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Completely opened in the plane, the surface is composed of a basic tessellation of equilateral triangles that are divided further (F right triangle represents the decom six equal parts of the large equila Fig. 0). The position into teral triangle, which defines the grid of the entire pattern. The large equilateral modules are arran ged i columns and their bisectors deli inéa n offset te three Figure 12: Possible conformations of the Ron Resch pattern.

Figure 0 Completely opened in the plane, the surface is composed of a basic tessellation of equilateral triangles that are divided further (F right triangle represents the decom six equal parts of the large equila Fig. 0). The position into teral triangle, which defines the grid of the entire pattern. The large equilateral modules are arran ged i columns and their bisectors deli inéa n offset te three Figure 12: Possible conformations of the Ron Resch pattern.

Related Figures (12)

Figure 1: Ron Resch pattern. Valley folds are shown in red and mountain folds in blue. Black represents the mountain folds that sur- round the visible faces when the surface is completely folded.
Figure 1: Ron Resch pattern. Valley folds are shown in red and mountain folds in blue. Black represents the mountain folds that sur- round the visible faces when the surface is completely folded.
Computational geometry. Prefiguring the point/vertex whe rithm to control t and introducing tl in the represen mM he ‘articulated sur re Ne ne gated and prefig form is based nodal program tation software ovement of the folded surface ured. The method adopted is model in space is made possible by geometri- cally controlling the basic constituent entities of faces’: the surface pattern, the line/hinge between the faces, and the the hinges meet. The algo- on geometry, ming present allows the to be investi- based on specifying the geometric algorithms that connect the basic entities of the folded sur- faces, guaranteeing topological invariance of the moving form. By acting on the variables in
Computational geometry. Prefiguring the point/vertex whe rithm to control t and introducing tl in the represen mM he ‘articulated sur re Ne ne gated and prefig form is based nodal program tation software ovement of the folded surface ured. The method adopted is model in space is made possible by geometri- cally controlling the basic constituent entities of faces’: the surface pattern, the line/hinge between the faces, and the the hinges meet. The algo- on geometry, ming present allows the to be investi- based on specifying the geometric algorithms that connect the basic entities of the folded sur- faces, guaranteeing topological invariance of the moving form. By acting on the variables in
Figure 3: the movement of folded surface gives an expressive value with high communi- cational impact.
Figure 3: the movement of folded surface gives an expressive value with high communi- cational impact.
Figure 4: Ilustration of the folds in mountain (green) and valley (red) conformations. are articulated to respond to predetermined in- put. The surface module is already widely used in architectural facades as a solution for varia- ble shading. In addition to environmental and formal qualities, the use of these surfaces im- plies local configurations that find a form of communication in the overall configuration.
Figure 4: Ilustration of the folds in mountain (green) and valley (red) conformations. are articulated to respond to predetermined in- put. The surface module is already widely used in architectural facades as a solution for varia- ble shading. In addition to environmental and formal qualities, the use of these surfaces im- plies local configurations that find a form of communication in the overall configuration.
During the synchronous movem two tiles, point P, which pertains moves along circular path c, but si ent of the to face S3 nce it also pertains to Sa, it moves along d as well. Circles c and d are centred on Ki and Kaz, tions of point P onto EF and HG, wh the projec- ich are the hinges of the respective rotations. The position of P in space is a point common to th e two Cir-
During the synchronous movem two tiles, point P, which pertains moves along circular path c, but si ent of the to face S3 nce it also pertains to Sa, it moves along d as well. Circles c and d are centred on Ki and Kaz, tions of point P onto EF and HG, wh the projec- ich are the hinges of the respective rotations. The position of P in space is a point common to th e two Cir-
Figure 6: Square module composed of three faces. Colors identify the mountain and valley folds. ule into mesh surfaces. Each face of the module becomes a mesh face and each fold becomes a line connecting two vertices. The two flat tiles are discretized by simple
Figure 6: Square module composed of three faces. Colors identify the mountain and valley folds. ule into mesh surfaces. Each face of the module becomes a mesh face and each fold becomes a line connecting two vertices. The two flat tiles are discretized by simple
Figure 7: During the movement, the biggest face becomes part of a cone. We can tessellate the biggest face with radial lines which connect the vertex (O) of the module with the boundary.
Figure 7: During the movement, the biggest face becomes part of a cone. We can tessellate the biggest face with radial lines which connect the vertex (O) of the module with the boundary.
Figure 8: The Kinematic scheme shows the boundary (A, B) impulses and constrain (P) which allows the movement. The text below describes the algorithm that is then translated into a nodal construction.
Figure 8: The Kinematic scheme shows the boundary (A, B) impulses and constrain (P) which allows the movement. The text below describes the algorithm that is then translated into a nodal construction.
lon La imulating a configu lent surfaces at OA han mo 180° to create untain fold). g the line passing through th nd B (Fig. 8). Iti lirection of movement of the tw S necessary ration that p and OB with e same points to indicate the o triangles by aces the inci- an angle less the sense of the movement During the movement, fold )M can only behave like a a valley fold. mmr. ff... yyy, |_. ns i: i: je
lon La imulating a configu lent surfaces at OA han mo 180° to create untain fold). g the line passing through th nd B (Fig. 8). Iti lirection of movement of the tw S necessary ration that p and OB with e same points to indicate the o triangles by aces the inci- an angle less the sense of the movement During the movement, fold )M can only behave like a a valley fold. mmr. ff... yyy, |_. ns i: i: je
Figure 10: Completely unfolded Ron Resch pattern.
Figure 10: Completely unfolded Ron Resch pattern.
Figure 11: Completely folded Ron Resch pattern.
Figure 11: Completely folded Ron Resch pattern.
al p p th From this image we capture the data, which, together with the inform ex plannin re precisely due to a specific creative desire, ropose a static solution to a problem. Archi- tecture and design find the fulfilment of a com- g process in creating the work, in e concluded form. But the main characteristic of nature, i ation and functions that ts continual change and _ transfor- Figure 13: Tessellation of part of a torus. The faces are not deformed in this configura- tion.
al p p th From this image we capture the data, which, together with the inform ex plannin re precisely due to a specific creative desire, ropose a static solution to a problem. Archi- tecture and design find the fulfilment of a com- g process in creating the work, in e concluded form. But the main characteristic of nature, i ation and functions that ts continual change and _ transfor- Figure 13: Tessellation of part of a torus. The faces are not deformed in this configura- tion.
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