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Fig. 4. Planarization method shown in iterations: (A) planarization of extruded mesh edges 0- 600 iteration (B) intersection of lines to average planes (C) the full sequence of planarization.

Figure 4 Planarization method shown in iterations: (A) planarization of extruded mesh edges 0- 600 iteration (B) intersection of lines to average planes (C) the full sequence of planarization.

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Modelling Workflow for Segmented Timber Shells Using Wood-Wood Connections
Modelling Workflow for Segmented Timber Shells Using Wood-Wood Connections
Fig. 2. The research context: Al — Mountain forestry, A2 - Tree species — Epicéa, A3 - CAD interface, A4 - CNC cutting, A5 - joinery. Modelling workflow: B1 - surface, B2 - discretization and planarization, B3 — CNC milling and cutting, B4.1/2 Box component, Solid element component B5.1/2 Prototypes.
Fig. 2. The research context: Al — Mountain forestry, A2 - Tree species — Epicéa, A3 - CAD interface, A4 - CNC cutting, A5 - joinery. Modelling workflow: B1 - surface, B2 - discretization and planarization, B3 — CNC milling and cutting, B4.1/2 Box component, Solid element component B5.1/2 Prototypes.
Fig. 3. Planarization method consists of two main steps: (A) planarization of extruded mesh edges (support structure) (B) intersection of lines to average planes of line ends (C) planar polyhedron The planarization method is based on support structures of polygonal cell packing [5]. The aim is to compute polyhedrons, which are solids with only planar face boundaries from arbitrary surface subdivision [6]. Similar research [7] implemented plane pro- jection methods on quad meshes with small gaps at each mesh vertex. Other possibility is to use Voronoi diagrams for planarization [5]. Another technique is to apply a circle packing of triangle meshes whose incircles form a packing [8]. A third method uses circular and conical meshes [9].
Fig. 3. Planarization method consists of two main steps: (A) planarization of extruded mesh edges (support structure) (B) intersection of lines to average planes of line ends (C) planar polyhedron The planarization method is based on support structures of polygonal cell packing [5]. The aim is to compute polyhedrons, which are solids with only planar face boundaries from arbitrary surface subdivision [6]. Similar research [7] implemented plane pro- jection methods on quad meshes with small gaps at each mesh vertex. Other possibility is to use Voronoi diagrams for planarization [5]. Another technique is to apply a circle packing of triangle meshes whose incircles form a packing [8]. A third method uses circular and conical meshes [9].
Table 1. Source code of planarization.
Table 1. Source code of planarization.
Several existing publications describe the automation of assembly path that influences the joinery geometry (type of joint and an insertion direction) [10-12]. It is also possible to look at this problem from a user perspective when the assembly path is ready known. Proposed methodology is based on the existing state-of-the-art method 7] and extended to polygonal meshes, which are not restricted to triangle or quad iscretization. Moreover, graph-search methods such as Breadth-First-Search could be pplied to compute an assembly order (see Fig. 7). Edges of this graph whose nodes are olygon centers give insertion direction. This vector has to be compared against onnected edge direction to know if the insertion vector is not parallel. BFS is a fast pproach when a user does not have a sequential order how to assemble elements one fter another. Other methods such as a grid-like assembly could be applied when the initial topology is regular. Lastly, several large patches could be assembled together too. It often requires special details, as multiple edges may not have uniform insertion vector applicable to all elements within a group. =) sa pf 2 2 2 Oo
Several existing publications describe the automation of assembly path that influences the joinery geometry (type of joint and an insertion direction) [10-12]. It is also possible to look at this problem from a user perspective when the assembly path is ready known. Proposed methodology is based on the existing state-of-the-art method 7] and extended to polygonal meshes, which are not restricted to triangle or quad iscretization. Moreover, graph-search methods such as Breadth-First-Search could be pplied to compute an assembly order (see Fig. 7). Edges of this graph whose nodes are olygon centers give insertion direction. This vector has to be compared against onnected edge direction to know if the insertion vector is not parallel. BFS is a fast pproach when a user does not have a sequential order how to assemble elements one fter another. Other methods such as a grid-like assembly could be applied when the initial topology is regular. Lastly, several large patches could be assembled together too. It often requires special details, as multiple edges may not have uniform insertion vector applicable to all elements within a group. =) sa pf 2 2 2 Oo
Fig. 7. Graph search algorithm — Breadth-First-Search used for an assembly path and joinery orientation. BFS connectivity graph from center points of hexagons (A), graph edge is used as a vector for each polygon edge joint orientation (B), physical test (Lina Vestarte master’s thesis in a collaboration with Petras Vestartas, Romualdas Kuéinskas https://www.linavestarte.com/ Assembly-of-Double-curved-Self-supporting-Structure) (2) from cardboard (C).
Fig. 7. Graph search algorithm — Breadth-First-Search used for an assembly path and joinery orientation. BFS connectivity graph from center points of hexagons (A), graph edge is used as a vector for each polygon edge joint orientation (B), physical test (Lina Vestarte master’s thesis in a collaboration with Petras Vestartas, Romualdas Kuéinskas https://www.linavestarte.com/ Assembly-of-Double-curved-Self-supporting-Structure) (2) from cardboard (C).
