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Sage Interactions - Graphics

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Contents

Sage Interactions - Graphics

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

-  ⇤ ← Revision 7 as of 2009-02-04 04:53:04 → 
  Size: 7674
  Editor: TimothyClemans
  Comment:
+   ← Revision 24 as of 2020-06-02 15:13:32 → ⇥
  Size: 14300
  Editor: kcrisman
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 7:
+== 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}}
-Line 8:
+Line 51:
-{{{
+{{{#!sagecell
-Line 64:
+Line 107:
-        print "Bug selecting plot?"
+        print("Bug selecting plot?")
-Line 68:
+Line 111:
-    html('<h2>%s</h2>'%example)
+    pretty_print(html('<h2>%s</h2>'%example))
-Line 70:
+Line 113:
-        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)
-Line 78:
+Line 121:
-{{{
+{{{#!sagecell
-Line 91:
+Line 134:
-{{{
+{{{#!sagecell
-Line 102:
+Line 145:
-         viewer='tachyon' if tachyon else 'jmol',
+         viewer='tachyon' if tachyon else 'threejs',
-Line 114:
+Line 157:
-{{{
+{{{#!sagecell
-Line 120:
+Line 163:
-@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):
-Line 131:
+Line 175:
-{{{
@interact
def color_experimenter(expression=input_box('', 'Expression', str), color=Color('red')):
+{{{#!sagecell
@interact
def color_experimenter(expression=input_box('x^2', 'Expression', str), color=Color('red')):
-Line 138:
+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 142:
+Line 188:
-== Interactive 2d Plotting ==
+== Interactive 2D Plotting ==
-Line 144:
+Line 190:
-{{{
+{{{#!sagecell
-Line 146:
+Line 192:
-    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))
-Line 154:
+Line 200:
-            print error_msg('This is not an expression.')
+            print(error_msg('This is not an expression.'))
-Line 159:
+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 165:
+Line 211:
-                    print "var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression))
+                    print("var('%s')\nplot(%s)" % (expression.variables()[0], repr(expression)))
-Line 168:
+Line 214:
-            print error_msg('This expression has more than one variable.')
+            print(error_msg('This expression has more than one variable.'))
-Line 171:
+Line 217:
-            print error_msg("This expression contains an unknown function.")
+            print(error_msg("This expression contains an unknown function."))
-Line 175:
+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 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

pretty_print(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}}

Diff for "interact/graphics"

Sage Interactions - Graphics

Curves of Pursuit

Catalog of 3D Parametric Plots

Interactive rotatable raytracing with Tachyon3d

Interactive 3d plotting

Somewhat Silly Egg Painter

Plot Coloring

Interactive 2D Plotting

Interact with matplotlib

Spirograph