Surfacing curve networks with normal control

Stanko, Tibor; Hahmann, Stéfanie; Bonneau, Georges-Pierre; Saguin-Sprynski, Nathalie

doi:10.1016/j.cag.2016.07.001

Cited by 12 publications

(9 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to smooth arbitrary triangle meshes while satisfying G 1 boundary conditions, a new algorithm was presented in [17] to numerically solve a PDE with the discrete Laplace-Beltrami operator and 1-neighborhood based discretization of the mean curvature normal at a vertex. The discrete Laplace-Beltrami operator was also used to obtain variational minimization for surface deformations in [18], estimate surface normal in [14], and perform surface reconstruction in [15].…”

Section: Methodsmentioning

confidence: 99%

“…PDE-based geometric modeling has been intensively studied. Various numerical methods such as the finite element method [9,10,11], finite difference method [12,13], and direct discretization of polygonal models using a discrete Laplace operator [14,15] etc. have been proposed to solve PDEs for hybrid subdivision surface design [16], surface reconstruction [15], estimation of surface normal [14], smoothing arbitrary triangle meshes [17], surface deformations [18], defining geometric solid models [19], surface modeling [20,9], and direct shape manipulation [8] etc.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interactive PDE patch-based surface modeling from vertex-frames

Wang

Xia

You

et al. 2022

Engineering with Computers

View full text Add to dashboard Cite

Polygon, subdivision, and NURBS are three mainstream modeling techniques widely applied in commercial software packages. They require heavy manual operations, and involve a lot of design variables leading to big data, high storage costs and slow network transmissions. In this paper, we integrate the strengths of boundary-based surface creation and partial differential equation (PDE) based geometric modeling to obtain the first analytical C 0 continuous 4-sided PDE patches involving sculpting force-based shape creation and manipulation and use them to develop an interactive modeling technique for easy and quick creation of 3D models with small data from vertex-frames. With this modeling technique, a vertex frame is defined by eight vertices, and a C 0 continuous 4-sided PDE patch is created from the vertex-frame through an analytical solution to a vector-valued second-order PDE subjected to the boundary conditions determined by the eight vertices of a vertex-frame. A user-friendly interface is developed from the obtained analytical solution, which enables users to interactively input and modify vertex-frame models easily and create 3D models in real time. Different surface modeling tasks are carried out to test the developed interactive tool and compare our proposed method with polygon and NURBS modeling and Coons surfaces. The results demonstrate the effectiveness of our proposed method and its advantages in reducing design variables, saving storage costs, and effective shape creation and manipulation.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interactive PDE patch-based surface modeling from vertex-frames

Wang

Xia

You

et al. 2022

Engineering with Computers

View full text Add to dashboard Cite

show abstract

“…However, freehand 3D sketches are highly unstructured (e.g., incomplete strokes, over-sketching, missing junctions, etc. ), whereas existing methods for surfacing 3D wireframes generally require a clean, connected graph [Bessmeltsev et al 2012;Pan et al 2015;Stanko et al 2016]. Due to its resilience to sparse and non-uniform sampling, our method is well-suited to perform this challenging surfacing task.…”

Section: Comparisonsmentioning

confidence: 95%

Variational implicit point set surfaces

Huang

Carr

2019

ACM Trans. Graph.

View full text Add to dashboard Cite

We propose a new method for reconstructing an implicit surface from an un-oriented point set. While existing methods often involve non-trivial heuristics and require additional constraints, such as normals or labelled points, we introduce a direct definition of the function from the points as the solution to a constrained quadratic optimization problem. The definition has a number of appealing features: it uses a single parameter (parameter-free for exact interpolation), applies to any dimensions, commutes with similarity transformations, and can be easily implemented without discretizing the space. More importantly, the use of a global smoothness energy allows our definition to be much more resilient to sampling imperfections than existing methods, making it particularly suited for sparse and non-uniform inputs. CCS Concepts: • Computing methodologies → Point-based models; Volumetric models.

show abstract

“…If a patch contains rulings, then the corresponding 3D curves can be trivially associated to a mesh by triangulating consecutive rulings, which does not require the introduction of interior points. If not, we generate a surface with minimal mean curvature interpolating the 3D border using the variational Laplacian approach [27,2]. In this case, the connectivity of this mesh is generated using a Delaunay triangulation of the 2D patch contours, where triangles are constrained to have a maximal area of 10% of the diagonal of the input image.…”

Section: Developable Surface Generationmentioning

confidence: 99%

Patterns from photograph: Reverse-engineering developable products

Fondevilla

Bousseau

Rohmer

et al. 2017

Computers & Graphics

Self Cite

View full text Add to dashboard Cite

Developable materials are ubiquitous in design and manufacturing. Unfortunately, general-purpose modeling tools are not suited to modeling 3D objects composed of developable parts. We propose an interactive tool to model such objects from a photograph. Users of our system load a single picture of the object they wish to model, which they annotate to indicate silhouettes and part boundaries. Assuming that the object is symmetric, we also ask users to provide a few annotations of symmetric correspondences. The object is then automatically reconstructed in 3D. At the core of our method is an algorithm to infer the 2D projection of rulings of a developable surface from the traced silhouettes and boundaries. We impose that the surface normal is constant along each ruling, which is a necessary property for the surface to be developable. We complement these developability constraints with symmetry constraints to lift the curve network in 3D. In addition to a 3D model, we output 2D patterns enabling to fabricate real prototypes of the object on the photo. This makes our method well suited for reverse engineering products made of leather, bent cardboard or metal sheets.

show abstract

Surfacing curve networks with normal control

Cited by 12 publications

References 42 publications

Interactive PDE patch-based surface modeling from vertex-frames

Interactive PDE patch-based surface modeling from vertex-frames

Variational implicit point set surfaces

Patterns from photograph: Reverse-engineering developable products

Contact Info

Product

Resources

About