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112
Laplacian Surface Editing
, 2004
"... Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We p ..."
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Cited by 177 (22 self)
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Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive freeform deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.
Fast surface reconstruction using the level set method
 In VLSM ’01: Proceedings of the IEEE Workshop on Variational and Level Set Methods
, 2001
"... In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data ..."
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Cited by 120 (11 self)
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In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surfacelike model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
Level Set Surface Editing Operators
 ACM TRANSACTIONS ON GRAPHICS
, 2002
"... We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed fun ..."
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Cited by 87 (5 self)
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We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines predefined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, selfintersection cannot occur, which guarantees the generation of physicallyrealizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scanconverted models.
Freeform Sketching with Variational Implicit Surfaces
 Computer Graphics Forum
, 2002
"... With the advent of sketchbased methods for shape construction, there is a new degree of power availablecreating several models. ..."
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Cited by 61 (3 self)
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With the advent of sketchbased methods for shape construction, there is a new degree of power availablecreating several models.
ShapeShop: SketchBased Solid Modeling with BlobTrees
, 2005
"... Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketchbased modeling system utilizes Hierarchical Implicit Volume M ..."
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Cited by 57 (15 self)
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Various systems have explored the idea of inferring 3D models from sketched 2D outlines. In all of these systems the underlying modeling methodology limits the complexity of models that can be created interactively. The ShapeShop sketchbased modeling system utilizes Hierarchical Implicit Volume Models (BlobTrees) as an underlying shape representation. The BlobTree framework supports interactive creation of complex, detailed solid models with arbitrary topology. A new technique is described for inflating 2D contours into rounded threedimensional implicit volumes. Sketchbased modeling operations are defined that combine these basic shapes using standard blending and CSG operators. Since the underlying volume hierarchy is by definition a construction history, individual sketched components can be nonlinearly edited and removed. For example, holes can be interactively dragged through a shape. ShapeShop also provides 2D drawing assistance using a new curvesketching system based on variational contours. A wide range of models can be sketched with ShapeShop, from cartoonlike characters to detailed mechanical parts. Examples are shown which demonstrate significantly higher model complexity than existing systems.
Constructive Volume Geometry
 Computer Graphics Forum
, 2000
"... We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar fields as fundamental building blocks, CVG provides highlevel algebraic representations of objects that are defined mathematically ..."
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Cited by 46 (17 self)
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We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar fields as fundamental building blocks, CVG provides highlevel algebraic representations of objects that are defined mathematically or built upon sampled or simulated datasets. It models amorphous phenomena as well as solid objects, and describes the interior as well as the exterior of objects. We also describe a hierarchical representation scheme for CVG, and a direct rendering method with a new approach for consistent sampling. The work has demonstrated the feasibility of combining a variety of graphics data types in a coherent modelling scheme.
A Procedural Approach to Authoring Solid Models
, 2002
"... We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our fra ..."
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Cited by 39 (2 self)
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We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our framework treats simulation as a modeling operator rather than simply as a tool for animation, thereby suggesting a new paradigm for modeling as well as a new level of abstraction for interacting with simulation environments.
Adaptive implicit surface polygonization using marching triangles
 COMPUTER GRAPHICS FORUM
, 2001
"... This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of t ..."
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Cited by 39 (6 self)
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This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crackclosing method invoked at the end of the mesh growing step. Eventually, we show that the marching triangles can be used as an incremental meshing technique in an interactive modeling environment. In contrast to existing incremental techniques based on spatial sudvision, no extra datastructure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.
Spatial Transfer Functions  A Unified Approach to Specifying Deformation in Volume Modeling and Animation
, 2003
"... In this paper, we introduce the concept of spatial transfer functions as a unified approach to volume modeling and animation. A spatial transfer function is a function that defines the geometrical transformation of a scalar field in space, and is a generalization and abstraction of a variety of defo ..."
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Cited by 28 (8 self)
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In this paper, we introduce the concept of spatial transfer functions as a unified approach to volume modeling and animation. A spatial transfer function is a function that defines the geometrical transformation of a scalar field in space, and is a generalization and abstraction of a variety of deformation methods. It facilitates a fieldbased representation, and can thus be embedded into a volumetric scene graph under the algebraic framework of constructive volume geometry. We show that when spatial transfer functions are treated as spatial objects, constructive operations and conventional transfer functions can be applied to such spatial objects. We demonstrate spatial transfer functions in action with the aid of a collection of examples in volume visualization, sweeping, deformation and animation. In association with these example, we describe methods for modeling and realizing spatial transfer functions, including simple procedural functions, operational decomposition of complex functions, large scale domain decomposition and temporal spatial transfer functions. We also discuss the implementation of spatial transfer functions in the vlib API and our efforts in deploying the technique in volume animation.
Interactive decal compositing with discrete exponential maps
 ACM Trans. Graph
, 2006
"... Figure 1: A clay elephant statue (left) was modeled using sketchbased implicitsurface modeling software. Then, a lapped base texture and 25 feature textures were extracted from 22 images taken with a digital camera and composited on the surface. Photography, image creation, and texture positioning ..."
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Cited by 21 (6 self)
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Figure 1: A clay elephant statue (left) was modeled using sketchbased implicitsurface modeling software. Then, a lapped base texture and 25 feature textures were extracted from 22 images taken with a digital camera and composited on the surface. Photography, image creation, and texture positioning was completed in under an hour. A method is described for texturing surfaces using decals, images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O(N logN) discrete approximation to the exponential map which requires only a single additional step in Dijkstra’s graphdistance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/featurematching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.