Fast generation of 3D deformable moving surfaces

Dynamic surface modeling is an important subject of geometric modeling due to their extensive applications in engineering design, entertainment and medical visualization. Many deformable objects in the real world are dynamic objects as their shapes change over time. Traditional geometric modeling methods are mainly concerned with static problems, therefore unsuitable for the representation of dynamic objects. Apart from the definition of a dynamic modeling problem, another key issue is how to solve the problem. Because of the complexity of the representations, currently the finite element method or finite difference method is usually used. Their major shortcoming is the excessive computational cost, hence not ideal for applications requiring real-time performance. We propose a representation of dynamic surface modeling with a set of fourth order dynamic partial differential equations (PDEs). To solve these dynamic PDEs accurately and efficiently, we also develop an effective resolution method. This method is further extended to achieve local deformation and produce n-sided patches. It is demonstrated that this new method is almost as fast and accurate as the analytical closed form resolution method and much more efficient and accurate than the numerical methods

On the spine of a PDE surface

yesThe spine of an object is an entity that can characterise the object¿s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes

Partial differential equations for function based geometry modelling within visual cyberworlds

We propose the use of Partial Differential Equations (PDEs) for shape modelling within visual cyberworlds. PDEs, especially those that are elliptic in nature, enable surface modelling to be defined as boundary-value problems. Here we show how the PDE based on the Biharmonic equation subject to suitable boundary conditions can be used for shape modelling within visual cyberworlds. We discuss an analytic solution formulation for the Biharmonic equation which allows us to define a function based geometry whereby the resulting geometry can be visualised efficiently at arbitrary levels of shape resolutions. In particular, we discuss how function based PDE surfaces can be readily integrated within VRML and X3D environment

A Level Set Approach for Denoising and Adaptively Smoothing Complex Geometry Stereolithography Files

abstract: Stereolithography files (STL) are widely used in diverse fields as a means of describing complex geometries through surface triangulations. The resulting stereolithography output is a result of either experimental measurements, or computer-aided design. Often times stereolithography outputs from experimental means are prone to noise, surface irregularities and holes in an otherwise closed surface. A general method for denoising and adaptively smoothing these dirty stereolithography files is proposed. Unlike existing means, this approach aims to smoothen the dirty surface representation by utilizing the well established levelset method. The level of smoothing and denoising can be set depending on a per-requirement basis by means of input parameters. Once the surface representation is smoothened as desired, it can be extracted as a standard levelset scalar isosurface. The approach presented in this thesis is also coupled to a fully unstructured Cartesian mesh generation library with built-in localized adaptive mesh refinement (AMR) capabilities, thereby ensuring lower computational cost while also providing sufficient resolution. Future work will focus on implementing tetrahedral cuts to the base hexahedral mesh structure in order to extract a fully unstructured hexahedra-dominant mesh describing the STL geometry, which can be used for fluid flow simulations.Dissertation/ThesisMasters Thesis Aerospace Engineering 201

3D Modelling with C2 Continuous PDE Surface Patches

In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly

Customizing personal objects: a pilot study using a smartphone to "design" a mini vase

This research tests a prototype design application (app) that uses real time sensor data, captured and processed via a smartphone, to generate a series of unique vase forms. Smartphone technology, with the support of embedded sensors, the app, and 3D printing processes, are applied in the design and instantiation of the vases. The users' feedback on the complete process is also examined. The research found that the described design process could be successfully applied to the design, and ultimately manufacture, of unique vase forms. Users stated that the app was easy to use, and allowed them to create intriguing forms they could not otherwise design. While both designers and non-designers found the app usable, they had different expectations from it. This uncovered areas where future iterations of the app could be improved