y)
        # Determine left, right, top, bottom borders which is dependent on the ordering of
        # the from-to-values
        left = min(self.x_from, self.x_to)
        right = max(self.x_from, self.x_to)
        bottom = min(self.y_from, self.y_to)
        top = max(self.y_from, self.y_to)
        # For each border, determine if the value does not fit because it has crossed out
        # of the drawing area at that border
        outside = (x < left) * 1
        outside |= (x > right) * 2
        outside |= (y < bottom) * 4
        outside |= (y > top) * 8
        return outside


    def mapLine(self, x_start, y_start, x_end, y_end):
        # We have to draw something on the screen if either both points are in the plottable area
        # or at least one point is in the plottable area (then, we need to determine the intersection
        # with the bounding-box of the drawing area to know the point the line will be connected to).
        # But in fact, there is a third possibility: If none of the points is in the drawing area,
        # there could be two intersections with the bounding-box (like the line entering and leaving
        # the area) and we would have to draw the connection between these two intersections.
        # Summarizing, the sum of points in the drawing area and the number of intersections with the
        # bounding box need to be 2.
        # Due to numeric issues, values can be in the drawing area AND intersect with the borders.
        # Therefore, we collect the values in a set() after mapping. After mapping, the intersection
        # and the point itself will most probably be the same and not be added twice to the set.
        mapping_points = set()
        # First, check for the two points if they are in the drawing area
        xlim = Interval(self.x_from, self.x_to)
        ylim = Interval(self.y_from, self.y_to)
        if self.fits(x_start, y_start):
            mapping_points.add(self.map(x_start, y_start))
        if self.fits(x_end, y_end):
            mapping_points.add(self.map(x_end, y_end))
        # Now, check for intersections with the drawing area bounding box, for speedup only check
        # if more points are missing.
        if len(mapping_points) != 2:
            a = (x_start, y_start)
            b = (x_end, y_end)
            c0 = (self.x_from, self.y_from) # corner point, lower left
            c1 = (self.x_from, self.y_to) # upper left
            c2 = (self.x_to, self.y_to) # upper right
            c3 = (self.x_to, self.y_from) # lower right
            error, x, y = get_intersect(a, b, c0, c1)
            if not error:
                mapping_points.add(self.map(x,y))
            error, x, y = get_intersect(a, b, c1, c2)
            if not error:
                mapping_points.add(self.map(x,y))
            error, x, y = get_intersect(a, b, c2, c3)
            if not error:
                mapping_points.add(self.map(x,y))
            error, x, y = get_intersect(a, b, c3, c0)
            if not error:
                mapping_points.add(self.map(x,y))

        # Now, if we have exactly two mapping points, we will go on
        if len(mapping_points) != 2:
            return []
        # Now, continuing with a list so that we can consider one point the start
        # and the other point the end of the line segment.
        mapping_points = list(mapping_points)

        # For the sampling points of the mapping, we determine if it is a flat or a steep line
        # (with respect to the mapped bins).
        # If it is steep, we use all integers in the y-interval; if it is flat, use the x-interval. This
        # prevents us from having a non-continuous line or even no line at all, imagine a completely vertical
        # line ...
        DEBUG("mapping_points: {}".format(str(mapping_points)))
        #ah, av = self.map(mapping_points[0][0], mapping_points[0][1], rounding=False)
        #bh, bv = self.map(mapping_points[1][0], mapping_points[1][1], rounding=False)
        ah, av = mapping_points[0][0], mapping_points[0][1]
        bh, bv = mapping_points[1][0], mapping_points[1][1]
        if bv-av == 0 and bh-ah == 0:
            return []
        is_steep = (bh-ah == 0) or (abs((bv-av)/(bh-ah)) > 1)
        DEBUG(str(is_steep))
        if is_steep: # swap horizontal and vertical for the following calculations (straight line equation)
            ah, av, bh, bv = av, ah, bv, bh
        slope = (bv-av) / (bh-ah)
        line = []
        for h in Interval(ah, bh).arange():
            v = (h-ah) * slope + av
            h, v = int(round(h)), int(round(v))
            point = (h,v) if not is_steep else (v,h)
            line.append(point)
        return line


class Grapher(object):
    seriesList = []
    legend = False
    colorList = [2, 3, 4, 5, 6, 7]
    autoAxis = True
    draw_lines = True

