Dear Vincent,
Sorry I did not paste it...Here it goes. You'll also find it in attachment.
It is to be noted that I just ran the code again after a lo,g while and it
now exits upon a "print" instruction instruction supposedly in line 33.
My guess is that the code is more and more compatible with the SageMath
celle interpreter version... I'll dig on that. If you have any idea they
are welcome.
KInd regards,
B
<html>
<head>
<meta name="description" content="Maria Gaetana Agnesi's Versiera (aka
Witch) meets arcs.">
<meta name="description" content="A mathematical meditation on breast
geometry.">
<meta name="version" content="9.05">
<meta name="keywords" content="
HTML,JavaScript,Python,SageMathCell,Geometry,Breast">
<meta name="author" content="Floozman">
<meta name="credit" content="circle-cirlcle intersection by Xaedes (Github)
">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width">
<title> VmA </title>
<script src="https://sagecell.sagemath.org/static/embedded_sagecell.js";>
</script>
<script>
// Make the div with id 'mycell' a Sage cell
sagecell.makeSagecell({inputLocation: '#mycell',
template: sagecell.templates.minimal,
evalButtonText: 'Let there be breasts !'});
</script>
</head>
<body>
<h2> Versiera meets arcs </h2>
Click the button below to make Maria Gaetana Agnesi's Versiera and arcs
meet in beauty
<div id="mycell"><script type="text/x-sage">
from __future__ import division
import numpy as np
import scipy.optimize
"""
circle-circle intersection
credit: Xaedes (Github)
"""
#!/usr/bin/env python2
#-*- coding: utf-8 -*-
#from __future__ import division
#import numpy as np
from math import cos, sin, pi, sqrt, atan2
d2r = pi/180
class Geometry(object):
def circle_intersection(self, circle1, circle2):
'''
@summary: calculates intersection points of two circles
@param circle1: tuple(x,y,radius)
@param circle2: tuple(x,y,radius)
@result: tuple of intersection points (which are (x,y) tuple)
'''
# return self.circle_intersection_sympy(circle1,circle2)
x1,y1,r1 = circle1
x2,y2,r2 = circle2
# http://stackoverflow.com/a/3349134/798588
dx,dy = x2-x1,y2-y1
d = sqrt(dx*dx+dy*dy)
if d > r1+r2:
print "#1"
return None # no solutions, the circles are separate
if d < abs(r1-r2):
print "#2"
return None # no solutions because one circle is contained within the other
if d == 0 and r1 == r2:
print "#3"
return None # circles are coincident and there are an infinite number of
solutions
a = (r1*r1-r2*r2+d*d)/(2*d)
h = sqrt(r1*r1-a*a)
xm = x1 + a*dx/d
ym = y1 + a*dy/d
xs1 = xm + h*dy/d
xs2 = xm - h*dy/d
ys1 = ym - h*dx/d
ys2 = ym + h*dx/d
return (xs1,ys1),(xs2,ys2)
def circle_intersection_sympy(self, circle1, circle2):
from sympy.geometry import Circle, Point
x1,y1,r1 = circle1
x2,y2,r2 = circle2
c1=Circle(Point(x1,y1),r1)
c2=Circle(Point(x2,y2),r2)
intersection = c1.intersection(c2)
if len(intersection) == 1:
intersection.append(intersection[0])
p1 = intersection[0]
p2 = intersection[1]
xs1,ys1 = p1.x,p1.y
xs2,ys2 = p2.x,p2.y
return (xs1,ys1),(xs2,ys2)
"""
Interaction in the sagemath cell
"""
@interact
def VmA(nipple_x=(1,1.7)):
# recommended values for r = 1 : x=(1, 1.5+)
var ('u,v,w,x,y,z')
var ('breastarc_x,nipple_x,nipple_y')
#presentation parameters
showmaths = True #print maths
showinvisible = True #Above and beyond breast, print curves in dotted line
thk = 2 # thickness of the visible
wi = 5 # width of the frame
#geometry parameters
r = 1 # Versiera radius
d=2*r # Versiera diameter
ptinf= (2*r)/sqrt(3) # Versiera positive point of inflexion
breastarc_r=0.9 # breast circle radius
areo_ratio=4.4 # ratio breast circle / areola circle
# Versiera curve
versiera = 8*(r^3)/((x^2) + 4*(r^2))
# Versiera curve (parametric)
t= var ('t')
xvp = d*t
yvp = d/(t^2+1)
#W=parametric_plot((xvp,yvp-r),(t,0,1))
# Find the y coordinate of the target intersection between versiera and
breast arc when x = nipple_x
nipple_y = 8*(r^3)/((nipple_x^2) + 4*(r^2))
# Plot versiera from offset to nipple_x (heigth is shifted down 0.5 by
subtracting the radius).
