{"id":412,"date":"2023-08-29T16:08:27","date_gmt":"2023-08-29T16:08:27","guid":{"rendered":"https:\/\/inventorics.com\/?p=412"},"modified":"2023-10-04T16:39:48","modified_gmt":"2023-10-04T16:39:48","slug":"regular-tetrahedral-cells-vs-cluster-modules","status":"publish","type":"post","link":"https:\/\/inventorics.com\/?p=412","title":{"rendered":"Cluster 1: Regular Tetrahedral Cells vs. Cluster Modules"},"content":{"rendered":"\n

After aggregating regular tetrahedra following different set of rules<\/a> these tetra-units are replaced by by various bike-frame cluster modules<\/a>.
Each of these cluster modules is made up of 2-3 bike frames from the scanned set<\/a> and fitted into a regular tetrahedral container. For this study only copies of one single cluster type are populated throughout the aggregated frameworks replacing the regular tetra-units. This is done assuming that other bike-frames within a certain tolerance range can be used to form the same combinations (possibly with a slightly different clipping at the joint-plate areas). The bigger the inventory of bike frames, the more likely it is to find very similar bike-frames.<\/p>\n\n\n\n

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Fig.1: Bike Cluster TYPE 12 is used for the first study. Dependening on the bike-frames orientation within one tetrahedral cell informed by the respective connection logic (from left to right: face to face, edge to edge, vertex to vertex) the amount of “empty space” locally<\/strong> within one unit varies immensely.<\/sub><\/em><\/p>\n\n\n\n\n\n\n\n

This in combination with the global aggregation logic<\/a> leads to a range of structures with varying degrees of densities:<\/p>\n\n\n\n

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Fig. 2: The same boundary volume filled with tetra-units (upper row) which in turn contain the same exact same bike-frame cluster (bottom row) but in its 3 different orientation possibilities (Fig.1).<\/sub><\/em><\/p>\n\n\n\n

The face to face aggregation (left column) fits 428 tetrahedra and 1284 bike-frames, the edge to edge (middle) 838 tetrahedra and 2496 bike-frames and the vertex to vertex (right) 1036 tetrahedra and 3108 bike-frames inside that specific boundary volume.<\/p>\n\n\n

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Fig 3: face to face<\/sub><\/em><\/figcaption><\/figure>\n<\/div>\n\n
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Fig.4 : edge to edge<\/sub><\/em><\/figcaption><\/figure>\n<\/div>\n\n
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Fig. 5: vertex to vertex<\/sub><\/em><\/figcaption><\/figure>\n<\/div>\n\n\n

As all of these bike cluster types leave 1-3 connection plane vacant (the 3 bike frames serve 3 of the 4 faces or vertices and only 3 of the 6 edges), the resulting frameworks have a lot of open loops. These open ends follow the aggregation logic and could be compensated\/bridged by either reorienting the frames within the individual tetra-units or by a second iteration aggregation of single frames to connect in between…<\/p>\n\n\n\n

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Fig. 6: edge to edge aggregation, isolated single layer(s) (upper row: horizontal, bottom: horizontal and vertical)<\/sup><\/em><\/p>\n\n\n\n

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Fig. 7: vertex to vertex aggregation, isolated single layer(s) (upper row: horizontal, bottom: horizontal and vertical)<\/sup><\/em><\/p>\n\n\n\n

A special type of bike cluster (TYPE 18) serves all 4 vertices and produces a global aggregation with closed loops and therefore a structurally viable framework without any additional modifications:<\/p>\n\n\n\n

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Fig. 8: edge to edge typology of bike cluster TYPE 18 on the left in omparison with TYPE 12 of the previous aggregations, which does not serve connection vertex 1 (marked with a pink sphere)<\/sub><\/em><\/p>\n\n\n\n

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Fig. 9: vertex to vertex aggregation with bike cluster TYPE 18, resulting in local and global loops.<\/em><\/sub><\/p>\n","protected":false},"excerpt":{"rendered":"

After aggregating regular tetrahedra following different set of rules these tetra-units are replaced by by various bike-frame cluster modules.Each of these cluster modules is made up of 2-3 bike frames from the scanned set and fitted into a regular tetrahedral container. For this study only copies of one single cluster type are populated throughout the […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7],"tags":[30,20,27,4,31,6],"class_list":["post-412","post","type-post","status-publish","format-standard","hentry","category-digital-studies","tag-aggregation","tag-bike-frames","tag-cluster-1","tag-discrete","tag-tetrahedra","tag-wasp"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/inventorics.com\/index.php?rest_route=\/wp\/v2\/posts\/412","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/inventorics.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/inventorics.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/inventorics.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/inventorics.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=412"}],"version-history":[{"count":6,"href":"https:\/\/inventorics.com\/index.php?rest_route=\/wp\/v2\/posts\/412\/revisions"}],"predecessor-version":[{"id":538,"href":"https:\/\/inventorics.com\/index.php?rest_route=\/wp\/v2\/posts\/412\/revisions\/538"}],"wp:attachment":[{"href":"https:\/\/inventorics.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/inventorics.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/inventorics.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}