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goto [:interact:interact main page] goto [[interact|interact main page]]


<<TableOfContents>>

== Curves of Pursuit ==
by Marshall Hampton.
{{{#!sagecell
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]))
        paths.append([[rx,ry]])
    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):
            paths[j].append(npath[j])
        oldpath = npath
    return paths
html('<h3>Curves of Pursuit</h3>')
@interact
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]))]
    else:
        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)
}}}
{{attachment:pcurves.png}}
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{{{ {{{#!sagecell
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attachment:parametricplot3d.png {{attachment:parametricplot3d.png}}
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{{{ {{{#!sagecell
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attachment:tachyonrotate.png {{attachment:tachyonrotate.png}}
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{{{ {{{#!sagecell
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attachment:tachyonplot3d.png

[[Anchor(eggpaint)]]
{{attachment:tachyonplot3d.png}}

<<Anchor(eggpaint)>>
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{{{ {{{#!sagecell
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@interact
def _(band_number = selector(range(1,5)), current_color = Color('red')):

@interact
def _(band_number = selector(range(1,5)), current_color = Color('red'), auto_update=False):
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attachment:eggpaint.png {{attachment:eggpaint.png}}

== Plot Coloring ==
by Timothy Clemans
{{{#!sagecell
@interact
def color_experimenter(expression=input_box('', 'Expression', str), color=Color('red')):
    if expression:
        try:
            plot(SR(expression), rgbcolor=color).show()
        except TypeError:
            print "There's a problem with your expression."
}}}
{{attachment:color_of_plot_changer.png}}

== Interactive 2D Plotting ==
by Timothy Clemans
{{{#!sagecell
def error_msg(msg):
    print '<html><p style="font-family:Arial, sans-serif;color:#000"><span style="color:red;font-weight:bold">Error</span>: %s</p></html>' % msg

@interact
def interactive_2d_plotter(expression=input_box('sin(x)', 'Expression', str), x_range=range_slider(-10,10,1,(0,10), label='X Range'), square=checkbox(True, 'Square'), axes=checkbox(False, 'Show Axes')):
    if expression:
        try:
            expression = SR(expression) # turn string into a Sage expression
        except TypeError:
            print error_msg('This is not an expression.')
            return
        try:
                xmin, xmax = x_range
                if square or not axes:
                    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 '')
                    if square:
                        plot(expression, xmin, xmax).show(aspect_ratio=1, axes=axes)
                    else:
                        plot(expression, xmin, xmax).show(axes=axes)
                else:
                    print "var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression))
                    plot(expression, xmin, xmax).show(axes=axes)
        except ValueError:
            print error_msg('This expression has more than one variable.')
            return
        except TypeError:
            print error_msg("This expression contains an unknown function.")
            return
}}}
{{attachment:interactive_2d_plotting.png}}

== Interact with matplotlib ==
{{{#!sagecell
# 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

@interact
def plot_norm(loc=(0,(0,10)), scale=(1,(1,10))):
    rv = stats.norm(loc, scale)
    x = np.linspace(-10,10,1000)
    plt.plot(x,rv.pdf(x))
    plt.grid(True)
    plt.savefig('plt.png')
    plt.clf()
}}}
{{attachment:matplotlib_interact.png}}

== Spirograph ==
{{{#!sagecell
#---------------------------#
# Javier Pérez Lázaro #
# Logroño (Spain) #
# [email protected] #
#---------------------------#

#introduction

html('<h1><center>Spirograph</center></h1>')
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

@interact
def fun(
tex1=text_control(text1), tex2=text_control(text2), tex3=text_control(text3),
h=('Select:',list(['epitrochoid','hypotrochoid'])),
tex4=text_control('Radius of the circle. Should be a rational number with shape p/q.'),
b=input_box(default=7/30,label='radius'),
tex5=text_control("Rate between the distance of the point to the circle's center and the radius."),
rate=input_box(default=1),
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 %'),
frames=100,
cir_bool=checkbox(True, "Show circles?"),
auto_update=false):
    draw=True
    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"
        draw=False
    if draw==True:
        if h=='hypotrochoid': b=-b
        var('t')
        cx=(1+b)*cos(t*b/(1+b))
        cy=(1+b)*sin(t*b/(1+b))
        px=cx-b*rate*cos(t)
        py=cy-b*rate*sin(t)
        axeM=1+max([0,b+abs(b)*rate])
        if u=='Plot the curve. Slider of % below enabled.':
            tMax=pi*denominator(b/(b+1))*per/50
            L=parametric_plot((px,py),(t,0,max([0.001,tMax])),plot_points=10*rate*tMax)
            if cir_bool:
                p=point((px(t=tMax),py(t=tMax)),pointsize=30,color='blue')
                c=point((cx(t=tMax),cy(t=tMax)),pointsize=30,color='red')
                cir=circle((cx(t=tMax),cy(t=tMax)),b,color='red')
                lin=line([(cx(t=tMax),cy(t=tMax)),(px(t=tMax),py(t=tMax))])
                L+=circle((0,0),1)+cir+lin+p+c
            show(L,aspect_ratio=1,xmin=-axeM,xmax=axeM,ymin=-axeM,ymax=axeM)
        if u=='Build an animation of the plot with the number of frames specified below.':
            tMax=2*pi*denominator(b/(b+1))
            step=tMax/(frames-1)
            curva=Graphics()
            v=[]
            for a in srange(step,tMax,step):
                curva+=parametric_plot((px,py),(t,a-step,a))
                L=curva
                if cir_bool:
                    cx_a=cx(t=a)
                    cy_a=cy(t=a)
                    px_a=cx_a-b*rate*cos(a)
                    py_a=cy_a-b*rate*sin(a)
                    p=point((px_a,py_a),pointsize=30,color='blue')
                    c=point((cx_a,cy_a),pointsize=30,color='red')
                    cir=circle((cx_a,cy_a),b,color='red')
                    lin=line([(cx_a,cy_a),(px_a,py_a)])
                    L+=circle((0,0),1)+cir+lin+c+p
                v.append(L)
            animate(v,xmin=-axeM,xmax=axeM,ymin=-axeM,ymax=axeM,aspect_ratio=1).show()
}}}
{{attachment:interactive_animate_spirograph.png}}

Sage Interactions - Graphics

goto interact main page

Curves of Pursuit

by Marshall Hampton.

pcurves.png

Catalog of 3D Parametric Plots

parametricplot3d.png

Interactive rotatable raytracing with Tachyon3d

tachyonrotate.png

Interactive 3d plotting

tachyonplot3d.png

Somewhat Silly Egg Painter

by Marshall Hampton (refereed by William Stein)

eggpaint.png

Plot Coloring

by Timothy Clemans

color_of_plot_changer.png

Interactive 2D Plotting

by Timothy Clemans

interactive_2d_plotting.png

Interact with matplotlib

matplotlib_interact.png

Spirograph

interactive_animate_spirograph.png

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