offset=r-breastarc_r
P=plot(versiera-r,offset+0.12,nipple_x,fill=0,rgbcolor="black",fillcolor='white',thickness=thk)
S=P
# Find the x coordinate of the center of a circle with radius breastarc_r
to which belongs point (nipple_x, nipple_y)
eqdelta = (nipple_y-r)^2 + z^2 == breastarc_r^2
soldelta = solve([eqdelta],z,solution_dict=True)
breastarc_x=nipple_x-soldelta[1][z]
# Areola as a circle of center (areo_x,areo_y) and radius areo_r
areo_r = nipple_x/ areo_ratio
areo_x = nipple_x
areo_y = nipple_y-r
# Store the circles
tuplebreast= breastarc_x, 0, breastarc_r
tupleareo = areo_x, areo_y, areo_r
# Draw the breast arc
var('m,n')
arcbreast = (m-breastarc_x)^2 + (n-0) ^2 == breastarc_r^2
U=implicit_plot(arcbreast, (m, offset,r*2),
(n,-r,nipple_y-r),color='black',linewidth=thk)
S=S+U
# Find areola low intersection point with circle
geom = Geometry()
getint = geom.circle_intersection(circle1=tuplebreast, circle2=tupleareo)
areoint_x = getint[0][0]
# Find areola intersection point with Versiera
function ('xt') (t)
function ('yt') (t)
function ('f') (t)
function ('df') (t)
xt(t) = 2*t
yt(t) = d/(t^2+1)-r
f(t)= (xt(x=t)-areo_x)^2 + (yt(x=t)-areo_y)^2 - areo_r^2
#st = solve([f(t) == 0],t)
df(t) = f(x=t).derivative()
# Use Newton-Raphson approximation
var ('xstart')
xstart=nipple_x/3.3
iter = 100
son = scipy.optimize.newton(f,xstart,df, maxiter= iter)
dyvp=(yt(son))
# Draw the areola circle between intersection points
var ('o,p')
arcareo = (o-areo_x)^2 + (p-areo_y)^2 == areo_r^2
V=implicit_plot(arcareo, (o,0,areoint_x),
(p,-r,dyvp),color='black',linewidth=thk)
S=S+V
# Draw the vertical line perpendicular to x axis at Versiera's positive
point of inflexion
L=line( [ (ptinf , -r), (ptinf, r) ], color="purple", thickness=1,
linestyle="-.")
S=S+L
# Plot the whole shebang
if showinvisible :
IPV=plot(versiera-r,nipple_x,wi,fill=0,rgbcolor='black',fillcolor='white',linestyle='dotted')
S=S+IPV
IPV2 = plot(versiera-r,-wi,
offset+0.12,fill=0,rgbcolor='black',fillcolor='white',linestyle='dotted')
S=S+IPV2
IPC = implicit_plot(arcbreast, (m, -r,r*2), (n,-r,r),color='black',
linestyle='dotted')
S=S+IPC
IPA = implicit_plot(arcareo, (o,0,wi), (p,-0.5,1),color='black',
linestyle='dotted')
S=S+IPA
S.show (axes=true,aspect_ratio=1)
if showmaths :
show ('nipple coordinates : x = ', nipple_x, ' y = ', nipple_y-r)
show ('areola / breast circle intersection coordinates : x = ', areoint_x,
' y = ', nipple_y-r)
show ('areola / Versiera intersection coordinates : x = ', xt(son), ' y =
', dyvp)
show ('numerical resolution : ')
show (' f(t) : ', f(t))
show (' dérivée df(t) : ', df)
show (' t approximation for f(t) = 0 (Newton-Raphson method) : ', son)
#show ('df(t) = 0 : ', st)
return
</script>
</div>
</body>
</html>
On Sun, Feb 16, 2020 at 8:51 PM Vincent Delecroix <20100.delecr...@gmail.com>
wrote:
> Dear Bertrand,
>
> Where is "the code below"?
>
> Vincent
>
> Le 16/02/2020 à 15:44, Bertrand Cayzac a écrit :
> > Hello,
> >
> > The code below worked happlily each time I launched it in SageMathCell
> > until recently. It now exits with the error below in a call to
> > scipy.optimize.newton while I didn't make any change;
> >
> > I gathered that the casting rules have changed but it seems that ufunc
> doesn't take a "casting" argument in version 1.16 and I can't seem to fin a
> way to override
> >
> > the safe rule. I don't know how to import or install a different version
> in a cell.
> >
> > Any idea?
