C ∞ smooth freeform surfaces over hyperbolic domains

Efficient optimal design of smooth optical freeform surfaces using ray targeting

This Special Issue of JCISE is drawn from outstanding papers presented at the 2002 ACM Solid Modeling symposium. This is the second year that JCISE and ACM have collaborated to produce such a Special Issue, in what promises to become an annual tradition. Previously, JCISE V1, N4 (December 2001) contained selected papers from the 2001 symposium. The ACM/SIGGRAPH Symposia on Solid Modeling and Applications provide a premier international forum for the exchange of original research results and important practical applications in all areas of solid modeling and its applications. The symposia series brings together leading researchers, practitioners and graduate students working in this field. The seventh ACM Symposium on Solid Modeling and Applications was held at the Max Planck Institute for Informatics in Saarbruecken, Germany on June 17–21, 2002, the first to be held outside North America. The symposium was co-chaired by Hans-Peter Seidel of the Max Planck Institute and Vadim Shapiro of the University of Wisconsin, Madison, USA. The international program committee was co-chaired by Kunwoo Lee of Seoul National University, Seoul, Korea and Nicholas M. Patrikalakis of the Massachusetts Institute of Technology, Cambridge, Mass., USA. The program committee comprised of 25 leading experts on solid modeling theory and its applications from academia and industry working in 10 different countries from around the world. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan, 1999 and 2001. Starting with 2002, the Symposium is expected to be held annually, alternating in location between the USA and other countries within a two year period. Ninety-three papers were submitted to the 2002 symposium and reviewed by one member of the program committee and at least three additional referees. Based on these review results, the program co-chairs selected 26 papers for plenary presentation and 17 papers for poster presentation at the symposium. From the 26 plenary papers, the program co-chairs selected 9 papers for this special issue of JCISE. The selection was based on quality and engineering relevance. All selected papers were updated and extended since the version published in the conference proceedings, and were reviewed again by at least two additional referees and revised accordingly. The topics of the papers selected cover the following solid modeling areas: editing of free-form surfaces with haptic methods; reverse engineering of surface models; meshing of implicit surfaces; topological frameworks for part families; free-form surface design; design of transport elements in complex aircraft structures; collaborative framework for part and assembly modeling; modeling of heterogeneous solids; and iso-surface extraction methods. We wish to thank the authors for revising and extending their papers for this special issue of JCISE and the referees for their valuable comments, which improved the quality of the papers included. We hope that you the readers of JCISE will find these papers stimulating and interesting and that this will encourage you to participate in future solid modeling conferences and submit papers on this important area to these conferences and to regular issues of this ASME Transactions, JCISE, which also officially co-sponsored by ACM.

3D imaging has become a standard tool in medical diagnostics and, while software is available to visualize volumetric data sets, we do not yet have software that can efficiently transform 3D scan data to solid models that are useful for engineering design and analysis. Why not? Currently, deriving solid models from 3D scans involves 3 steps: (1) segmentation: identification of voxels associated with the structure; (2) polygonization: computing a set of polygons that approximate the surface of the structure; and (3) repair: removing stray voxels and polygons, specifying connectivity, and establishing consistent orientation. Significant progress has been made on accurate, automated segmentation (recent work by Hu et al. (Image Segmentation and Registration for the Analysis of Joint Motion From 3D MRI,” Proc SPIE 6141, pp. 133–142, Medical Imaging: Visualization, Image-Guided Procedures, & Display, 2006), combining graph cuts with level sets is of particular interest) but effective polygonization cannot be guaranteed. In the worst case, manual repairs are needed to patch holes and remove stray elements. Even if a valid boundary representation (b-rep) model is obtained, accurate models contain so many polygons that modeling operations become unfeasible. Moreover, regardless of accuracy, the surface of a polyhedral model will never be truly smooth. In previous work (Storti, D., et al., Artifact vs. Anatomy: Dealing With Conflict of Geometric Modeling Descriptions,” SAE 2007 Transactions Journal of Passenger Cars: Electronic and Electrical Systems, Paper No. 2007-01-2450, Vol. 116, pp. 813–823, 2007), we proposed overcoming the barriers to creating solid models from 3D scans by employing a new solid modeling description, wavelet SDF-reps, that lies much closer to the native 3D scan format and eliminates polygonization. Here, we focus on the ability to produce models with smooth surfaces that are important for various biomedical simulations. For example, careful studies of joint function involve detailed modeling of ligament wrapping; i.e., connective tissue moving across bone surface as the joint configuration changes. Realistic behavior cannot be obtained if the ligament is snagging on or snapping across convex vertices of a polyhedral model. Similarly, haptic simulation of a catheter navigating through the circulatory system cannot be realistic if the catheter gets stuck in concave vertices of the anatomical model. How can the new modeling format address such issues? Wavelet SDF-reps take advantage of a by-product of the segmentation algorithm (Hue et al.) which converts the raw voxel intensity values to a grid of signed distance values. Applying an appropriate interpolant such as Daubechies wavelets (Daubechies, I., Wavelets, CBMS-NS Series in Applied Mathematics, SIAM Publications, Philadelphia, 1992) then produces an implicit or function-based (f-rep) solid model of the segmented structure. Wavelet SDF-reps are inherently multi-resolution and support significant data compression and medial axis computation. We illustrate the capability of wavelet SDF-reps to support smooth models and enable analysis of curvature features.

