This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as ma...
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This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammars such that we obtain physically manufacturable building blocks of controllable granularity while retaining variability, i.e., the ability to construct many different, related shapes. Simplification is performed by sequences of two types of elementary Operations: non-local joint edge collapses in the tile graphs reduce the granularity of the decomposition and approximate replacement Operations reduce redundancy. We evaluate our method on abstract graph grammars in addition to computing several physical construction sets, which are manufactured using a commodity 3D printer.
A new polygon class taking linear-time and space for triangulation, called an if-polygon, is defined. After describing an algorithm for triangulating this class, we show that some triangulation-linear classes previous...
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A new polygon class taking linear-time and space for triangulation, called an if-polygon, is defined. After describing an algorithm for triangulating this class, we show that some triangulation-linear classes previously known, such as a convex polygon, a spiral polygon, an edge-visible polygon and a chain-visible polygon have the same property, called the if-property, as the newly defined class. Consequently, a monotone-separable polygon and a star-shaped polygon can be considered as a union of two if-polygons, respectively. Also, we present a modified algorithm for triangulating a star-shaped polygon without decomposition. As a result, the algorithm is simpler to implement and easier to understand and its correctness can be easily verified.
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