Shape differentiation of freeform surfaces using a similarity measure based on an integral of Gaussian curvature

Fu, Jianzhong; Joshi, Sanjay; Simpson, Timothy W.

doi:10.1016/j.cad.2007.11.006

Cited by 22 publications

(11 citation statements)

References 24 publications

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“…In the methodology [10], there is a process used for parametric surfaces and another similar one for discrete surfaces. When dealing with point clouds, it is necessary to use the discrete one and therefore to work on a triangular mesh M composed by a vertex set V={v i }  R 3 , a edges set E={e j =v j1 v j2 } which connect the vertexes and a triangles set (Fig.8).…”

Section: Gaussian Curvature: Percentiles (Methods 3)mentioning

confidence: 99%

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Study and development of morphological analysis guidelines for point cloud management: The “decisional cube”

Vezzetti¹

2011

Computer-Aided Design

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When talking about reverse engineering, it is necessary to focus on the management of point clouds. Generally speaking, every 3D scanner device codifies simple and complex geometries providing different point cloud densities as an output. Point cloud density is usually more correlated with the technical specifications of the device employed rather than with the morphology of the object acquired. This situation is due to the frequent use of structured grids by a large quantity of devices. In order to solve this problem, we therefore need to integrate the classical structured grid acquisition with a smart selective one, which is able to identify different point cloud densities in accordance with the morphological complexity of the object regions acquired. Currently, we can reach the destination in many different ways. Each of them is able to provide different performances depending on the object morphology and the performances of 3D scanner devices. Unfortunately, there does not yet exist one universal approach able to be employed in all cases. For this reason, the present paper aims to propose a first analysis of the available methodologies and parameters, in order to provide final users with some guidelines for supporting their decisions according to the specific application they are facing. Moreover, the developed guidelines have been illustrated and validated by a series of case studies of the proposed method.

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Section: Gaussian Curvature: Percentiles (Methods 3)mentioning

confidence: 99%

“…As a consequence of this, the Gaussian curvature K T [10], used in the differentiable surfaces, can be approximated in the discrete ones as the sum of the T i K in each vertex in a specific region. Hence, in a specific vertex v i the curvature integral can be approximated from [12,4]:…”

Section: Figure 8 : Vertex and Related Variablesmentioning

confidence: 99%

Study and development of morphological analysis guidelines for point cloud management: The “decisional cube”

Vezzetti¹

2011

Computer-Aided Design

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“…Extensive literatures on geometry search could be reviewed in several aspects, such as global and partial retrieval [21], geometry [22] or topology method [23], semantic feature based [24] or none-featured graph method [25,26], solid model oriented [27] or surface model [4], for rigid shape [28,29] or for non-rigid shape [30], in single resolution level [3] or in level of detail (LOD) [31], by single descriptors or by combined descriptor and learning technique [32], etc. Indeed, there is no one best solution for all cases, and when considering reuse of tool sequence for cavity machining, some property of cavity FFS could be considered.…”

Section: Geometry Searchmentioning

confidence: 99%

“…In the field of surface retrieval, Fu et al [3] found that although shape distribution is of robustness and efficiency, it is not effective when adapting to surface retrieval, where a product family tends to share common global shape but different curvature variation. Integral of Gaussian curvature distribution in concentric regions is proposed, but the number of regions is empirical and alignment of targeting surfaces is required.…”

Section: Geometry Searchmentioning

confidence: 99%

“…Freeform surface (FFS), also called sculptured surface, is ubiquitous in these designs for visual and functional requirements. Usually, similar geometric shapes are shared by products belonging to the same product family or different generations, and reuse of similar manufacturing process is desirable [2][3][4]. Consequently, efficient production of these similar sculptured surfaces based on previous cases is essential to computer-integrated manufacturing and competitiveness of mould company.…”

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confidence: 99%

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A geometry search approach in case-based tool reuse for mould manufacturing

Zhou

Liu

et al. 2015

Int J Adv Manuf Technol

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Similar freeform surfaces are widely adopted in product family or different generations. Manufacturing of these surfaces with efficiency is essential to competitiveness of the company. Conventionally, milling tools were chosen mainly by experience; therefore, reuse of existing experience is essential to advanced manufacturing. This paper proposed a novel geometry search approach to recommend tool selection for review and reuse based on previous cases. First, a hierarchical representation is extracted from freeform meshes. Then, qualitative and quantitative properties were defined to support matching and comparison in the level of detail. Geometry search algorithm is then adapted with boundary condition to find best sequence of tools, where existing cases were stored in layered slices along with their tool information, and new case of cavity is explored in a sequence to progressively find the best match of each layer. Finally, retrieved tools were adapted to review and assist for process planners. A prototype system and a case study are provided to demonstrate the proposed method.

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Physics-informed geometric operators to support surrogate, dimension reduction and generative models for engineering design

Khan,

Masood,

Usama

et al. 2025

Advanced Engineering Informatics

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Shape differentiation of freeform surfaces using a similarity measure based on an integral of Gaussian curvature

Cited by 22 publications

References 24 publications

Study and development of morphological analysis guidelines for point cloud management: The “decisional cube”

Study and development of morphological analysis guidelines for point cloud management: The “decisional cube”

A geometry search approach in case-based tool reuse for mould manufacturing

Physics-informed geometric operators to support surrogate, dimension reduction and generative models for engineering design

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