    def __init__(self, window):
        # Reset seriesList for consecutive calls
        self.seriesList = []
        # Initialize borders
        self.border_left = LEFTBORDER
        self.border_bottom = BOTTOMBORDER
        # Setup the window
        self.setWindow(window)
        # Initalise color
        curses.start_color()
        curses.use_default_colors()
        for i in range(curses.COLORS):
            curses.init_pair(i+1, i, -1)

    def setWindow(self, window):
        self.window = window # TODO: Setup borders with window
        self.getPlotArea()

    def getPlotArea(self):
        self.height, self.width = self.window.getmaxyx()
        self.left = self.border_left
        self.right = self.width-1
        self.top = 0
        self.bottom = self.height-1-self.border_bottom

    def setAxis(self, x_min=0, x_max=0, y_min=0, y_max=0, auto=False):
        self.autoAxis = auto
        self.x_min = x_min
        self.x_max = x_max
        self.y_min = y_min
        self.y_max = y_max

    """
    If self.autoAxis is True, scans all the data series in self.seriesList
    and determines x_min, x_max, y_min, y_max.
    """
    def updateAxis(self):
        if self.autoAxis:
            seriesXMins = []
            seriesXMaxs = []
            seriesYMins = []
            seriesYMaxs = []
            for ds in self.seriesList:
                seriesXMins.append(min(ds.X))
                seriesXMaxs.append(max(ds.X))
                DEBUG("Series XMax %f" % max(ds.X))
                seriesYMins.append(min(ds.Y))
                seriesYMaxs.append(max(ds.Y))
            self.x_min = min(seriesXMins)
            self.x_max = max(seriesXMaxs)
            self.y_min = min(seriesYMins) - 0.1 * (max(seriesYMaxs) - min(seriesYMins))
            self.y_max = max(seriesYMaxs) + 0.1 * (max(seriesYMaxs) - min(seriesYMins))

    def autosize(self):
        self.autoAxis = True
        self.redraw()

    """
    The next x methods: quick and dirty resize and move.
    """
    def getxsize(self):
        center = (self.x_max + self.x_min) / 2
        size = self.x_max - self.x_min
        return (center, size)
    def setxsize(self, center, size):
        self.autoAxis = False
        self.x_max = center + size / 2
        self.x_min = center - size / 2
        self.redraw()

    def getysize(self):
        center = (self.y_max + self.y_min) / 2
        size = self.y_max - self.y_min
        return (center, size)
    def setysize(self, center, size):
        self.autoAxis = False
        self.y_max = center + size / 2
        self.y_min = center - size / 2
        self.redraw()

    def changex(self, relmove, relzoom):
        center, size = self.getxsize()
        center = center + relmove * size
        size = size * relzoom
        self.setxsize(center, size)
    def zoominx(self):
        self.changex(0, 3/4)
    def zoomoutx(self):
        self.changex(0, 4/3)
    def moveright(self):
        self.changex(.2, 1)
    def moveleft(self):
        self.changex(-.2, 1)

    def changey(self, relmove, relzoom):
        center, size = self.getysize()
        center = center + relmove * size
        size = size * relzoom
        self.setysize(center, size)
    def zoominy(self):
        self.changey(0, 3/4)
    def zoomouty(self):
        self.changey(0, 4/3)
    def moveup(self):
        self.changey(.2, 1)
    def movedown(self):
        self.changey(-.2, 1)

    """
    The next methods: Determine nice grid points
    """
    def getgridpoints(self, size, minNum, zmin, zmax):
        # maximum allowed distance between two grid points
        maxDistance = size / minNum
        maxMagnitude = math.log10(maxDistance)
        # upper = 100 or 1 or .00001 or something, but it's bigger than maxDistance,
        # so .1 * upper < maxDistance < upper
        upper = 10 ** math.ceil(maxMagnitude)
        upperMagnitude = upper
        candidates = [.5 * upper, .25 * upper, .2 * upper, .1 * upper]
        DEBUG("size = {}, maxdist = {}, upper = {}".format(size, maxDistance, upper))
        distance = None
        for candidate in candidates:
            if candidate < maxDistance:
                distance = candidate
                break
        if distance == None:
            raise Exception('There should be at least .1 * upperBound smaller than maxDistance!')
        # distance is now a value like 250, 1000, .5, .00002
        # now we have to find the values between min and max that match
        # divide the lower bound of the axis by the distance, ceil(), and add distance as long as we are smaller than the upper bound of the axis
        gridpoints = []
        point = math.ceil(zmin / distance) * distance
        while point < zmax:
            gridpoints.append(point)
            point = point + distance
        return gridpoints

