Slices

Abstract

selection of user study models with user prescribed slices input mesh computed planar slices geometric features with associated planes slicing result on a model not in the training set physical paper puppet Figure 1: Based on a user study, where participants abstracted meshes of common objects using a small collection of planar slices, we develop an automatic algorithm to create planar slice based abstractions of (untrained) models. Starting from a set of planar slices, approximating the object's geometric features, the algorithm picks a subset of planes based on relative feature importance learned from the user study. AbstractMinimalist object representations or shape-proxies that spark and inspire human perception of shape remain an incompletely understood, yet powerful aspect of visual communication. We explore the use of planar sections, i.e., the contours of intersection of planes with a 3D object, for creating shape abstractions, motivated by their popularity in art and engineering. We first perform a user study to show that humans do define consistent and similar planar section proxies for common objects. Interestingly, we observe a strong correlation between user-defined planes and geometric features of objects. Further we show that the problem of finding the minimum set of planes that capture a set of 3D geometric shape features is both NP-hard and not always the proxy a user would pick. Guided by the principles inferred from our user study, we present an algorithm that progressively selects planes to maximize feature coverage, which in turn influence the selection of subsequent planes. The algorithmic framework easily incorporates various shape features, while their relative importance values are computed and validated from the user study data. We use our algorithm to compute planar slices for various objects, validate their utility towards object abstraction using a second user study, and conclude showing the potential applications of the extracted planar slice shape proxies.

Carbon-[n]Triangulenes and Sila-[n]Triangulenes: Which Are Planar?

“…The answer is negative if one recalls that there are many fruitful concepts in chemistry that are not so. , Still, we may conjecture about using statistics to define an index of planarity likelihood, a topic that will not be pursued in this work. Suffice it to emphasize that planes are well-known geometric primitives, the fundamental nature of which is easily perceived by recalling that slices of a 3D object are used as proxies for creating shape abstractions in art and engineering . In fact, it was the key nature of planarity that posed the motivation for this work jointly with the asset that triangulenes possess unique magnetic properties (hence, are of great interest in materials science , ).…”

“…Suffice it to emphasize that planes are well-known geometric primitives, the fundamental nature of which is easily perceived by recalling that slices of a 3D object are used as proxies for creating shape abstractions in art and engineering. 67 In fact, it was the key nature of planarity that posed the motivation for this work jointly with the asset that triangulenes possess unique magnetic properties (hence, are of great interest in materials science 1 , 68 ). Indeed, it is not clear which [ n ]triangulenes and sila-[ n ]]triangulenes are planar among the numerous members of their families.…”

State of the art on stylized fabrication

“…In [MSM11], the authors proposed an algorithm to create minimalistic representations of 3D objects using a limited set of planar 2D cross-sections. A user study was performed to understand how humans approximate a given object using cross-sectioning planes.…”

Agile structural analysis for fabrication-aware shape editing

“…For instance, in architecture geometry, Liu et al (2006Liu et al ( , 2011 developed algorithms to design planar quad mesh for freeform architectural surface to reduce the fabrication cost. To facilitate the 3D shape fabrication, algorithms have been designed to convert the 3D shape into planar slices (Hildebrand et al, 2012;McCrae et al, 2011). Given a 3D furniture model, Fig.…”