3dImplicitSurfaceExtractorByThickening

Computes the zero level set of the given polynomial.

Usage: 3dImplicitSurfaceExtractorByThickening [options] input

Allowed options are :

-h [ --help ]                         display this message
-p [ --polynomial ] arg               the implicit polynomial whose 
                                      zero-level defines the shape of 
                                      interest.
-a [ --minAABB ] arg (=-10)           the min value of the AABB bounding box 
                                      (domain)
-A [ --maxAABB ] arg (=10)            the max value of the AABB bounding box 
                                      (domain)
-g [ --gridstep ] arg (=1)            the gridstep that defines the 
                                      digitization (often called h). 
-t [ --thickness ] arg (=0.01)        the thickening parameter for the 
                                      implicit surface.
-P [ --project ] arg (=Newton)        defines the projection: either No or 
                                      Newton.
-e [ --epsilon ] arg (=9.9999999999999995e-07)
                                      the maximum precision relative to the 
                                      implicit surface in the Newton 
                                      approximation of F=0.
-n [ --max_iter ] arg (=500)          the maximum number of iteration in the 
                                      Newton approximation of F=0.
-v [ --view ] arg (=Normal)           specifies if the surface is viewed as 
                                      is (Normal) or if places close to 
                                      singularities are highlighted 
                                      (Singular), or if unsure places should 
                                      not be displayed (Hide). 

Example:

3dImplicitSurfaceExtractorByThickening -p "x^2-y*z^2" -g 0.1 -a -2 -A 2 -v Singular

You should obtain such a result:

resulting visualisation.

You could also use other implicit surfaces:

• whitney : x^2-y*z^2
• 4lines : x*y*(y-x)*(y-z*x)
• cone : z^2-x^2-y^2
• simonU : x^2-z*y^2+x^4+y^4
• cayley3 : 4*(x^2 + y^2 + z^2) + 16*x*y*z - 1
• crixxi : -0.9*(y^2+z^2-1)^2-(x^2+y^2-1)^3

Some other examples (more difficult):

3dImplicitSurfaceExtractorByThickening -a -2 -A 2 -p "((y^2+z^2-1)^2-(x^2+y^2-1)^3)*(y*(x-1)^2-z*(x+1))^2" -g 0.025 -e 1e-6 -n 50000 -v Singular -t 0.5 -P Newton
3dImplicitSurfaceExtractorByThickening -a -2 -A 2 -p "(x^5-4*z^3*y^2)*((x+y)^2-(z-x)^3)" -g 0.025 -e 1e-6 -n 50000 -v Singular -t 0.05 -P Newton

See also

3dImplicitSurfaceExtractorByThickening.cpp