Oscar Benjamin wrote: > On Sun, 9 Dec 2018 at 16:37, Brian Christiansen > <brian_christi...@hotmail.com> wrote: >> >> I have been messing with a program that is inspried by a video on >> youtube that is about the vizualization of pi. I might make a post >> about that program someday, but I want to talk about something else. >> One of the ways of visualizing it is to put dots corresponding to each >> digits in a spiral pattern, in a color corresponding to what the digit >> is. I think this would be easiest, at least in the initial calculation >> of the point would be to use polar coordinates. >> >> For example, if I were to use a very simple archimedian spiral, r = 0 + >> (1 x theta), the "first 4" points, if theta increases by 1 degree >> (2pi/360 radians), are (0,0) (2pi/360 "units",2pi/360"radians") >> (4pi/360, 4pi/360) (6pi/360,6pi/360). >> >> The problem is that python (more specifically tkinter or graphics.py >> file that I downloaded) can't use polar coordinates directly to plot >> points (or at least I don't think they can). The polar coordinates have >> to be converted to cartesian coordinates, then converted to the >> coordinate system that a computer uses to actually plot points on the >> screen. > > Hi Brian, > > I don't think anything exists (apart from matplotlib) to do this for you: > https://matplotlib.org/examples/pylab_examples/polar_demo.html > > Converting from polar to Cartesian coordinates is easy enough though. > For your case if xc_p, yc_p are the pixel coordinates of the centre of > your window and rq and thetaq are the polar coordinates for point q > then > > from math import sin, cos > xq_p = xc_p + r * cos(theta) * pix_scale > yq_p = yc_p - r * sin(theta) * pix_scale > > gives the pixel coordinates for q. The parameter pix_scale is the > number of pixels that corresponds to a distance of 1 in your polar > coordinate system. You might choose this parameter based on the > height/width in pixels of the window. Depending on what you're doing > you may need to convert xq_p and yq_p to int rounding in some way.
Python has native support for complex numbers. With these: >>> def angle(deg): ... return cmath.rect(1, math.radians(deg)) ... >>> def point(c): ... return (int(c.real), int(c.imag)) ... >>> center = 350 + 350j >>> p = center + 350 >>> point(p) (700, 350) To rotate p around the center by 90 degrees: >>> point((p-center) * angle(90) + center) (350, 700) Scaling can also be performed with a single multiplication >>> scale = 2 + 2j >>> p * 2 (1400+700j) Another option is to let the Canvas widget do it: http://effbot.org/tkinterbook/canvas.htm#Tkinter.Canvas.scale-method -- https://mail.python.org/mailman/listinfo/python-list
