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Space filling polygons – Stereotomy Semantic Classification

Stereotomy Semantic Classification

Space filling polygons

Space filling polygons is an umbrella term which includes various mathematical strategies to partition a surface into regions based on a set of points which exist in that surface. This problem has been tackled throughout history by Kepler, Descartes, Snow, Dirichlet or Voronoy. The latter set the foundations for the ubiquitously used Voronoi diagram: “the partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other” (Weisstein, 2019c). This definition sometimes causes eccentric polygons unsuitable for construction applications, and so possible solutions based on this theme have been studied, like Centroidal Voronoi Tesselations, Hodge-optimized triangulations or Circle packing dual mesh.

Works featuring this facet:

Facets:

Show all Semantics
  • E Equilibrium

    • EA Macro-shape

      • EAA Generation method

        • EAAA Top down

          • EAAAA Constant generatrix

          • EAAAB Varying generatrix

        • EAAB Bottom up

          • EAABA Hanging models

          • EAABB Graphic statics

      • EAB Continuity

        • EABA Segmented

        • EABB Continuous

    • EB Structural functioning

      • EBA Compression only

      • EBB Compression and tension

        • EBBA Tension resistant voussoirs

        • EBBB External reinforcement

      • EBC Tension only

    • EC Surface subdivision

      • ECA One level subdivision

        • ECAA Pattern

          • ECAAA Periodic

            • ECAAAA Developable

            • ECAAAB Constant principal curvature

          • ECAAB Non-periodic

            • ECAABA Topological approach

              • ECAABAA Regular

              • ECAABAB Semi regular

            • ECAABB Space filling polygons

        • ECAB Performative subdivision

          • ECABA Curvature

          • ECABB Aesthetics

          • ECABC Voussoir dimensions

      • ECB Multiple level subdivision

        • ECBA Courses and voussoirs

        • ECBB Micro voussoirs within macro voussoirs

    • ED Foundation

      • EDA Site fixation

        • EDAA Pre-existing static base

        • EDAB Purposed static base

        • EDAC Tensioned springers

        • EDAD Wall or lintel supports

      • EDB Springer

        • EDBA Materiality

          • EDBAA Same as voussoir

          • EDBAB Different material

        • EDBB Geometry

          • EDBBA Subdivision continuity

          • EDBBB Specific design

  • T Tomotechny

    • TA Materialisation Processes

      • TAA Subtractive

        • TAAA 2D cut

          • TAAAA Milling (2D cut)

          • TAAAB Laser

        • TAAB 3D cut

          • TAABA Milling (3D cut)

          • TAABB Saw (3D cut)

          • TAABC Wire cutter

          • TAABD Water jet

        • TAAC 3D carve

          • TAACA Chisel and Mallet

          • TAACB Milling (3D carve)

          • TAACC Saw (3D carve)

      • TAB Additive

        • TABA Material extrusion

        • TABB Binder jetting

      • TAC Formative

        • TACA One-off Mould

        • TACB Reconfigurable Mould

    • TB Centering

      • TBA Temporary

        • TBAA Support structure below

          • TBAAA Extruded grid

          • TBAAB Per-Voussoir

          • TBAAC Along lines

        • TBAB Tensioned voussoirs above

      • TBB Permanent

      • TBC Inexistent (Centering)

        • TBCA Self supported

        • TBCB Additionally supported

    • TC Technical drawing method

      • TCA Two dimensional drafting

        • TCAA Trait

        • TCAB Descriptive geometry

      • TCB Three dimensional modelling

        • TCBA Computerized model

        • TCBB Computational model

  • V Voussoirs

    • VA Material

      • VAA Sustainability

        • VAAA Extraction

        • VAAB Transportation

        • VAAC Processing

        • VAAD Fabrication

      • VAB Structural performance

        • VABA Compression

        • VABB Tension

        • VABC Density

      • VAC Material Typology

        • VACA Subtractable materials

        • VACB Formable materials

        • VACC Additive materials

    • VB Intrados and Extrados

      • VBA Surface

        • VBAA Double Curvature

        • VBAB Single Curvature

        • VBAC Planar (Intrados and Extrados Surface)

        • VBAD Textured

      • VBB Perimeter

        • VBBA Concavity

          • VBBAA Convex

          • VBBAB Concave

        • VBBB Correspondence

          • VBBBA Analogous

          • VBBBB Differentiated

    • VC Contact surface

      • VCA Geometry

        • VCAA Ruled

        • VCAB Planar (Contact Surface)

        • VCAC Composite

      • VCB Friction

        • VCBA Smooth

        • VCBB Rough

      • VCC Mortar

        • VCCA Inexistent (Mortar)

        • VCCB Gap filling

        • VCCC Binding

      • VCD Interlock

        • VCDA Alignment

        • VCDB Sliding prevention

        • VCDC Cantilevering

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