Differences between revisions 11 and 17 (spanning 6 versions)
 ⇤ ← Revision 11 as of 2009-03-21 19:43:41 → Size: 9947 Editor: MarshallHampton Comment: ← Revision 17 as of 2012-04-07 04:44:22 → ⇥ Size: 14162 Editor: jason Comment: Deletions are marked like this. Additions are marked like this. Line 9: Line 9: {{{ {{{#!sagecell#!sagecell Line 46: Line 46: (sum(lpaths)+nested+polys).save('/Users/mh/Desktop/Pursuit1.pdf',axes = False, figsize = [5,5], xmin = -1, xmax = 1, ymin = -1, ymax =1) Line 52: Line 51: {{{ {{{#!sagecell Line 122: Line 121: {{{ {{{#!sagecell Line 135: Line 134: {{{ {{{#!sagecell Line 158: Line 157: {{{ {{{#!sagecell Line 164: Line 163: }}}{{{#!sagecell Line 175: Line 176: {{{ {{{#!sagecell Line 186: Line 187: == Interactive 2d Plotting == == Interactive 2D Plotting == Line 188: Line 189: {{{ {{{#!sagecell Line 219: Line 220: == 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. {{{#!sagecell#!sagecell npi = RDF(pi) from math import cos,sin def rot(t):

def pursuit(n,x0,y0,lamb,steps = 100, threshold = .01):

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)

}}}

## 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)