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| playground:playground [2019/03/25 20:56] – oroehrig | playground:playground [2019/03/25 20:59] – oroehrig |
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| ====== application topaz ====== | ====== application topaz ====== |
| The __TOP__ology __A__pplication __Z__oo deals with abstract simplicial complexes.\\ A complex is given as a list of facets. You can ask for its global properties (''[[playground/playground/SimplicialComplex#MANIFOLD |manifold recognition]]'',\\ ''[[playground/playground/SimplicialComplex#HOMOLOGY |homology groups]]'', etc.), explore the local vertex environment (''[[playground/playground#star |stars]]'', ''[[playground/playground#link |links]]'', etc.), and make a lot\\ of constructions.\\ The visualization means are constrained, as they are mostly based on the ''[[playground/playground/SimplicialComplex#GRAPH |GRAPH]]'' (1-skeleton) of a complex. | The __TOP__ology __A__pplication __Z__oo deals with abstract simplicial complexes.\\ A complex is given as a list of facets. You can ask for its global properties ([[playground/playground/SimplicialComplex#MANIFOLD |manifold recognition]],\\ [[playground/playground/SimplicialComplex#HOMOLOGY |homology groups]], etc.), explore the local vertex environment ([[playground/playground#star |stars]], [[playground/playground#link |links]], etc.), and make a lot\\ of constructions.\\ The visualization means are constrained, as they are mostly based on the ''[[playground/playground/SimplicialComplex#GRAPH |GRAPH]]'' (1-skeleton) of a complex. |
| imports from: | imports from: |
| * [[graph|application graph]] | * [[graph|application graph]] |
| * ''[[playground/playground/SimplicialComplex# |SimplicialComplex]]'' ''complex'' : | * ''[[playground/playground/SimplicialComplex# |SimplicialComplex]]'' ''complex'' : |
| * ''[[playground/playground#Rational |Rational]]'' ''width'' : default: 0 | * ''[[playground/playground#Rational |Rational]]'' ''width'' : default: 0 |
| * Create a triangulated tubular neighborhood of a ''[[playground/playground/SimplicialComplex#PURE |pure]]'' 2-complex.\\ If the complex is a link\\ with the property that each vertex and its two neighbours are in general\\ position after projection to the x,y-plane, then one might specify\\ a rational number //width// to tell the client to compute ''[[playground/playground/GeometricSimplicialComplex#COORDINATES |COORDINATES]]''\\ of the triangulated tubular neighborhood. If the //width/// is\\ chosen too large, the computed realization will be self intersecting.\\ If each connected component of the link has an even number of facets,\\ then the following holds:\\ An edge of the resulting complex is contained in an odd number of\\ facets iff it corresponds to one of the edges of the link. | * Create a triangulated tubular neighborhood of a [[playground/playground/SimplicialComplex#PURE |pure]] 2-complex.\\ If the complex is a link\\ with the property that each vertex and its two neighbours are in general\\ position after projection to the x,y-plane, then one might specify\\ a rational number //width// to tell the client to compute ''[[playground/playground/GeometricSimplicialComplex#COORDINATES |COORDINATES]]''\\ of the triangulated tubular neighborhood. If the //width/// is\\ chosen too large, the computed realization will be self intersecting.\\ If each connected component of the link has an even number of facets,\\ then the following holds:\\ An edge of the resulting complex is contained in an odd number of\\ facets iff it corresponds to one of the edges of the link. |
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