Generalized cylinder decomposition

Abstract

Decomposing a complex shape into geometrically simple primitives is a fundamental problem in geometry processing. We are interested in a shape decomposition problem where the simple primitives sought are generalized cylinders, which are ubiquitous in both organic forms and man-made artifacts. We introduce a quantitative measure of cylindricity for a shape part and develop a cylindricitydriven optimization algorithm, with a global objective function, for generalized cylinder decomposition. As a measure of geometric simplicity and following the minimum description length principle, cylindricity is defined as the cost of representing a cylinder through skeletal and cross-section profile curves. Our decomposition algorithm progressively builds local to non-local cylinders, which form over-complete covers of the input shape. The over-completeness of the cylinder covers ensures a conservative buildup of the cylindrical parts, leaving the final decision on decomposition to global optimization. We solve the global optimization by finding an exact cover, which optimizes the global objective function. We demonstrate results of our optimal decomposition algorithm on numerous examples and compare with other alternatives.

An interactive computer‐based simulation system for endovascular aneurysm repair surgeries

“…Once the stent graft is in position, the blood flow will be confined to the interior of the stent graft, instead of the sac of the aneurysm. In the system, a generalized cylinder‐based (GC‐based) mesh is used to represent the geometry of the stent graft. The physical behavior of the stent graft is modeled by a mass‐spring system.…”

A Survey of Simple Geometric Primitives Detection Methods for Captured 3D Data

“…Examples of Primitive Growing Methods The processing is started by assigning seeds to random [OLA16, LMM98] or regular [ZYH*15] positions in the data. The growing of points into regions can be performed through a neighbour search using efficient data structures such as a neighbour graph [FTK14, AEH15].…”

“…Some methods oversegment the data into patches, super‐points or super‐regions [LGZ*13] that can be joined together to form the final segmentation. Algorithms used to merge these patches include rectangle fitting [MPM*14, OLA16], candidate generation and selection [MMBM15], linear interpolation [TGB13] or automatic merge of neighbouring shapes [LMM98, AFS06, ZYH*15]. Making use of the efficient structure of images, a few methods offer a speed‐up over point cloud–based methods [TGRC13, KHB*15, AEH15].…”

Data‐Driven Bending Elasticity Design by Shell Thickness

“…The skeleton 𝒮 and virtual cross‐sections of an input model H are generated by the rotational symmetry axis (ROSA) technique [TZCO09,ZYH*15]. We also follow the assumption of [TZCO09] on generalized cylindrical regions to be the shapes of interest.…”