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Editor: kcrisman
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== Curves of Pursuit ==
by Marshall Hampton.
npi = RDF(pi)
def rot(t):
    from math import cos, sin
    return matrix([[cos(t),sin(t)],[-sin(t),cos(t)]])

def pursuit(n,x0,y0,lamb,steps = 100, threshold = .01):
    paths = [[[x0,y0]]]
    for i in range(1,n):
        rx,ry = list(rot(2*npi*i/n)*vector([x0,y0]))
    oldpath = [x[-1] for x in paths]
    for q in range(steps):
        diffs = [[oldpath[(j+1)%n][0]-oldpath[j][0],oldpath[(j+1)%n][1]-oldpath[j][1]] for j in range(n)]
        npath = [[oldpath[j][0]+lamb*diffs[j][0],oldpath[j][1]+lamb*diffs[j][1]] for j in range(n)]
        for j in range(n):
        oldpath = npath
    return paths
html('<h3>Curves of Pursuit</h3>')
def curves_of_pursuit(n = slider([2..20],default = 5, label="# of points"),steps = slider([floor(1.4^i) for i in range(2,18)],default = 10, label="# of steps"), stepsize = slider(srange(.01,1,.01),default = .2, label="stepsize"), colorize = selector(['BW','Line color', 'Filled'],default = 'BW')):
    outpaths = pursuit(n,0,1,stepsize, steps = steps)
    mcolor = (0,0,0)
    outer = line([q[0] for q in outpaths]+[outpaths[0][0]], rgbcolor = mcolor)
    polys = Graphics()
    if colorize=='Line color':
        colors = [hue(j/steps,1,1) for j in range(len(outpaths[0]))]
    elif colorize == 'BW':
        colors = [(0,0,0) for j in range(len(outpaths[0]))]
        colors = [hue(j/steps,1,1) for j in range(len(outpaths[0]))]
        polys = sum([polygon([outpaths[(i+1)%n][j+1],outpaths[(i+1)%n][j], outpaths[i][j+1]], rgbcolor = colors[j]) for i in range(n) for j in range(len(outpaths[0])-1)])
        #polys = polys[0]
        colors = [(0,0,0) for j in range(len(outpaths[0]))]
    nested = sum([line([q[j] for q in outpaths]+[outpaths[0][j]], rgbcolor = colors[j]) for j in range(len(outpaths[0]))])
    lpaths = [line(x, rgbcolor = mcolor) for x in outpaths]
    show(sum(lpaths)+nested+polys, axes = False, figsize = [5,5], xmin = -1, xmax = 1, ymin = -1, ymax =1)
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{{{ {{{#!sagecell
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        print "Bug selecting plot?"         print("Bug selecting plot?")
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    html('<h2>%s</h2>'%example)     pretty_print(html('<h2>%s</h2>'%example))
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        html('<h3><a target="_new" href="%s">%s</a></h3>'%(url,url))
    show(P, viewer='tachyon' if tachyon else 'jmol', frame=frame)
        pretty_print(html('<h3><a target="_new" href="%s">%s</a></h3>'%(url,url)))
    show(P, viewer='tachyon' if tachyon else 'threejs', frame=frame)
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{{{ {{{#!sagecell
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{{{ {{{#!sagecell
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         viewer='tachyon' if tachyon else 'jmol',          viewer='tachyon' if tachyon else 'threejs',
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{{{ {{{#!sagecell
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def _(band_number = selector(range(1,5)), current_color = Color('red')):

def _(band_number = selector(range(1,5)), current_color = Color('red'), auto_update=False):
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def color_experimenter(expression=input_box('', 'Expression', str), color=Color('red')):
def color_experimenter(expression=input_box('x^2', 'Expression', str), color=Color('red')):
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            print "There's a problem with your expression."             print("There's a problem with your expression.")
        print("Be sure to enter a plottable expression")
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== Interactive 2d Plotting == == Interactive 2D Plotting ==
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{{{ {{{#!sagecell
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    print '<html><p style="font-family:Arial, sans-serif;color:#000"><span style="color:red;font-weight:bold">Error</span>: %s</p></html>' % msg     pretty_print(html('<p style="font-family:Arial, sans-serif;color:#000"><span style="color:red;font-weight:bold">Error</span>: %s</p>' % msg))
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            print error_msg('This is not an expression.')             print(error_msg('This is not an expression.'))
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                    print "var('%s')\nplot(%s).show(%s%s%s)" % (expression.variables()[0], repr(expression), 'aspect_ratio=1' if square else '', ', ' if square and not axes else '', 'axes=False' if not axes else '')                     print("var('%s')\nplot(%s).show(%s%s%s)" % (expression.variables()[0], repr(expression), 'aspect_ratio=1' if square else '', ', ' if square and not axes else '', 'axes=False' if not axes else ''))
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                    print "var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression))                     print("var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression)))
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            print error_msg('This expression has more than one variable.')             print(error_msg('This expression has more than one variable.'))
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            print error_msg("This expression contains an unknown function.")             print(error_msg("This expression contains an unknown function."))
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== Interact with matplotlib ==
# Simple example demonstrating how to interact with matplotlib directly.
# Comment plt.clf() to get the plots overlay in each update.
# Gokhan Sever & Harald Schilly (2010-01-24)

from scipy import stats
import numpy as np
import matplotlib.pyplot as plt

def plot_norm(loc=(0,(0,10)), scale=(1,(1,10))):
    rv = stats.norm(loc, scale)
    x = np.linspace(-10,10,1000)

== Spirograph ==
# Javier Pérez Lázaro #
# Logroño (Spain) #
# [email protected] #


text1='Spirograph is a tool for drawing hypotrochoids and epitrochoids.'
text2='Assume that a A is a point attached to a circle. A can be attached to the boundary of the circle or to any exterior or interior place. If the circle rolls around the outside of a fixed circle, the curve traced by the point A is called an epitrochoid. In case the circle rolls around the inside of a fixed circle, the curve is an hypotrochoid.'
text3='If the quotient between the radii of the circles is a rational number, then the curves are periodic.'

#the code

def fun(
tex1=text_control(text1), tex2=text_control(text2), tex3=text_control(text3),
tex4=text_control('Radius of the circle. Should be a rational number with shape p/q.'),
tex5=text_control("Rate between the distance of the point to the circle's center and the radius."),
u=selector(['Plot the curve. Slider of % below enabled.',
'Build an animation of the plot with the number of frames specified below.'],label='Choose:'),
per=slider(0,100,1,default=100,label='graph %'),
cir_bool=checkbox(True, "Show circles?"),
    if h == 'hypotrochoid' and (b >= 1 or b <= 0):
        print("In a hypotrochoid, radius must be between 0 and 1.")
        draw = False
    if h == 'epitrochoid' and b <= 0:
        print("In a epitrochoid, radius must be positive")
    if draw==True:
        if h=='hypotrochoid': b=-b
        if u=='Plot the curve. Slider of % below enabled.':
            if cir_bool:
        if u=='Build an animation of the plot with the number of frames specified below.':
            for a in srange(step,tMax,step):
                if cir_bool:

Sage Interactions - Graphics

goto interact main page

Curves of Pursuit

by Marshall Hampton.


Catalog of 3D Parametric Plots


Interactive rotatable raytracing with Tachyon3d


Interactive 3d plotting


Somewhat Silly Egg Painter

by Marshall Hampton (refereed by William Stein)


Plot Coloring

by Timothy Clemans


Interactive 2D Plotting

by Timothy Clemans


Interact with matplotlib




interact/graphics (last edited 2020-06-02 15:13:32 by kcrisman)