> >
> >
> >
> > Last lines of the trace :
> >
> >
> /home/sc_serv/sage/local/lib/python2.7/site-packages/numpy/core/numeric.pyc
> in isclose(a, b, rtol, atol, equal_nan) 2519 y = array(y, dtype=dt,
> copy=False, subok=True) 2520 -> 2521 xfin = isfinite(x) 2522
> yfin = isfinite(y) 2523 if all(xfin) and all(yfin):
> > TypeError: ufunc 'isfinite' not supported for the input types, and the
> inputs could not be safely coerced to any supported types according to the
> casting rule ''safe''
> >
> >
> >
> > The curent versions in SageMathCell are the following (I don't know what
> > they used to be when the code was working)
> >
> > Python : 2.7.15 (default, Oct 6 2019, 03:20:16) [GCC 7.4.0]
> > Numpy : 1.16.1
> > Scipy : 1.2.0
> >
> >
> > I gathered that the casting rules have changed but it seems that ufunc
> doesn't take a "casting" argument in version 1.16 and I can't seem to fin a
> way to override
> >
> > the safe rule. I don't know how to import or install a different version
> in a cell.
> >
> > Any idea?
> >
> >
> > Thanks and regards,
> >
> > Bertrand Cayzac bnhmcay...@gmail.com
> >
>
> --
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>
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<html>
<head>
<meta name="description" content="Maria Gaetana Agnesi's Versiera (aka
Witch) meets arcs.">
<meta name="description" content="A mathematical meditation on breast
geometry.">
<meta name="version" content="9.05">
<meta name="keywords"
content="HTML,JavaScript,Python,SageMathCell,Geometry,Breast">
<meta name="author" content="Floozman">
<meta name="credit" content="circle-cirlcle intersection by Xaedes
(Github)">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width">
<title> VmA </title>
<script
src="https://sagecell.sagemath.org/static/embedded_sagecell.js";></script>
<script>
// Make the div with id 'mycell' a Sage cell
sagecell.makeSagecell({inputLocation: '#mycell',
template: sagecell.templates.minimal,
evalButtonText: 'Let there be breasts !'});
</script>
</head>
<body>
<h2> Versiera meets arcs </h2>
Click the button below to make Maria Gaetana Agnesi's Versiera and arcs meet
in beauty
<div id="mycell"><script type="text/x-sage">
from __future__ import division
import numpy as np
import scipy.optimize
"""
circle-circle intersection
credit: Xaedes (Github)
"""
#!/usr/bin/env python2
#-*- coding: utf-8 -*-
#from __future__ import division
#import numpy as np
from math import cos, sin, pi, sqrt, atan2
d2r = pi/180
class Geometry(object):
def circle_intersection(self, circle1, circle2):
'''
@summary: calculates intersection points of two circles
@param circle1: tuple(x,y,radius)
@param circle2: tuple(x,y,radius)
@result: tuple of intersection points (which are (x,y) tuple)
'''
# return self.circle_intersection_sympy(circle1,circle2)
x1,y1,r1 = circle1
x2,y2,r2 = circle2
# http://stackoverflow.com/a/3349134/798588
dx,dy = x2-x1,y2-y1
d = sqrt(dx*dx+dy*dy)
if d > r1+r2:
print "#1"
return None # no solutions, the circles are separate
if d < abs(r1-r2):
print "#2"
return None # no solutions because one circle is contained within
the other
if d == 0 and r1 == r2:
print "#3"
return None # circles are coincident and there are an infinite
number of solutions
a = (r1*r1-r2*r2+d*d)/(2*d)
h = sqrt(r1*r1-a*a)
xm = x1 + a*dx/d
ym = y1 + a*dy/d
xs1 = xm + h*dy/d
xs2 = xm - h*dy/d
ys1 = ym - h*dx/d
ys2 = ym + h*dx/d
return (xs1,ys1),(xs2,ys2)
def circle_intersection_sympy(self, circle1, circle2):
from sympy.geometry import Circle, Point
x1,y1,r1 = circle1
x2,y2,r2 = circle2
c1=Circle(Point(x1,y1),r1)
c2=Circle(Point(x2,y2),r2)
intersection = c1.intersection(c2)
if len(intersection) == 1:
intersection.append(intersection[0])
p1 = intersection[0]
p2 = intersection[1]
xs1,ys1 = p1.x,p1.y
xs2,ys2 = p2.x,p2.y
return (xs1,ys1),(xs2,ys2)
"""
Interaction in the sagemath cell
"""
@interact
def VmA(nipple_x=(1,1.7)):
# recommended values for r = 1 : x=(1, 1.5+)
var ('u,v,w,x,y,z')
var ('breastarc_x,nipple_x,nipple_y')
#presentation parameters
showmaths = True #print maths
showinvisible = True #Above and beyond breast, print curves in dotted
line
thk = 2 # thickness of the visible
wi = 5 # width of the frame
#geometry parameters
r = 1 # Versiera radius
d=2*r # Versiera diameter
ptinf= (2*r)/sqrt(3) # Versiera positive point of inflexion
breastarc_r=0.9 # breast circle radius
areo_ratio=4.4 # ratio breast circle / areola circle
# Versiera curve
versiera = 8*(r^3)/((x^2) + 4*(r^2))
# Versiera curve (parametric)
t= var ('t')
xvp = d*t
yvp = d/(t^2+1)
#W=parametric_plot((xvp,yvp-r),(t,0,1))
# Find the y coordinate of the target intersection between versiera and
breast arc when x = nipple_x
nipple_y = 8*(r^3)/((nipple_x^2) + 4*(r^2))
# Plot versiera from offset to nipple_x (heigth is shifted down 0.5 by
subtracting the radius).