Fig. 8B). Afterwards, the tile polyline is inserted into the existing planar outline. Another modelling methodology is tested for the Round-Wood prototype. It does not rely on mesh topology but rather on basic geometric transformations and tiling operations for single curved arcs. The planar blocks of the arch are generated using five steps (see Fig. 8). First, curves are divided into points and normal planes are computed from curve derivatives. Two planar outlines are generated using perpendicular planes (see Fig. 8A). Second, a finger joint is drawn as a tile to generate the butt connections for each element. This allows the shape of the connector to be changed any other 2D-joint later. The tile is then oriented from the original plane to the perpendicular frames on the curve (see Fig. 8B). Afterwards, the tile polyline is inserted into the existing planar outline.
Fig. 8B). Afterwards, the tile polyline is inserted into the existing planar outline. Another modelling methodology is tested for the Round-Wood prototype. It does not rely on mesh topology but rather on basic geometric transformations and tiling operations for single curved arcs. The planar blocks of the arch are generated using five steps (see Fig. 8). First, curves are divided into points and normal planes are computed from curve derivatives. Two planar outlines are generated using perpendicular planes (see Fig. 8A). Second, a finger joint is drawn as a tile to generate the butt connections for each element. This allows the shape of the connector to be changed any other 2D-joint later. The tile is then oriented from the original plane to the perpendicular frames on the curve (see Fig. 8B). Afterwards, the tile polyline is inserted into the existing planar outline.
Fig. 9. A sequence of fabrication: (Al) round-wood (A2-A3) cutting planes for a blade saw (A4) milling (A5) cutting grooves (A6) target geometry. Sequence of assembly (B1) Assembly of an arch (B2) Assembly of arch (B3) finished prototype Modelling Workflow for Segmented Timber Shells Using Wood-Wood Connection:
Fig. 9. A sequence of fabrication: (Al) round-wood (A2-A3) cutting planes for a blade saw (A4) milling (A5) cutting grooves (A6) target geometry. Sequence of assembly (B1) Assembly of an arch (B2) Assembly of arch (B3) finished prototype Modelling Workflow for Segmented Timber Shells Using Wood-Wood Connection:
Fig. 10. CNC fabrication of a round-wood specimen. (A) Protype (B) CNC Fabrication.
Fig. 10. CNC fabrication of a round-wood specimen. (A) Protype (B) CNC Fabrication.
[The proposed modelling framework was applied for a series of free-from surfaces anging from low-resolution and high-curvature (see Fig. 11A—B) to high-resolution ind low-curvature geometries (see Fig. 11C—D-E). The shift between polyhedrons is nevitable but acceptable, depending on a Gaussian curvature. In addition, planarized ind original polyhedron shapes are similar and do not have large distortions, which nakes this workflow useful for our material-based exploration within specific range of ‘urface curvatures. Two prototypes were made using this modelling framework (see Figs. 1, 12, 13). While the underlying geometry of both study cases were similar, we used different CNC fabrication approaches. The plate model was fabricated using CNC cutting while the round-wood specimen required a combination of tools (saw-blade, milling and drilling) and an additional rig for lifting the trunks. Both models were assembled manually with the arch resting on one side so that the elements could be easily assembled on top of each other sequentially. Upon the completion of the assembly the whole specimen was lifted and rotated by 90° to its intended position. A geometry mesh library was made for this polygonal surface discretization workflow. It is based on triangle meshes that are grouped to N-Gon representation. The
[The proposed modelling framework was applied for a series of free-from surfaces anging from low-resolution and high-curvature (see Fig. 11A—B) to high-resolution ind low-curvature geometries (see Fig. 11C—D-E). The shift between polyhedrons is nevitable but acceptable, depending on a Gaussian curvature. In addition, planarized ind original polyhedron shapes are similar and do not have large distortions, which nakes this workflow useful for our material-based exploration within specific range of ‘urface curvatures. Two prototypes were made using this modelling framework (see Figs. 1, 12, 13). While the underlying geometry of both study cases were similar, we used different CNC fabrication approaches. The plate model was fabricated using CNC cutting while the round-wood specimen required a combination of tools (saw-blade, milling and drilling) and an additional rig for lifting the trunks. Both models were assembled manually with the arch resting on one side so that the elements could be easily assembled on top of each other sequentially. Upon the completion of the assembly the whole specimen was lifted and rotated by 90° to its intended position. A geometry mesh library was made for this polygonal surface discretization workflow. It is based on triangle meshes that are grouped to N-Gon representation. The
Fig. 12. Prototype from planks.
Fig. 12. Prototype from planks.
5 Challenges in Scaling
5 Challenges in Scaling
Fig. 14. Concept model for a larger application. within robotic fabrication framework that has been recently implemented for the research scope.
Fig. 14. Concept model for a larger application. within robotic fabrication framework that has been recently implemented for the research scope.
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