263 research outputs found

    Designing Volumetric Truss Structures

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    We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself

    Smooth quasi-developable surfaces bounded by smooth curves

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    Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

    Triangular Gk-splines

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    In this paper a new approach is presented to construct piecewise polynomial G^k-surfaces of arbitrary topology and smoothness order k>= 1 of degree O(k). This approach generalizes some results presented in 1997 in CAGD and in 1999 at the St. Malo conference, respectively. In our construction only 4n polynomial patches are needed to fill an n-sided hole in a generalized C^k-(half)-boxspline surface. This is achieved by coalescing certain control points while at the same time maintaining a regular parametrization

    A novel approach for computing C-2-continuous offset of NURBS curves

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    Computing offset curves is an important geometric operation in areas of CAD/CAM, robotics, cam design and many industrial applications. In this paper, an algorithm for computing offsets of NURBS curves using C-2-continuous B-spline curves is presented. The progenitor curve in database is initially approximated by a line-fitting curve, and then the exact offset of this line-fitting curve is introduced as an initial offset. Based on the initial offset and a set of selected knots, an intended C-2-continuous B-spline curve is subsequently constructed. The method uses a new error-measuring scheme, which is based on the convex hull property of Bezier curves and the idea of cumulative errors, to calculate the global error bound of offset approximation. The method obtains offset curves with C-2 continuity and guarantees that the actual error bound is precisely within the prescribed tolerance. In addition, it also allows one to selectively parametrize the offset curve

    Smooth Subdivision Surfaces: Mesh Blending and Local Interpolation

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    Subdivision surfaces are widely used in computer graphics and animation. Catmull-Clark subdivision (CCS) is one of the most popular subdivision schemes. It is capable of modeling and representing complex shape of arbitrary topology. Polar surface, working on a triangle-quad mixed mesh structure, is proposed to solve the inherent ripple problem of Catmull-Clark subdivision surface (CCSS). CCSS is known to be C1 continuous at extraordinary points. In this work, we present a G2 scheme at CCS extraordinary points. The work is done by revising CCS subdivision step with Extraordinary-Points-Avoidance model together with mesh blending technique which selects guiding control points from a set of regular sub-meshes (named dominative control meshes) iteratively at each subdivision level. A similar mesh blending technique is applied to Polar extraordinary faces of Polar surface as well. Both CCS and Polar subdivision schemes are approximating. Traditionally, one can obtain a CCS limit surface to interpolate given data mesh by iteratively solving a global linear system. In this work, we present a universal interpolating scheme for all quad subdivision surfaces, called Bezier Crust. Bezier Crust is a specially selected bi-quintic Bezier surface patch. With Bezier Crust, one can obtain a high quality interpolating surface on CCSS by parametrically adding CCSS and Bezier Crust. We also show that with a triangle/quad conversion process one can apply Bezier Crust on Polar surfaces as well. We further show that Bezier Crust can be used to generate hollowed 3D objects for applications in rapid prototyping. An alternative interpolating approach specifically designed for CCSS is developed. This new scheme, called One-Step Bi-cubic Interpolation, uses bicubic patches only. With lower degree polynomial, this scheme is appropriate for interpolating large-scale data sets. In sum, this work presents our research on improving surface smoothness at extraordinary points of both CCS and Polar surfaces and present two local interpolating approaches on approximating subdivision schemes. All examples included in this work show that the results of our research works on subdivision surfaces are of high quality and appropriate for high precision engineering and graphics usage

    NX 10 for Engineering Design -- Learning Edition

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    NX is one of the world’s most advanced and tightly integrated CAD/CAM/CAE product development solution. Spanning the entire range of product development, NX delivers immense value to enterprises of all sizes. It simplifies complex product designs, thus speeding up the process of introducing products to the market. The NX software integrates knowledge-based principles, industrial design, geometric modeling, advanced analysis, graphic simulation, and concurrent engineering. The software has powerful hybrid modeling capabilities by integrating constraint-based feature modeling and explicit geometric modeling. In addition to modeling standard geometry parts, it allows the user to design complex free-form shapes such as airfoils and manifolds. It also merges solid and surface modeling techniques into one powerful tool set. This self-guiding tutorial provides a step-by-step approach for users to learn NX 10. It is intended for those with no previous experience with NX. However, users of previous versions of NX may also find this tutorial useful for them to learn the new user interfaces and functions. The user will be guided from starting an NX 10 session to creating models and designs that have various applications. Each chapter has components explained with the help of various dialog boxes and screen images. These components are later used in the assembly modeling, machining and finite element analysis. The files of components are also available online to download and use. We first released the tutorial for Unigraphics 18 and later updated for NX 2 followed by the updates for NX 3, NX 5, NX 7 and NX 9. This write-up further updates to NX 10. Our previous efforts to prepare the NX self-guiding tutorial were funded by the National Science Foundation’s Advanced Technological Education Program and by the Partners of the Advancement of Collaborative Engineering Education (PACE) program

    Controlling the interpolation of NURBS curves and surfaces

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    The primary focus of this thesis is to determine the best methods for controlling the interpolation of NURBS curves and surfaces. The various factors that affect the quality of the interpolant are described, and existing methods for controlling them are reviewed. Improved methods are presented for calculating the parameter values, derivative magnitudes, data point spacing and twist vectors, with the aim of producing high quality interpolants with minimal data requirements. A new technique for obtaining the parameter values and derivative magnitudes is evaluated, which constructs a C1^1 cubic spline with orthogonal first and second derivatives at specified parametric locations. When this data is used to create a C2^2 spline, the resulting interpolant is superior to those constructed using existing parameterisation and derivative magnitude estimation methods. Consideration is given to the spacing of data points, which has a significant impact on the quality of the interpolant. Existing methods are shown to produce poor results with curves that are not circles. Three new methods are proposed that significantly reduce the positional error between the interpolant and original geometry. For constrained surface interpolation, twist vectors must be estimated. A method is proposed that builds on the Adini method, and is shown to have improved error characteristics. In numerical tests, the new method consistently outperforms Adini. Interpolated surfaces are often required to join together smoothly along their boundaries. The constraints for joining surfaces with parametric and geometric continuity are discussed, and the problem of joining NN patches to form an NN-sided region is considered. It is shown that regions with odd NN can be joined with G1^1 continuity, but those with even NN or requiring G2^2 continuity can only be obtained for specific geometries

    Sketch-based path design

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    We first present a novel approach to sketching 2D curves with minimally varying curvature as piecewise clothoids. A stable and efficient algorithm fits a sketched piecewise linear curve using a number of clothoid segments with G2 continuity based on a specified error tolerance. We then present a system for conceptually sketching 3D layouts for road and other path networks. Our system makes four key contributions. First, we generate paths with piecewise linear curvature by fitting 2D clothoid curves to strokes sketched on a terrain. Second, the height of paths above the terrain is automatically determined using a new constraint optimization formulation of the occlusion relationships between sketched strokes. Third, we present the break-out lens, a novel widget inspired by break-out views used in engineering visualization, to facilitate the in-context and interactive manipulation of paths from alternate view points. Finally, our path construction is terrain sensitive. ii Acknowledgements I would like to acknowledge the efforts of my supervisor, Karan Singh, and thank him for his guidance over the duration of the Masters program. I learned much from him a
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