offset=r-breastarc_r
P=plot(versiera-r,offset+0.12,nipple_x,fill=0,rgbcolor="black",fillcolor='white',thickness=thk)
S=P
# Find the x coordinate of the center of a circle with radius breastarc_r
to which belongs point (nipple_x, nipple_y)
eqdelta = (nipple_y-r)^2 + z^2 == breastarc_r^2
soldelta = solve([eqdelta],z,solution_dict=True)
breastarc_x=nipple_x-soldelta[1][z]
# Areola as a circle of center (areo_x,areo_y) and radius areo_r
areo_r = nipple_x/ areo_ratio
areo_x = nipple_x
areo_y = nipple_y-r
# Store the circles
tuplebreast= breastarc_x, 0, breastarc_r
tupleareo = areo_x, areo_y, areo_r
# Draw the breast arc
var('m,n')
arcbreast = (m-breastarc_x)^2 + (n-0) ^2 == breastarc_r^2
U=implicit_plot(arcbreast, (m, offset,r*2),
(n,-r,nipple_y-r),color='black',linewidth=thk)
S=S+U
# Find areola low intersection point with circle
geom = Geometry()
getint = geom.circle_intersection(circle1=tuplebreast, circle2=tupleareo)
areoint_x = getint[0][0]
# Find areola intersection point with Versiera
function ('xt') (t)
function ('yt') (t)
function ('f') (t)
function ('df') (t)
xt(t) = 2*t
yt(t) = d/(t^2+1)-r
f(t)= (xt(x=t)-areo_x)^2 + (yt(x=t)-areo_y)^2 - areo_r^2
#st = solve([f(t) == 0],t)
df(t) = f(x=t).derivative()
# Use Newton-Raphson approximation
var ('xstart')
xstart=nipple_x/3.3
iter = 100
son = scipy.optimize.newton(f,xstart,df, maxiter= iter)
dyvp=(yt(son))
# Draw the areola circle between intersection points
var ('o,p')
arcareo = (o-areo_x)^2 + (p-areo_y)^2 == areo_r^2
V=implicit_plot(arcareo, (o,0,areoint_x),
(p,-r,dyvp),color='black',linewidth=thk)
S=S+V
# Draw the vertical line perpendicular to x axis at Versiera's positive
point of inflexion
L=line( [ (ptinf , -r), (ptinf, r) ], color="purple", thickness=1,
linestyle="-.")
S=S+L
# Plot the whole shebang
if showinvisible :
IPV=plot(versiera-r,nipple_x,wi,fill=0,rgbcolor='black',fillcolor='white',linestyle='dotted')
S=S+IPV
IPV2 = plot(versiera-r,-wi,
offset+0.12,fill=0,rgbcolor='black',fillcolor='white',linestyle='dotted')
S=S+IPV2
IPC = implicit_plot(arcbreast, (m, -r,r*2), (n,-r,r),color='black',
linestyle='dotted')
S=S+IPC
IPA = implicit_plot(arcareo, (o,0,wi), (p,-0.5,1),color='black',
linestyle='dotted')
S=S+IPA
S.show (axes=true,aspect_ratio=1)
if showmaths :
show ('nipple coordinates : x = ', nipple_x, ' y = ', nipple_y-r)
show ('areola / breast circle intersection coordinates : x = ',
areoint_x, ' y = ', nipple_y-r)
show ('areola / Versiera intersection coordinates : x = ', xt(son), '
y = ', dyvp)
show ('numerical resolution : ')
show (' f(t) : ', f(t))
show (' dérivée df(t) : ', df)
show (' t approximation for f(t) = 0 (Newton-Raphson method) :
', son)
#show ('df(t) = 0 : ', st)
return
</script>
</div>
</body>
</html>