    def getxgrid(self):
        center, size = self.getxsize()
        return self.getgridpoints(size, 2, self.x_min, self.x_max)
    def getygrid(self):
        center, size = self.getysize()
        return self.getgridpoints(size, 3, self.y_min, self.y_max)

    def plotGridlines(self):
        return # TODO deactivated until we have nicer color support
        xgrid = self.getxgrid()
        ygrid = self.getygrid()
        for x in xgrid:
            col = self.mapx(x)
            for row in range(self.top, self.bottom):
                self.window.addstr(row, col, '|') # TODO Replace by unicode box-drawing character
        for y in ygrid:
            row = self.mapy(y)
            for col in range(self.left, self.right):
                self.window.addstr(row, col, '-') # TODO see above
    
    def plotGrid(self):
        if not self.border_bottom or not self.border_left:
            return
        xgrid = self.getxgrid()
        ygrid = self.getygrid()
        for col in range(self.left, self.right+1):
            self.window.addstr(self.bottom+1, col, '─')
        for row in range(self.top, self.bottom+1):
            self.window.addstr(row, self.left-1, '│')
        self.window.addstr(self.bottom+1, self.left-1, '└')
        for x in xgrid:
            col = self.mapping.mapx(x)
            text = str(x)
            self.window.addstr(self.bottom+1, col, '┴') # self.bottom+1 == self.height-2 (line before last line)
            if col + len(text) > self.width-1:
                col = self.width-1 - len(text)
            self.window.addstr(self.bottom+2, col, text) # self.bottom+2 == self.height-1 (last line)
        for y in ygrid:
            row = self.mapping.mapy(y)
            self.window.addstr(row, self.border_left-1, '├')
            text = str(y)
            # The left-border text length should be <= border_left-1 --> len <= border_left-2 + " "
            if len(text) > self.border_left-2:
                text = text[0:self.border_left-2] + " "
            else:
                text = " " * (self.border_left-2-len(text)) + text + " "
            self.window.addstr(row, 0, text)

    """
    Plots the coordinate system axis, the ordinate and abscissa.
    """
    # TODO If the coordinate base lies outside of the drawing area, what will happen?
    def plotAxis(self):
        # Calculate x, y values at y, x axis
        centercol, centerrow = self.mapping.map(0, 0)
        # Plot y axis
        if self.mapping.fitsx(0):
            for row in range(self.top, self.bottom+1):
                self.window.addstr(row, centercol, "│")
            self.window.addstr(self.top, centercol, "↑") # arrow
        # Plot x axis
        if self.mapping.fitsy(0):
            for col in range(self.left, self.right+1):
                self.window.addstr(centerrow, col, "─")
            self.window.addstr(centerrow, self.right, "→") # arrow
        # Plot origin
        if self.mapping.fits(0, 0):
            self.window.addstr(centerrow, centercol, "┼")

    def toggleLegend(self):
        self.legend = not self.legend
        self.redraw() # this calls updateLegend(), too

    def toggleTicks(self):
        if self.border_left and self.border_bottom:
            self.border_left = 0
            self.border_bottom = 0
        else:
            self.border_left = LEFTBORDER
            self.border_bottom = BOTTOMBORDER
        self.redraw()

    def toggleLines(self):
        self.draw_lines = not self.draw_lines
        self.redraw()

    """
    If self.legend is True, plots a legend box in the upper right corner.
    """
    def updateLegend(self):
        if not self.legend:
            return
        y = 0
        labelLengths = []
        for ds in self.seriesList:
            labelLengths.append(len(ds.label))
        x = self.right+1 - max(labelLengths)
        for ds in self.seriesList:
            self.window.addstr(y, x, " "*max(labelLengths), curses.color_pair(ds.color) | curses.A_REVERSE)
            self.window.addstr(y, x, ds.label, curses.color_pair(ds.color) | curses.A_REVERSE)
            y += 1

    def updateMapping(self):
        self.mapping = Mapping(self.x_min, self.x_max, self.left, self.right, self.y_min, self.y_max, self.bottom, self.top)

