Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the...Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the center with the vertices in the certain cube, the cube is divided into six pyramids. And if we glued six pyramids to the faces of the cube, we obtain a ＇rhombic dodecahedron＇. Since cubes are packing a space, rhombic dodecahedra are also space-filling polyhedra and a rhombic dodecahedron is divided into two regular tetrahcdra and one regular octahedron. In this study, we present how rhombic dodecahedron can be split into tetrahedra and octahedron. In this process, we can research a variety of divisions of regular polyhedron.展开更多
The contour of the slices of SLA parts is composed of a great deal of small lines. When offsetting the contour to compensate for the radius of laser spot, many self-intersection contours come into being, which decreas...The contour of the slices of SLA parts is composed of a great deal of small lines. When offsetting the contour to compensate for the radius of laser spot, many self-intersection contours come into being, which decrease the precision of formed parts. A new lemma to judge the local self-intersection contour and the global self-intersection contour separately is put forward, according to which self-intersection contour can be removed reliably. Meanwhile, a new beam offsetting algorithm for SLA parts is described, which brings about good resuits in the practical manufacturing process.展开更多
文摘Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the center with the vertices in the certain cube, the cube is divided into six pyramids. And if we glued six pyramids to the faces of the cube, we obtain a ＇rhombic dodecahedron＇. Since cubes are packing a space, rhombic dodecahedra are also space-filling polyhedra and a rhombic dodecahedron is divided into two regular tetrahcdra and one regular octahedron. In this study, we present how rhombic dodecahedron can be split into tetrahedra and octahedron. In this process, we can research a variety of divisions of regular polyhedron.
文摘The contour of the slices of SLA parts is composed of a great deal of small lines. When offsetting the contour to compensate for the radius of laser spot, many self-intersection contours come into being, which decrease the precision of formed parts. A new lemma to judge the local self-intersection contour and the global self-intersection contour separately is put forward, according to which self-intersection contour can be removed reliably. Meanwhile, a new beam offsetting algorithm for SLA parts is described, which brings about good resuits in the practical manufacturing process.
