Differences between revisions 9 and 23 (spanning 14 versions)
 ⇤ ← Revision 9 as of 2009-02-15 08:40:55 → Size: 9365 Editor: MarshallHampton Comment: ← Revision 23 as of 2020-06-02 15:12:19 → ⇥ Size: 14286 Editor: kcrisman Comment: Deletions are marked like this. Additions are marked like this. Line 9: Line 9: {{{ {{{#!sagecell Line 11: Line 11: from math import cos,sin Line 13: Line 12: from math import cos, sin Line 30: Line 30: def curves_of_pursuit(n = slider([2..20],default = 6, label="# of points"),steps = slider([2^i for i in range(1,10)],default = 10, label="# of steps"), stepsize = slider(srange(.01,1,.01),default = .2, label="stepsize"), colorize = checkbox(default = False)):    outpaths = pursuit(n,1,0,stepsize, steps = steps) 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) Line 34: Line 34: if colorize: polys = Graphics()    if colorize=='Line color': Line 36: Line 37: elif colorize == 'BW':        colors = [(0,0,0) for j in range(len(outpaths[0]))] Line 37: Line 40: 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] Line 40: Line 46: show(sum(lpaths)+nested, axes = False, figsize = [5,5], xmin = -1, xmax = 1, ymin = -1, ymax =1) show(sum(lpaths)+nested+polys, axes = False, figsize = [5,5], xmin = -1, xmax = 1, ymin = -1, ymax =1) Line 45: Line 51: {{{ {{{#!sagecell Line 101: Line 107: print "Bug selecting plot?" print("Bug selecting plot?") Line 105: Line 111: html('

%s

'%example) pretty_print(html('

%s

'%example)) Line 107: Line 113: html('

%s

'%(url,url))    show(P, viewer='tachyon' if tachyon else 'jmol', frame=frame) pretty_print(html('

%s

'%(url,url)))    show(P, viewer='tachyon' if tachyon else 'threejs', frame=frame) Line 115: Line 121: {{{ {{{#!sagecell Line 128: Line 134: {{{ {{{#!sagecell Line 139: Line 145: viewer='tachyon' if tachyon else 'jmol', viewer='tachyon' if tachyon else 'threejs', Line 151: Line 157: {{{ {{{#!sagecell Line 157: Line 163: @interactdef _(band_number = selector(range(1,5)), current_color = Color('red')): @interactdef _(band_number = selector(range(1,5)), current_color = Color('red'), auto_update=False): Line 168: Line 175: {{{@interactdef color_experimenter(expression=input_box('', 'Expression', str), color=Color('red')): {{{#!sagecell@interactdef color_experimenter(expression=input_box('x^2', 'Expression', str), color=Color('red')): Line 175: Line 182: print "There's a problem with your expression." print("There's a problem with your expression.")    else:        print("Be sure to enter a plottable expression") Line 179: Line 188: == Interactive 2d Plotting == == Interactive 2D Plotting == Line 181: Line 190: {{{ {{{#!sagecell Line 183: Line 192: print '

Error: %s

' % msg pretty_print(html('

Error: %s

' % msg)) Line 191: Line 200: print error_msg('This is not an expression.') print(error_msg('This is not an expression.')) Line 196: Line 205: 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 '')) Line 202: Line 211: print "var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression)) print("var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression))) Line 205: Line 214: print error_msg('This expression has more than one variable.') print(error_msg('This expression has more than one variable.')) Line 208: Line 217: print error_msg("This expression contains an unknown function.") print(error_msg("This expression contains an unknown function.")) Line 212: Line 221: == 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 statsimport numpy as npimport matplotlib.pyplot as plt@interactdef 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] ##---------------------------##introductionhtml('

Spirograph

')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@interactdef 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

## Curves of Pursuit

by Marshall Hampton.

## Somewhat Silly Egg Painter

by Marshall Hampton (refereed by William Stein)

## Plot Coloring

by Timothy Clemans

## Interactive 2D Plotting

by Timothy Clemans

## Spirograph

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