3d Graph Points Curves

## Description

This interact lets the user plot a function of 2 variables on a specified xyz range, along with parametric curves.

## Sage Cell

#### Code

x,y, t, u, v =var('x y t u v')
INI_func='x^2-2*x+y^2-2*y'
INI_box='-1,3.2,-1,3.2'
INI_points='(1,1,\'green\'),(3/2,3/2),(0,1),(1,0),(0,0,\'black\'),(3,0,\'black\'),(0,3,\'black\')'
INI_curves='(t,0,0,3,\'red\'),(0,t,0,3,\'green\'),(t,3-t,0,3)'
@interact
def _(func=input_box(INI_func,label="f(x,y)=",type=str),\
bounds=input_box(INI_box,label="xmin,xmax,ymin,ymax",type=str),\
st_points=input_box(INI_points,\
label="points <br><small><small>(comma separated pairs, optionally with color)</small></small>", type=str),\
bnd_curves=input_box(INI_curves,label="curves on boundary<br> <small><small><i>(x(t),y(t),tmin,tmax,'opt_color')</i></small></small>", type=str),\
show_planes=("Show zero planes", False),  show_axes=("Show axes", True),
show_table=("Show table", True)):
f=sage_eval('lambda x,y: ' + func)
pretty_print(html(r'Function $f(x,y)=%s$ '%latex(f(x,y))))
xmin,xmax,ymin,ymax=sage_eval('('+bounds+')')
A=plot3d(f(x,y),(x,xmin,xmax),(y,ymin,ymax),opacity=0.5)
if not(bool(st_points=='')):
st_p=sage_eval('('+st_points+',)')
html(r'<table border=1>')
for current in range(len(st_p)):
point_color='red'
if bool(len(st_p[current])==3):
point_color=st_p[current][2]
x0=st_p[current][0]
y0=st_p[current][1]
z0=f(x0,y0)
if show_table:
pretty_print(html(r'<tr><td>$\quad f(%s,%s)\quad$</td><td>$\quad %s$</td>\
</tr>'%(latex(x0),latex(y0),z0.n())))
A=A+point3d((x0,y0,z0),size=9,rgbcolor=point_color)
html(r'</table>')
if not(bool(bnd_curves=='')):
bnd_cc=sage_eval('('+bnd_curves+',)',locals={'t':t})
for current in range(len(bnd_cc)):
bnd_c=bnd_cc[current]+('black',)
A=A+parametric_plot3d((bnd_c[0],bnd_c[1],f(bnd_c[0],bnd_c[1])),\
(t,bnd_c[2],bnd_c[3]),thickness=3,rgbcolor=bnd_c[4])
if show_planes:
A=A+plot3d(0,(x,xmin,xmax),(y,ymin,ymax),opacity=0.3,rgbcolor='gray')
zmax=A.bounding_box()[1][2]
zmin=A.bounding_box()[0][2]
A=A+parametric_plot3d((u,0,v),(u,xmin,xmax),(v,zmin,zmax),opacity=0.3,rgbcolor='gray')
A=A+parametric_plot3d((0,u,v),(u,ymin,ymax),(v,zmin,zmax),opacity=0.3,rgbcolor='gray')
if show_axes:
zmax=A.bounding_box()[1][2]
zmin=A.bounding_box()[0][2]
show(A)


none

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## Attribute

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Date: 29 Jul 2020 22:15

Submitted by: Zane Corbiere