    def plotAll(self):
        # The naive approach here is to plot all lines between data points first (so that they
        # end up in the background) and then plot all data points on top of them. This works but
        # slows down the application if there are a lot of data points involved. Maybe, this is
        # due to the fact that for each connection line, we have to determine if it will be drawn
        # which is done by checking if the start and end point are in the drawing area and, if not,
        # if there are intersections with the drawing-area-borders.
        # 1. To speed up, we have a vectorized Mapping.nofit() method which checks for each data
        # point if is is not in the drawing area and if so, encodes on which side(s) of the
        # drawing area it lies. Then, by checking if two consecutive data points are outside
        # of the drawing area on the same side (e.g. both points are on the left side of the
        # drawing area), we can omit the connection line because there is no chance of the line
        # crossing the drawing area borders. Furthermore, we only determine if the points are
        # in the drawing area once in this method here (it could be done once more in the
        # mapLine() or map() method but that's not our business here!)
        # 2. Furthermore, we check if two consecutive points which should be are mapped on the same
        # pixel. If so, we can skip one of that points and furthermore skip drawing that line. But
        # as it seems to me that drawing the same point twice yields no performance penalty (I guess
        # it just corresponds to setting a value in the underlying curses-array), we just draw every
        # point.
        for ds in self.seriesList:
            # First, determine where the data points lie outside of the drawing area
            outsides = self.mapping.nofit(ds.X, ds.Y)
            # 1. We can omit a line if two consecutive points share a nofit-direction
            # We only have to calculate this if we actually want to draw the lines
            if self.draw_lines:
                omitlines = outsides[0:-1] & outsides[1:]
                omitlines = numpy.append(omitlines, 15) # Hack so that the array sizes stay the same for iterating
            # 2. If two consecutive points are the same, omit the lines, too. To do so,
            # pre-calculate the mapping values.
            cols = numpy.empty(outsides.shape) # Pre initialize arrays for the mappings so that they have the
            rows = numpy.empty(outsides.shape) # same shape as the other array
            cols[outsides==0] = self.mapping.mapx(ds.X[outsides==0]) # Map the values
            rows[outsides==0] = self.mapping.mapy(ds.Y[outsides==0])
            cols = cols.astype(int) # Mapping.map() returns integer arrays but the types are changed when assigning
            rows = rows.astype(int) # to the bigger arrays. Ensure the types here again.
            # Try to draw the lines and draw the points
            for i in range(len(outsides)):
                # First try to draw the line if it is not obvious that it will not be drawn
                if self.draw_lines and not omitlines[i] and (rows[i], cols[i])!=(rows[i+1], cols[i+1]):
                    ax, ay, bx, by = ds.X[i], ds.Y[i], ds.X[i+1], ds.Y[i+1]
                    DEBUG(str(self.mapping))
                    DEBUG("{}, {}, {}, {}".format(ax, ay, bx, by))
                    for col, row in self.mapping.mapLine(ax, ay, bx, by):
                        self.window.addstr(row, col, "·", curses.color_pair(ds.color))
                # Then, draw the (current) point
                if not outsides[i]:
                    # The value is plottable, map it to a (px, py) plot location.
                    # col, row = self.mapping.map(ds.X[i],ds.Y[i])
                    # Plot the point at that location.
                    self.window.addstr(rows[i], cols[i], "+", curses.color_pair(ds.color))

        """
        DEPRECATED APPROACH
        # Plot the (straight) connection lines between the data points
        for ds in self.seriesList:
            for i in range(ds.length-1):
                ax, ay, bx, by = ds.X[i], ds.Y[i], ds.X[i+1], ds.Y[i+1]
                DEBUG(str(self.mapping))
                DEBUG("{}, {}, {}, {}".format(ax, ay, bx, by))
                for col, row in self.mapping.mapLine(ax, ay, bx, by):
                    self.window.addstr(row, col, "·", curses.color_pair(ds.color))
        # Plot the data points in front of the lines
        for ds in self.seriesList:
            DEBUG("NOTE ds.length %i" % ds.length)
            for i in range(ds.length):
                x, y = ds.X[i], ds.Y[i]
                # Check the value lies in the plottable area.
                if self.mapping.fits(x, y):
                    # The value is plottable, map it to a (px, py) plot location.
                    col, row = self.mapping.map(x,y)
                    # Plot the point at that location.
                    self.window.addstr(row, col, "+", curses.color_pair(ds.color))
        """

    def clearPlotArea(self):
        self.window.addstr(0, 0, " ")
        self.window.clrtobot()

    def clearData(self):
        self.seriesList = []

    def plot(self, X, Y, label="myData"):
        # Add the new data to the seriesList.
        self.seriesList.append(DataSeries(numpy.array(X), numpy.array(Y), label, color=self.colorList[len(self.seriesList)]))
        self.redraw()

    def redraw(self):
        # Determine the new size of the plotting area
        self.getPlotArea()
        # Clear the screen of any current plots.
        self.clearPlotArea()
        # Update axis limits
        self.updateAxis()
        # Update the mapping between x,y and row,col
        self.updateMapping()
        # Plot the background grid lines
        self.plotGridlines()
        # Plot axis lines
        self.plotAxis()
        # Re-plot each DataSeries.
        self.plotAll()
        # Plot the grid points
        self.plotGrid()
        # Update the legend.
        self.updateLegend()

