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nextstep

Joined: 06 Jan 2007
Posts: 538

Posted: Fri Sep 07, 2007 5:03 am    Post subject: "Mirrored" Isosurfaces

Hi all,
You can use this formula to obtain a mirrored view of an isosurface F() :
 Quote: G(x,y,z) = F(x,y,z)* F(x - 2*P(x,y,z)*a/R, y - 2*P(x,y,z)*b/R, z - 2*P(x,y,z)*c/R) Where : P(x,y,z) = ax+by+cz+d (Equation of the Plan) R = (a^2 + b^2 + c^2)

Maybe for future use in minimal surface?
Enjoy
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Abderrahman

Last edited by nextstep on Sun Oct 26, 2014 7:13 am; edited 1 time in total
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

 Posted: Fri Sep 14, 2007 11:44 pm    Post subject: can you publish an example? e.g. hyperbolic paraboloid x^2-y^2-z
nextstep

Joined: 06 Jan 2007
Posts: 538

Posted: Sat Sep 15, 2007 6:05 am    Post subject:

Hi all,
Here it is . I added the plan to the equation for better understanding. We can probably make interesting shapes by using this formulas especially for minimal surfaces...
 Quote: /* Hyperbol and it's mirrored image to the plan defined by : y = 4 (or y-4 =0) */ Name: Mirror_1 F(): (x^2-y^2-z) *(x^2-(y-2*(y-4))^2-z) : y-4: [x]: -4 , 4 [y]: -4 , 12 [z]: -4 , 4 ;

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Cheers,
Abderrahman
nextstep

Joined: 06 Jan 2007
Posts: 538

Posted: Sun Oct 26, 2014 7:16 am    Post subject:

Hi all,
For a Torus ((sqrt(x*x+y*y)-3)^2 + z*z -1) and a plan (P=y-z+4), this is what you get :
 Code: {     "Iso3D": {         "Name": [             "MirroredTorus"         ],         "Description": [             "Mirrored Torus"         ],         "Component": [             "TorusIso",             "Plan"         ],         "Const": [             "a=0",             "b=1",             "c=-1",             "d=4",             "R=(0^2 + (1)^2 + (-1)^2)"         ],         "Funct": [             "Torus = ((sqrt(x*x+y*y)-3)^2 + z*z -1)",             "P = (a*x+b*y+c*z+d)"         ],         "Fxyz": [             "Torus(x,y,z+1,t)*Torus(x-2*P(x,y,z,t)*a/R,y-2*P(x,y,z,t)*b/R,z+1-2*P(x,y,z,t)*c/R,t)",             "y-z+4"         ],         "Xmax": [             "4",             "4"         ],         "Xmin": [             "-4",             "-4"         ],         "Ymax": [             "8",             "8"         ],         "Ymin": [             "-6",             "-6"         ],         "Zmax": [             "9",             "9"         ],         "Zmin": [             "-4",             "-4"         ]     } }

MirroredTorus by taha_ab, on Flickr
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Cheers,
Abderrahman
nextstep

Joined: 06 Jan 2007
Posts: 538

Posted: Sun Oct 26, 2014 5:19 pm    Post subject:

Hi all,
This is a better script for the mirrored Torus, however, it should not work with MathMod previous versions... Hope to publish it as soon, stay tuned
 Quote: { "Iso3D": { "Component": [ "TorusIso", "Plan" ], "Const": [ "a=0", "b=1", "c=-1", "d=4", "R=(a^2 + b^2 + c^2)" ], "Description": [ "Mirrored Torus" ], "Funct": [ "Torus = ((sqrt(x*x+y*y)-3)^2 + z*z -1)", "P = (a*x+b*y+c*z+d)" ], "Fxyz": [ "Torus(x,y,z+1,t)*Torus(x-2*P(x,y,z,t)*a/R,y-2*P(x,y,z,t)*b/R,z+1-2*P(x,y,z,t)*c/R,t)", "a*x + b*y +c*z + d" ], "Name": [ "MirroredTorus" ], "Xmax": [ "4", "4" ], "Xmin": [ "-4", "-4" ], "Ymax": [ "4", "4" ], "Ymin": [ "-6", "-6" ], "Zmax": [ "8", "8" ], "Zmin": [ "-2", "-2" ] } }

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Abderrahman
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Thu Oct 30, 2014 11:24 am    Post subject: hello next step thanks
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