CoCalc Public FilesFunction Graphs and Contour Maps.sagews
Author: Thomas Krainer
Views : 30
Description: Worksheet to illustrate graphs and contour maps for functions of two variables
# Function Graphs and Contour Maps
# Author: Thomas Krainer (Penn State Altoona)
# Prior Version: 09/20/2011
# Version: 02/11/2016
#

x,y=var('x,y')

html('<h1>Graphs and contour maps for functions of 2 variables</h1>')
html('<p>With this worksheet graphs and contour maps for functions $z = f(x,y)$ can be explored.</p>')

@interact
def GraphsContourMaps(function=input_box(default=sin(x)*cos(y),type=SR,label='$f(x,y)=$'),\
xinterval=input_box(default='[0,4*pi]',type=str,label='$[x_{\\min},x_{\\max}]=$'),\
yinterval=input_box(default='[0,4*pi]',type=str,label='$[y_{\\min},y_{\\max}]=$'),\
numbercontours=slider(1,30,1,default=15,label='Number of level curves:'),\
levelslider=slider(0,100,1,default=40,display_value=False,label='Level:'),\
scalingconstrained=('Do not scale plots:',False)):

# Process input

f(x,y)=function
[xmin,xmax]=sage_eval(xinterval)
[ymin,ymax]=sage_eval(yinterval)

graph=plot3d(f(x,y),(x,xmin,xmax),(y,ymin,ymax),color=(135/255,180/255,250/255),plot_points=350)
minlevel=graph.bounding_box()[0][2]
maxlevel=graph.bounding_box()[1][2]
level=minlevel+(levelslider/100)*(maxlevel-minlevel)
plane=plot3d(level,(x,xmin,xmax),(y,ymin,ymax),color='green',opacity=0.8)
contourmap=contour_plot(f(x,y),(x,xmin,xmax),(y,ymin,ymax),colorbar=True,\
fill=False,cmap='hsv',contours=numbercontours)
levelcurve=implicit_plot(f(x,y)-level,(x,xmin,xmax),(y,ymin,ymax),linewidth=3,color='black')

html('Function: $f(x,y) = %s \\; \\textrm{for} \\; (x,y) \\in [%s,%s]\\times[%s,%s]$ </br>'%(latex(f(x,y)),latex(xmin),latex(xmax),latex(ymin),latex(ymax)))
html('Level Curve: $f(x,y) = %s$ </br>'%(latex(level)))

if (scalingconstrained==True):
show(graph+plane,aspect_ratio=1)
show(contourmap+levelcurve,aspect_ratio=1)
else:
show(graph+plane)
show(contourmap+levelcurve)


# Graphs and contour maps for functions of 2 variables

With this worksheet graphs and contour maps for functions $z = f(x,y)$ can be explored.