Free-form curves and surfaces represented by control points together with well-defined basis functions are widely used in computer aided geometric design. Efficient evaluation of points and derivatives of free-form curves and surfaces plays an important role in interactive rendering or CNC machining. In this paper we show that free-form curves with properly defined basis functions are the solutions of linear differential systems. By employing typical numerical methods for solving the differential systems, points and derivatives of free-form curves and surfaces can be computed in a dynamical way. Compared with traditional methods for evaluating free-form curves and surfaces there are two advantages of the proposed technique. First, the proposed method is universal and efficient for evaluating a large class of free-form curves and surfaces. Second, the evaluation needs only arithmetic operations even when the free-form curves and surfaces are defined using some transcendental functions.

We present new interaction and visualization paradigms relying on free form surfaces for studying and exploring human anatomy. We propose an interface for building three-dimensional anatomical scenes incorporating 3D anatomical organ models, freely orientated slices and free form surfaces extracted from the Visible Human dataset. Compared with planar slices, free form surfaces allow to follow curved anatomic structures such as the aorta tree or the pelvis. In the present paper, we describe in detail 3D interaction techniques for creating free form surfaces. The interactive placement of surface boundary curves relies on the combination of an interactive slice navigator and of a 3D visualization interface integrated within a single java applet. Surface boundary curve control points are placed with the mouse at the desired locations within the selected slices. The corresponding boundary curves are displayed in the 3D visualization interface as fat 3D cubic spline curves, which provide immediate feedback. Boundary curves may be easily duplicated, translated and modified. The specified boundary curves are interpolated by Coons patches, yielding a perfectly smooth surface. That surface may be visualized in combination with semi-transparent organ models. It may also be flattened and shown in a separate window. The presented application is available online as a Java applet (http://visiblehuman.epfl.ch).

Automated sequence arrangement of 3D point data for surface fitting in reverse engineering

The computer aided design and manufacturing CAD/CAM integration systems were focused on product representation techniques or product modeling. In product design process trends are currently tend to use freeform surface that modeling by using (Non-Uniform Rational B-Spline Surface (NURBS), B-spline, Bezier) technique to suit aesthetic, functional and manufacturability requirements. Set of problem are faced difficulties in recognizing freeform feature such polishing process after the finishing machining process by multi-axis CNC machine, sheet metal forming, and freeform surface machining. In this research, a new developed methodology has been introduced for automatic recognition of the depression and protrusion features. The 3D CAD solid model is designed by freeform surfaces of non-uniform B-spline technique and then extracts their parameter by IGES standard format file. The developed methodology has four major steps: Subdivision of Non-uniform B-spline surface, surface analysis, primitives shape detection, and recognition of geometric features.

Toolpath generation for ultraprecision machining: Freeform surface generation and extrapolation

Teichmuller shape space is a finite dimensional Riemannian manifold, where each point represents a class of surfaces, which are conformally equivalent, and a path represents a deformation process from one shape to the other. Two surfaces in the real world correspond to the same point in the Teichmuller space, only if they can be conformally mapped to each other. Teichmuller shape space can be used for surface classification purpose in shape modeling. This work focuses on the computation of the coordinates of high genus surfaces in the Teichmuller space. The coordinates are called as Fenchel-Nielsen coordinates. The main idea is to deform the surface conformally using surface Ricci flow, such that the Gaussian curvature is −1 everywhere. The surface is decomposed to several pairs of hyperbolic pants. Each pair of pants is a genus zero surface with three boundaries, equipped with hyperbolic metric. Furthermore, all the boundaries are geodesics. Each pair of hyperbolic pants can be uniquely described by the lengths of its boundaries. The way of gluing different pairs of pants can be represented by the twisting angles between two adjacent pairs of pants which share a common boundary. The algorithms are based on Teichmuller space theory in conformal geometry, and they utilize the discrete surface Ricci flow. Most computations are carried out using hyperbolic geometry. The method is automatic, rigorous and efficient. The Teichmuller shape space coordinates can be used for surface classification and indexing. Experimental results on surfaces acquired from real world showed the practical value of the method for geometric database indexing, shape comparison and classification.

