Variational surface modeling

Welch, William; Witkin, Andrew

doi:10.1145/133994.134033

Cited by 161 publications

(53 citation statements)

References 16 publications

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“…These simulation methods usually require the minimization of bending and stretching energies modeled with thin shell or thin plate functional [8,52,53] .…”

Section: Discussionmentioning

confidence: 99%

Gradient Domain Mesh Deformation — A Survey

Zhou

2009

J. Comput. Sci. Technol.

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This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variational optimization problem can be casted into a sparse linear system. Fast sparse linear solver can be adopted to generate deformation result interactively, or even in real-time. The nonlinear nature of gradient domain mesh deformation leads to the development of two categories of deformation methods: linearization methods and nonlinear optimization methods. Basically, the linearization methods only need to solve the linear least-squares system once. They are fast, easy to understand and control, while the deformation result might be suboptimal. Nonlinear optimization methods can reach optimal solution of deformation energy function by iterative updating. Since the computation of nonlinear methods is expensive, reduced deformable models should be adopted to achieve interactive performance. The nonlinear optimization methods avoid the user burden to input transformation at deformation handles, and they can be extended to incorporate various nonlinear constraints, like volume constraint, skeleton constraint, and so on. We review representative methods and related approaches of each category comparatively and hope to help the user understand the motivation behind the algorithms. Finally, we discuss the relation between physical simulation and gradient domain mesh deformation to reveal why it can achieve physically plausible deformation result.

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“…These simulation methods usually require the minimization of bending and stretching energies modeled with thin shell or thin plate functional [8,52,53] .…”

Section: Discussionmentioning

confidence: 99%

Gradient Domain Mesh Deformation — A Survey

Zhou

2009

J. Comput. Sci. Technol.

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“…Piegl [6] discussed a fundamental property of NURBS curves called the cross ratio which quantifies the push/pull effect of weights for NURBS curves. Piegl [6] and Welch [7] also reported various shape operator algorithms such as warp, flatten, bend, stretch, twist and taper. Fowler and Bartels [8] developed a shape operator, called the constraint-based curve and surface shaping, which forces a curve or surface to assume the specified derivatives at selected parameter values.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Constrained optimizations The idea of using constrained optimizations for directly manipulating freeform surfaces has been reported in previous works [7,20,21,22]. Sarraga [22] discussed methods for surface optimization so as to design the ''acceptable surface shape'' which depends critically on the surface designer, ranging from very demanding stylists who concentrate on aesthetics to manufacturing engineers who want simple shapes.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Within such limited objectives, excellent surface shapes can be automatically generated, sometimes with computer runtimes of less than one minute. Welch [7] presented an infinitely malleable piecewise smooth surface model for users to attach a point or curve constraint to the surface. The constrained variational optimization method has been used for the surface fairness (smooth) evaluation.…”

Section: Literature Reviewmentioning

confidence: 99%

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Constrained deformation of freeform surfaces using surface features for interactive design

Zheng

Chan

Gibson

2003

The International Journal of Advanced Manufacturing Technology

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There is an increasing demand in conceptual design for more intuitive methods for creating and modifying freeform curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters but also on the user's specified constraints and shapes. This paper presents a new surface representation model for freeform surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called a parent surface. Based on the surface model, the authors develop several novel deformation methods which are named SingleDef (Single-point constraint based deformation method), MultiDef (Multiplepoints constraints based deformation method), CurDef (Curve constraints based deformation method) and FeatDef (Feature constraint based deformation method). The techniques for freeform surface deformation allow conceptual designers to modify a parent surface by directly applying point constraints, curve constraint or a surface constraint to the parent surface. The deformation methods are implemented in an experimental CAD system. The results show that designers can easily and intuitively control the surface shape.

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“…In such cases where mathematical expression does not exist for f, one can find an interpolation function. In this manner, moving least square method [1,12], or several other methods [7,13,16,21,23] can be used.…”

Section: Introductionmentioning

confidence: 99%

A General Method for Evaluation of 2D and 3D Domain Integrals Without Domain Discretization and its Application in BEM

Hematiyan

2006

Comput Mech

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A robust method is presented to evaluate 2D and 3D domain integrals without domain discretization. Each domain integral is transformed into a double integral, a boundary integral and a 1D integral. Both integrals are evaluated by adaptive Simpson quadrature method. The method can be used to evaluate domain integrals over simply or multiply connected regions with any arbitrary form of integrands. As an application of the method, domain integrals produced in boundary element formulation of potential and elastostatic problems are analyzed. Several examples are provided to show the validity and accuracy of the method.

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Variational surface modeling

Cited by 161 publications

References 16 publications

Gradient Domain Mesh Deformation — A Survey

Gradient Domain Mesh Deformation — A Survey

Constrained deformation of freeform surfaces using surface features for interactive design

A General Method for Evaluation of 2D and 3D Domain Integrals Without Domain Discretization and its Application in BEM

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