class Figure(object):
    def __init__(self):
        self.seriesList = []

    def plot(self, x, y, label=""):
        self.seriesList.append(DataSeries(x, y, label))

    def show(self):
        curses.wrapper(lambda stdscr: self.drawingloop(stdscr))

    def drawingloop(self, stdscr):
        stdscr.clear()
        curses.curs_set(False)
        ax = Grapher(stdscr)
        for s in self.seriesList:
            ax.plot(s.X, s.Y, s.label)

        # DEBUG
        for i in range(0):
            ax.moveup()

        colornum = 0
        while True:
            k = stdscr.getkey()
            if k == 'q':
                break
            elif k == 'KEY_RESIZE':
                ax.redraw()
            elif k == 'r':
                ax.redraw()
            elif k == 'g':
                ax.toggleLegend()
            elif k == 't':
                ax.toggleTicks()
            elif k == 'c':
                ax.toggleLines()
            elif k == 'l':
                ax.moveright()
            elif k == 'h':
                ax.moveleft()
            elif k == 'j':
                ax.movedown()
            elif k == 'k':
                ax.moveup()
            elif k == 'w':
                ax.zoominy()
            elif k == 's':
                ax.zoomouty()
            elif k == 'a':
                ax.zoomoutx()
            elif k == 'd':
                ax.zoominx()
            elif k == 'x':
                ax.autosize()
            else:
                stdscr.addstr(0,0,k)

def plot(x, y, label=""):
    fig = Figure()
    fig.plot(x, y, label)
    fig.show()

"""
Convenience function to convert rising/falling-edge interrupt-timestamps and associated values into a plottable signal.
Assuming a digital signal that was recorded as (timestamp, value)-pairs while the value describes if we observed
a rising or a falling edge, this function converts the two lists timestamps and values into two corresponding
lists which, when plotted, look like the digital signal. In fact, this step only consists of repeating each samples
value at the timestamp of the next sample so that we get a nice chain of rectangles.

Although this implementation looks a little bit shitty, it is included here as a tribute to my friend learning programming
right now who had the task to implement this function. Compared to what happens when plotting the values, the inefficiency
of this implementation here is negligible.
"""
def interrupts2signal(Zeitpunkte, Werte): # German: Zeitpunkte = timestamps, Werte = values, neu = new
    # Lists containing the additional points so that the plot ends up nicely
    Werte_neu=[]
    Zeitpunkte_neu=[]
    # Artificial for-loop
    i=0
    while i<len(Werte):
        Werte_neu.append(Werte[i])
        Zeitpunkte_neu.append(Zeitpunkte[i])
        if i+1<len(Werte):
            Werte_neu.append(Werte[i])
            Zeitpunkte_neu.append(Zeitpunkte[i+1])
        # Part of the artificial for-loop
        i=i+1
    return Zeitpunkte_neu, Werte_neu

if __name__ == '__main__':
    import numpy
    import math
    import time
    
    #m = Mapping(-3, 3, 0, 10, -3, 3, 0, 10)
    #m.mapLine(-5,-12, 1,2)

    # Determine example plots
    x = numpy.arange(-11.5, 13.5, .001)
    #x = numpy.array([0, .1]) # DEBUG
    #ya = [math.sin(i) for i in x]
    #yb = [(1/4)*math.sin(4*i) for i in x]
    #yc = [math.sin(i) + (1/4)*math.sin(4*i) for i in x]
    ya = numpy.sin(x)
    yb = 1/4 * numpy.sin(4*x)
    yc = numpy.sin(x) + 1/4*numpy.sin(4*x)
    yd = numpy.cos(x) + 1/4*numpy.cos(4*x)

    print("First, demonstrating a direct plot ...")
    time.sleep(1)
    plot(x, ya, "sin(x)")
    # exit() # DEBUG

    print("Now, demonstrating multiple plots in a Figure object.")
    time.sleep(1)
    f = Figure()
    f.plot(x, ya, "sin(x)")
    f.plot(x, yb, "(1/4)sin(4x)")
    f.plot(x, yc, "sin(x)+(1/4)sin(4x)")
    f.plot(x, yd, "cos(x)+1/4*cos(4*x)")
    f.show()
    print("And, Figure objects can be reused (shown again) after they have been closed.")
    time.sleep(1)
    f.show()