3D solid models for parts with regular-form surfaces (PRFSs) are effectively generated using traditional parametric design techniques. A new model is obtained by changing some parameters defining the model. The parts with free-form surfaces (PFFSs), however, cannot be defined by several parameters. Usually they are defined by some geometric elements like profile curves. The traditional parametric design approaches have not easily dealt with the PFFSs. A method for generating a solid model and an engineering drawing for PFFSs is proposed in this paper: First, the new profiles are generated from input point data. Second, the profile information is extracted from the existing model. Last, the old profiles are replaced with the new profiles. This method can preserve the associative information of the existing model and automatically generate the drawing including views, dimensions, and annotations. The proposed method has been implemented using a commercial CAD/CAM system, Unigraphics, and API functions written in C-language, and were applied to the blades of a turbine generator. Some illustrative examples are provided in order to show the effectiveness of the proposed method.

The freeform surface is treated as a single machining region for most traditional toolpath generation algorithms. However, due to the complexity of a freeform surface, it is impossible to produce a high-quality surface using one unique machining process. Hence, region-based methods are widely investigated for freeform surface machining to achieve an optimized toolpath. The Non-Uniform Rational B-spline Surface (NURBS) represented freeform surface is not suitable for region-based toolpath generation because of the surface gaps caused by NURBS trimming and merging operations. To solve the limitation of the NURBS, T-spline is proposed with the advantages of being gap-free, having less control points, and local refinement, which is an ideal tool for region-based toolpath generation. Thus, T-spline is introduced to represent a freeform surface for its toolpath generation in the paper. A region-based toolpath generation method for the T-spline surface is proposed based on watershed technology. Firstly, watershed-based feature recognition is presented to divide the T-spline surface into a set of sub-regions. Secondly, the concept of a PolyBoundingBox that consists of a set of minimum bounding boxes is proposed to describe the sub-regions, and Manufacturing-Suitable Regions are constructed with the help of T-spline local refinement and the PolyBoundingBox. In the end, an optimized multi-rectangles toolpath generation algorithm is applied for sub-regions. The proposed method is tested using three synthetic T-spline surfaces, and the comparison results show the advantage in toolpath length and toolpath reversing number.

Mesh surfaces with planar hexagonal faces, what we refer to as PH meshes, offer an elegant way of paneling freeform architectural surfaces due to their node simplicity (i.e., valence-3 nodes) and naturally appealing layout. We investigate PH meshes to understand how the shape, size, and pattern of PH faces are constrained by surface geometry. This understanding enables us to develop an effective method for paneling freeform architectural surfaces with PH meshes. Our method first constructs an ideal triangulation of a given smooth surface, guided by surface geometry. We show that such an ideal triangulation leads to a Dupin-regular PH mesh via tangent duality on the surface. We have developed several novel and effective techniques for improving undesirable mesh layouts caused by singular behaviors of surface curvature. We compute support structures associated with PH meshes, including exact vertex offsets and approximate edge offsets, as demanded in panel manufacturing. The efficacy of our method is validated by a number of architectural examples.

Electroforming is a nonconventional manufacturing process of metallic parts by using electrodeposition on a pre-shaped cathodic mandrel. It can produce a metallic structure and builds the material by atom level. Smooth free surface and normal edge deposition are important to the electroforming of complex-shaped parts. A hybrid electroforming process combining mechanical particle polishing and auxiliary cathode was proposed to improve the quality of the free surface and inhibit the over-deposition on the mandrel edge. The smooth effect of particle polishing on the growing deposit surface was theoretical analyzed. The effect of the auxiliary cathode for a complex model with freeform surface was simulated. Contrast electroforming tests were performed in a bath without any addition agents under different conditions. The results positively proved the smooth effect and the overgrowth inhibition effect of the hybrid process. A nickel complex sample with smooth free surface and inconspicuous edge overgrowth was successfully electroformed.

Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels. This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces. The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface. We present a B-spline based optimization framework for efficient computing with D-strip models. In particular we study conical and circular models, which semi-discretize the network of principal curvature lines, and which enjoy elegant geometric properties. Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems.

This paper describes the use of a previously developed surface model for representing 3D geometric information that is subject to uncertainty. The proposed model is based on a geometric data fusion technique that allows the efficient approximation of arbitrary triangular meshes in space with smooth surfaces. This paper shows how the shape modifiers defined in the model can be used to represent both global and local uncertainty associated with the input data. The possibility of handling scattered 3D points, taking into account their corresponding uncertainties, makes this technique a suitable tool for modeling free-form surfaces acquired through sensing, as well as for integrating 3D data obtained from multiple sensors with different associated confidences.