Interactive Restoration of Three-Dimensional Implicit Surface with Irregular Parts

Implicit surface generation based on the interpolation of surface points is one of the well-known modeling methods in the area of computer graphics.Several methods for the implicit surface reconstruction from surface points have been proposed on the basis of radial basis functions,a weighted sum of local functions,splines,wavelets,and combinations of them.However,if the surface points contain errors or are sparsely distributed,irregular components,such as curvature-shaped redundant bulges and unexpectedly generated high-frequency components,are commonly seen.This paper presents a framework for restoring irregular components generated on and around surfaces.Users are assumed to specify local masks that cover irregular components and parameters that determine the degree of restoration.The algorithm in this paper removes the defects based on the user-specific masks and parameters.Experiments have shown that the proposed methods can effectively remove redundant protrusions and jaggy noise.

Efficient volume preserving approach for skeleton-based implicit surfaces

This paper presents an efficient way to preserve the volume of implicit surfaces generated by skeletons. Recursive subdivision is used to efficiently calculate the volume. The criterion for subdivision is obtained by using the property of density functions and treating different types of skeletons respectively to get accurate minimum and maximum distances from a cube to a skeleton. Compared with the criterion generated by other ways such as using traditional Interval Analysis, Affine Arithmetic, or Lipschitz condition, our approach is much better both in speed and accuracy.

Technologies for implicit surfaces sampling with particle systems

Point-based surface has been widely used in computer graphics for modeling, animation, visualization, simulation of liq- uid and so on. Furthermore, particle-based approach can distribute the surface sampling points and control its parameters according to the needs of the application. In this paper, we examine several kinds of algorithms presented over the last decades, with the main focus on particle sampling technologies for implicit surface. Therefore, we classify various algorithms into categories, describe main ideas behind each categories, and compare the advantages and shortcomings of the algorithms in each category.

Hermite variational implicit surface reconstruction

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit volume model which fits the data points and normal constraints. Compared with variational implicit surfaces, we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs, the proposed method only needs to solve an n×n positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets.

Reflection and Refraction on Implicit Surfaces

Implicit surfaces are often used in computer graphics. They can be easily modeled and rendered, and many objects are composed of them in our daily life. In this paper, based on the concept of virtual objects, a novel method of real-time rendering is presented for reflection and refraction on implicit surface. The method is used to construct virtual objects from real objects quickly, and then render the virtual objects as if they were real objects except for one more step of merging their images with the real objects＇ images. Characteristics of implicit surfaces are used to compute virtual objects effectively and quickly. GPUs （Graphics Processing Units） are used to compute virtual vertices quickly and further accelerate the computing and rendering processes. As a result, realistic effects of reflections and refractions on implicit surfaces are rendered in real time.

Surface Reconstruction of 3D Scattered Data with Radial Basis Functions

We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.

Specification of Initial Shapes for Dynamic Implicit Curve/Surface Reconstruction

The dynamic implicit curve/surface reconstruction demands no special requirement on the initial shapes in general. In order to speed up the iteration in the reconstruction, we discuss how to specify the initial shapes so as to reflect the geometric information and the topology structure of the given data. The basic idea is based on the combination of the distance function and the generalized eigenvector fitting model. Keywords Sampson distance, generalized eigenvector fitting, dynamic implicit surface reconstruction

Model the Solvent-Excluded Surface of 3D Protein Molecular Structures Using Geometric PDE-Based Level-Set Method

This paper presents an approach to model the solvent-excluded surface(SES)of 3D protein molecular structures using the geometric PDE-based level-set method.The level-set method embeds the shape of 3D molecular objects as an isosurface or level set corresponding to some isovalue of a scattered dense scalar field,which is saved as a discretely-sampled,rectilinear grid,i.e.,a volumetric grid.Our level-set model is described as a class of tri-cubic tensor product B-spline implicit surface with control point values that are the signed distance function.The geometric PDE is evolved in the discrete volume.The geometric PDE we use is the mean curvature specified flow,which coincides with the definition of the SES and is geometrically intrinsic.The technique of speeding up is achieved by use of the narrow band strategy incorporated with a good initial approximate construction for the SES.We get a very desirable approximate surface for the SES.

Multiview Visibility Estimation for Image-Based Modeling

In this paper, we investigate the problem of determining regions in 3D scene visible to some given viewpoints when obstacles are present in the scene. We assume that the obstacles are composed of some opaque objects with closed surfaces. The problem is formulated in an implicit framework where the obstacles are represented by a level set function. The visible and invisible regions of the given viewpoints are determined through an efficient implicit ray tracing technique. As an extension of our approach, we apply the multiview visibility estimation to an image-based modeling technique. The unknown scene geometry and multiview visibility information are incorporated into a variational energy functional. By minimizing the energy functional, the true scene geometry as well as the accurate visibility information of the multiple views can be recovered from a number of scene images. This makes it feasible to handle the visibility problem of multiple views by our approach when the true scene geometry is unknown.

Radial Supershapes for Solid Modeling

In the previous work, an efficient method has been proposed to represent solid objects as multiple combinations of globally deformed supershapes. In this paper, this framework is applied with a new supershape implicit function that is based on the notion of radial distance and results are presented on realistic models composed of hundreds of hierarchically globally deformed supershapes. An implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives~ implicit representations using R-function theory. The surface corresponding to the zero-set of the implicit equation is efficiently and directly polygonized using the primitives,parametric forms. Moreover, hierarchical global deformations are considered to increase the range of shapes that can be modeled. The potential of the approach is illustrated by representing complex models composed of several hundreds of primitives inspired from CAD models of mechanical parts.

A unified framework for isotropic meshing based on narrowband Euclidean distance transformation

In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.

Geometric Design of Letters in Times Roman Font via RBF Meshless Collocation Method

Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.