TY - GEN
T1 - Precise construction of micro-structures and porous geometry via functional composition
AU - Elber, Gershon
N1 - Publisher Copyright: © Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - We introduce a modeling constructor for micro-structures and porous geometry via curve-trivariate, surface-trivariate and trivariate-trivariate function (symbolic) compositions. By using 1-, 2- and 3-manifold based tiles and paving them multiple times inside the domain of a 3-manifold deforming trivariate function, smooth, precise and watertight, yet general, porous/micro-structure geometry might be constructed, via composition. The tiles are demonstrated to be either polygonal meshes, (a set of) Bézier or B-spline curves, (a set of) Bézier or B-spline (trimmed) surfaces, (a set of) Bézier or B-spline (trimmed) trivariates or any combination thereof, whereas the 3-manifold deforming function is either a Bézier or a B-spline trivariate. We briefly lay down the theoretical foundations, only to demonstrate the power of this modeling constructor in practice, and also present a few 3D printed tangible examples. We then discuss these results and conclude with some future directions and limitations.
AB - We introduce a modeling constructor for micro-structures and porous geometry via curve-trivariate, surface-trivariate and trivariate-trivariate function (symbolic) compositions. By using 1-, 2- and 3-manifold based tiles and paving them multiple times inside the domain of a 3-manifold deforming trivariate function, smooth, precise and watertight, yet general, porous/micro-structure geometry might be constructed, via composition. The tiles are demonstrated to be either polygonal meshes, (a set of) Bézier or B-spline curves, (a set of) Bézier or B-spline (trimmed) surfaces, (a set of) Bézier or B-spline (trimmed) trivariates or any combination thereof, whereas the 3-manifold deforming function is either a Bézier or a B-spline trivariate. We briefly lay down the theoretical foundations, only to demonstrate the power of this modeling constructor in practice, and also present a few 3D printed tangible examples. We then discuss these results and conclude with some future directions and limitations.
KW - Freeform deformation
KW - Freeform tiling
KW - Symbolic computation
KW - Trivariate splines
UR - http://www.scopus.com/inward/record.url?scp=85032678853&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-67885-6_6
DO - 10.1007/978-3-319-67885-6_6
M3 - منشور من مؤتمر
SN - 9783319678849
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 108
EP - 125
BT - Mathematical Methods for Curves and Surfaces - 9th International Conference, MMCS 2016, Revised Selected Papers
A2 - Mazure, Marie-Laurence
A2 - Schumaker, Larry L.
A2 - Floater, Michael
A2 - Lyche, Tom
A2 - Morken, Knut
T2 - 9th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2016
Y2 - 23 June 2016 through 28 June 2016
ER -