Create drawSines.py

Author: JorjMcKie

recipes/Python/Draw Sine Function in PDF/drawSines.py

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+import fitz, math
+"""
+Created on 2017-08-17
+
+@author: (c) 2017, Jorj X. McKie
+
+License: GNU GPL V3
+
+PyMuPDF Demo Program
+---------------------
+Create a PDF with drawings of the sine and cosine functions using PyMuPDF.
+Depending on how start and end points are located with respect to each
+other, horizontal or vertical drawings result.
+The vertical case can obviously be used for creating inverse function
+(arcus sine / cosine) graphs.
+
+The function graphs are pieced together in 90 degree parts, for which Bezier
+curves are used.
+
+Note that the 'alfa' and 'beta' constants represent values for use as 
+Bezier control points like so:
+x-values (written in degrees): [0, 30, 60, 90]
+corresponding y-values:        [0, alfa, beta, 1]
+
+These values have been calculated by the scipy.interpolate.splrep() method.
+They provide an excellent spline approximation of the sine / cosine
+functions - please look at SciPy documentation for background.
+
+"""
+def bsinPoints(pb, pe):
+    """Return Bezier control points, when pb and pe stand for a full period
+    from (0,0) to (2*pi, 0), respectively, in the user's coordinate system.
+    The returned points can be used to draw up to four Bezier curves for
+    the complete sine function graph from 0 to 2*pi.
+    """
+    f = abs(pe - pb) * 0.5 / math.pi     # represents the unit
+    alfa = 5.34295228e-01
+    beta = 1.01474288e+00
+    # adjust for either horizontal or vertical
+    if pb.y == pe.y:
+        y_ampl = (0, f)
+        y_alfa = (0, f * alfa)
+        y_beta = (0, f * beta)
+    elif pb.x == pe.x:
+        y_ampl = (-f, 0)
+        y_alfa = (-f * alfa, 0)
+        y_beta = (-f * beta, 0)
+    else:
+        raise ValueError("can only draw horizontal or vertical")
+
+    p0 = pb
+    p4 = pe
+    p1 = pb + (pe - pb)*0.25 - y_ampl
+    p2 = pb + (pe - pb)*0.5
+    p3 = pb + (pe - pb)*0.75 + y_ampl
+    k1 = pb + (pe - pb)*(1./12.)  - y_alfa
+    k2 = pb + (pe - pb)*(2./12.)  - y_beta
+    k3 = pb + (pe - pb)*(4./12.)  - y_beta
+    k4 = pb + (pe - pb)*(5./12.)  - y_alfa
+    k5 = pb + (pe - pb)*(7./12.)  + y_alfa
+    k6 = pb + (pe - pb)*(8./12.)  + y_beta
+    k7 = pb + (pe - pb)*(10./12.) + y_beta
+    k8 = pb + (pe - pb)*(11./12.) + y_alfa
+    return p0, k1, k2, p1, k3, k4, p2, k5, k6, p3, k7, k8, p4
+
+def bcosPoints(pb, pe):
+    """Return Bezier control points, when pb and pe stand for a full period
+    from (0,0) to (2*pi, 0), respectively, in the user's coordinate system.
+    The returned points can be used to draw up to four Bezier curves for
+    the complete cosine function graph from 0 to 2*pi.
+    """
+    f = abs(pe - pb) * 0.5 / math.pi     # represents the unit
+    alfa = 5.34295228e-01
+    beta = 1.01474288e+00
+    # adjust for either horizontal or vertical
+    if pb.y == pe.y:
+        y_ampl = (0, f)
+        y_alfa = (0, f * alfa)
+        y_beta = (0, f * beta)
+    elif pb.x == pe.x:
+        y_ampl = (-f, 0)
+        y_alfa = (-f * alfa, 0)
+        y_beta = (-f * beta, 0)
+    else:
+        raise ValueError("can only draw horizontal or vertical")
+        
+    p0 = pb - y_ampl
+    p4 = pe - y_ampl
+    p1 = pb + (pe - pb)*0.25
+    p2 = pb + (pe - pb)*0.5 + y_ampl
+    p3 = pb + (pe - pb)*0.75
+    k1 = pb + (pe - pb)*(1./12.)  - y_beta
+    k2 = pb + (pe - pb)*(2./12.)  - y_alfa
+    k3 = pb + (pe - pb)*(4./12.)  + y_alfa
+    k4 = pb + (pe - pb)*(5./12.)  + y_beta
+    k5 = pb + (pe - pb)*(7./12.)  + y_beta
+    k6 = pb + (pe - pb)*(8./12.)  + y_alfa
+    k7 = pb + (pe - pb)*(10./12.) - y_alfa
+    k8 = pb + (pe - pb)*(11./12.) - y_beta
+    return p0, k1, k2, p1, k3, k4, p2, k5, k6, p3, k7, k8, p4
+
+if __name__ == "__main__":
+    from fitz.utils import getColor
+    doc = fitz.open()
+    page = doc.newPage()
+    red    = getColor("red")      # line color for sine
+    blue   = getColor("blue")     # line color for cosine
+    yellow = getColor("py_color") # background color
+    w = 0.3                  # line width
+    #--------------------------------------------------------------------------
+    # define end points of x axis we want to use as 0 and 2*pi
+    # these may be oriented horizontally or vertically
+    #--------------------------------------------------------------------------
+    pb = fitz.Point(50, 200)      # example values for
+    pe = fitz.Point(550, 200)     # horizontal drawing
+    #pb = fitz.Point(300, 100)     # example values for
+    #pe = fitz.Point(300, 600)     # vertical drawing
+    page.drawLine(pb, pe, width = w)   # draw x-axis (default color)
+
+    # get all points for the sine function
+    pnt = bsinPoints(pb, pe)
+    # draw some points for better orientation
+    for i in (0, 3, 6, 9, 12):
+        page.drawCircle(pnt[i], 1, color = red)
+    # now draw a complete sine graph period in "red"
+    for i in (0, 3, 6, 9):        # draw all 4 function segments
+        page.drawBezier(pnt[i], pnt[i+1], pnt[i+2], pnt[i+3],
+                        color = red, width = w)
+
+    # same thing for cosine with "blue"
+    pnt = bcosPoints(pb, pe)
+    for i in (0, 3, 6, 9, 12):
+        page.drawCircle(pnt[i], 1, color = blue)
+    for i in (0, 3, 6, 9):        # draw all 4 function segments
+        page.drawBezier(pnt[i], pnt[i+1], pnt[i+2], pnt[i+3],
+                        color = blue, width = w)
+
+    # finally draw a rectangle around everything (in background):
+    rect = fitz.Rect(pb, pb)      # create smallest rectangle
+    for p in pnt:                 # containing all the points
+        rect = rect | p
+    # leave 5 px space around the picture
+    rect.x0 -= 5
+    rect.y0 -= 5
+    rect.x1 += 5
+    rect.y1 += 5
+    page.drawRect(rect, width = w, fill = yellow, overlay = False)
+    doc.save("drawSines.pdf")