Wow, very impressive (https://sage.math.washington.edu:8909/home/pub/4/
cells/0/sage0.png?1)! You should write some code for making more cool
3d graphics with Sage/Tachyon.
On Jan 11, 11:52 am, photonn <[EMAIL PROTECTED]> wrote:
> William,
>
> I remember when first tinkering with Sage some months ago, I stumbled
> across some example code you did. It was an elliptic curve (37a)
> rendered in Tachyon. That image stuck in my mind. It was really a
> nice picture. It really was what motivated me to dig further and
> start running a sage server.
>
> Well, I started playing with that image today ... just for some
> fun ... check out the result.
>
> (sorry for the length)
>
> t = Tachyon(xres=1000, yres=800, camera_center=(2,7,4),
> look_at=(2,0,0), raydepth=4)
> t.light((8,3,8), 1, (1,1,1))
>
> t.texture('black', ambient=0.6, diffuse=0.3, specular=0.1,
> opacity=1.0, color=(0,0,0))
> t.texture('red', color=(1,0,0))
> t.texture('grey', color=(.9,.9,.9))
> t.plane((0,0,0),(0,0,1),'grey')
> t.cylinder((0,0,0),(1,0,0),.01,'black')
> t.cylinder((0,0,0),(0,1,0),.01,'black')
> E = EllipticCurve('37a')
> P = E([0,0])
> Q = P
> n = 100
> for i in range(n):
> Q = Q + P
> c = i/n + .1
> t.texture('r%s'%i,color=(float(i/n),0,0))
> t.sphere((Q[0], -Q[1], .04), .04, 'r%s'%i)
>
> tx = 2 # translate the letters in the x direction
> ty = 1 # translate the letters in the y direction
> sc = 0.01 # scale factor, adjust this to make the letters larger or
> smaller
> rad = 5*sc # radius of cylinders that make the letters of the word
> sage
> hgt = 2*rad # height of letters off the plane, 1 means bottom of
> cylinder touching plane
>
> t.sphere((sc*85+tx,sc*9+ty,hgt),rad,'black') # this group makes the
> letter S in sage
> t.sphere((sc*32+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*32+tx,sc*49+ty,hgt),rad,'black')
> t.sphere((sc*85+tx,sc*49+ty,hgt),rad,'black')
> t.sphere((sc*8+tx,sc*83+ty,hgt),rad,'black')
> t.sphere((sc*85+tx,sc*83+ty,hgt),rad,'black')
> t.fcylinder((sc*85+tx,sc*9+ty,hgt),(sc*32+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*32+tx,sc*9+ty,hgt),
> (sc*32+tx,sc*49+ty,hgt),rad,'black')
> t.fcylinder((sc*32+tx,sc*49+ty,hgt),
> (sc*85+tx,sc*49+ty,hgt),rad,'black')
> t.fcylinder((sc*85+tx,sc*49+ty,hgt),
> (sc*85+tx,sc*83+ty,hgt),rad,'black')
> t.fcylinder((sc*85+tx,sc*83+ty,hgt),
> (sc*8+tx,sc*83+ty,hgt),rad,'black')
>
> t.sphere((sc*236+tx,sc*83+ty,hgt),rad,'black') # this group makes the
> AG combination
> t.sphere((sc*198+tx,sc*83+ty,hgt),rad,'black')
> t.sphere((sc*153+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*107+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*107+tx,sc*83+ty,hgt),rad,'black')
> t.sphere((sc*160+tx,sc*83+ty,hgt),rad,'black')
> t.sphere((sc*203+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*252+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*252+tx,sc*118+ty,hgt),rad,'black')
> t.sphere((sc*182+tx,sc*118+ty,hgt),rad,'black')
> t.fcylinder((sc*236+tx,sc*83+ty,hgt),
> (sc*198+tx,sc*83+ty,hgt),rad,'black')
> t.fcylinder((sc*198+tx,sc*83+ty,hgt),
> (sc*153+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*153+tx,sc*9+ty,hgt),
> (sc*107+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*107+tx,sc*9+ty,hgt),
> (sc*107+tx,sc*83+ty,hgt),rad,'black')
> t.fcylinder((sc*107+tx,sc*83+ty,hgt),
> (sc*160+tx,sc*83+ty,hgt),rad,'black')
> t.fcylinder((sc*160+tx,sc*83+ty,hgt),
> (sc*203+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*203+tx,sc*9+ty,hgt),
> (sc*252+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*252+tx,sc*9+ty,hgt),
> (sc*252+tx,sc*118+ty,hgt),rad,'black')
> t.fcylinder((sc*252+tx,sc*118+ty,hgt),
> (sc*182+tx,sc*118+ty,hgt),rad,'black')
>
> t.sphere((sc*365+tx,sc*83+ty,hgt),rad,'black') # this group makes
> the E in sage
> t.sphere((sc*273+tx,sc*83+ty,hgt),rad,'black')
> t.sphere((sc*273+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*343+tx,sc*9+ty,hgt),rad,'black')
> t.sphere((sc*343+tx,sc*49+ty,hgt),rad,'black')
> t.sphere((sc*290+tx,sc*49+ty,hgt),rad,'black')
> t.fcylinder((sc*365+tx,sc*83+ty,hgt),
> (sc*273+tx,sc*83+ty,hgt),rad,'black')
> t.fcylinder((sc*273+tx,sc*83+ty,hgt),
> (sc*273+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*273+tx,sc*9+ty,hgt),
> (sc*343+tx,sc*9+ty,hgt),rad,'black')
> t.fcylinder((sc*343+tx,sc*9+ty,hgt),
> (sc*343+tx,sc*49+ty,hgt),rad,'black')
> t.fcylinder((sc*343+tx,sc*49+ty,hgt),
> (sc*290+tx,sc*49+ty,hgt),rad,'black')
>
> t.show() # long time, e.g., 10-20 seconds
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