Universal attraction force-inspired freeform surface modeling for 3D sketching

This paper presents a novel freeform surface modeling method to construct a freeform surface from 3D sketch. The approach is inspired by Newton’s universal attraction force law to construct a surface model from rough boundary curves and unorganized interior characteristic curves which may cross the boundary curves or not. Based on these unorganized curves, an initial surface can be obtained for conceptual design and it can be improved later in a commercial package. The approach has been tested with examples and it is capable of dealing with unorganized design curves for surface modeling

Progressive surface modeling scheme from unorganised curves

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final surface. The base surface is first constructed as a regular Coons surface and upon receiving an interior curve sketch, it is then updated. With this progressive modelling scheme, a final surface with multiple sub-surfaces can be obtained from a set of unorganised curves and transferred to commercial surface modelling software for detailed modification. The approach has been tested with examples based on 3D motion sketches; it is capable of dealing with unorganised design curves for surface modelling in conceptual design. Its limitations have been discussed

High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

Efficient ordinary differential equation-based modelling and skin deformations for character animation.

In the area of character animation, skin surface modelling, rigging and skin deforamtion are three essential aspects. Due to the different complexity of the characters, the time cost on creating corresponding skin surface model, animation skeleton in order to achieve diverse skin de- formations, fluctuates from several hours to several weeks. More importantly, the data size of skin deformations could sharply influence the efficiency of generating animation. Smaller data size can also speed up character animation and transmission over computer networks. Over years, researchers have developed a variety of skin deformation techniques. Geometric skin deformation approaches have high efficiency but low realism. Example-based skin deformation approaches interpolate a set of given example poses to improve realism and effects that cannot be easily produced by geometric approaches. Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, many recent activities have initiated the research of integrating geometric, example-based, and physics-based skin deformation approaches. The current research is to develop techniques based on Ordinary Differentical Equations (ODE) to efficiently create C2 continuous skin surfaces through two boundary curves, automatically generate skeleton to make the rigging process fast enough for highly efficient computer animation applications, and achieve physically realistic skin deformations for character animation by integrating geometric, physical and data-driven methods. Meanwhile, it is the first attempt to obtain an analytical solution to realistic physics-based skin deformations for highly efficient computation, to avoid the solving of a large set of linear equations, which largely reduces data size and computing time. The basic idea is to build ODE mechanics model, involve isoparametric curves and Fourier Series representation, develop accurate and efficient solutions to calculate physical skin deformations through interpolating input realistic reconstructed 3D models. The proposed techniques will greatly avoid tedious manual work, reduce data size, improve skin deformation realism, and raise efficiency of producing character animation

Focus+Context via Snaking Paths

Focus+context visualizations reveal specific structures in high detail while effectively depicting its surroundings, often relying on transitions between the two areas to provide context. We present an approach to generate focus+context visualizations depicting cylindrical structures along snaking paths that enables the structures themselves to become the transitions and focal areas, simultaneously. A method to automatically create a snaking path through space by applying a path finding algorithm is presented. A 3D curve is created based on the 2D snaking path. We describe a process to deform cylindrical structures in segmented volumetric models to match the curve and provide preliminary geometric models as templates for artists to build upon. Structures are discovered using our constrained volumetric sculpting method that enables removal of occluding material while leaving them intact. We find the resulting visualizations effectively mimic a set of motivating illustrations and discuss some limitations of the automatic approach

Accurate geometry reconstruction of vascular structures using implicit splines

3-D visualization of blood vessel from standard medical datasets (e.g. CT or MRI) play an important role in many clinical situations, including the diagnosis of vessel stenosis, virtual angioscopy, vascular surgery planning and computer aided vascular surgery. However, unlike other human organs, the vasculature system is a very complex network of vessel, which makes it a very challenging task to perform its 3-D visualization. Conventional techniques of medical volume data visualization are in general not well-suited for the above-mentioned tasks. This problem can be solved by reconstructing vascular geometry. Although various methods have been proposed for reconstructing vascular structures, most of these approaches are model-based, and are usually too ideal to correctly represent the actual variation presented by the cross-sections of a vascular structure. In addition, the underlying shape is usually expressed as polygonal meshes or in parametric forms, which is very inconvenient for implementing ramification of branching. As a result, the reconstructed geometries are not suitable for computer aided diagnosis and computer guided minimally invasive vascular surgery. In this research, we develop a set of techniques associated with the geometry reconstruction of vasculatures, including segmentation, modelling, reconstruction, exploration and rendering of vascular structures. The reconstructed geometry can not only help to greatly enhance the visual quality of 3-D vascular structures, but also provide an actual geometric representation of vasculatures, which can provide various benefits. The key findings of this research are as follows: 1. A localized hybrid level-set method of segmentation has been developed to extract the vascular structures from 3-D medical datasets. 2. A skeleton-based implicit modelling technique has been proposed and applied to the reconstruction of vasculatures, which can achieve an accurate geometric reconstruction of the vascular structures as implicit surfaces in an analytical form. 3. An accelerating technique using modern GPU (Graphics Processing Unit) is devised and applied to rendering the implicitly represented vasculatures. 4. The implicitly modelled vasculature is investigated for the application of virtual angioscopy

Theory and applications of bijective barycentric mappings

Barycentric coordinates provide a convenient way to represent a point inside a triangle as a convex combination of the triangle's vertices, and to linearly interpolate data given at these vertices. Due to their favourable properties, they are commonly applied in geometric modelling, finite element methods, computer graphics, and many other fields. In some of these applications it is desirable to extend the concept of barycentric coordinates from triangles to polygons. Several variants of such generalized barycentric coordinates have been proposed in recent years. An important application of barycentric coordinates consists of barycentric mappings, which allow to naturally warp a source polygon to a corresponding target polygon, or more generally, to create mappings between closed curves or polyhedra. The principal practical application is image warping, which takes as input a control polygon drawn around an image and smoothly warps the image by moving the polygon vertices. A required property of image warping is to avoid fold-overs in the resulting image. The problem of fold-overs is a manifestation of a larger problem related to the lack of bijectivity of the barycentric mapping. Unfortunately, bijectivity of such barycentric mappings can only be guaranteed for the special case of warping between convex polygons or by triangulating the domain and hence renouncing smoothness. In fact, for any barycentric coordinates, it is always possible to construct a pair of polygons such that the barycentric mapping is not bijective. In the first part of this thesis we illustrate three methods to achieve bijective mappings. The first method is based on the intuition that, if two polygons are sufficiently close, then the mapping is close to the identity and hence bijective. This suggests to ``split'' the mapping into several intermediate mappings and to create a composite barycentric mapping which is guaranteed to be bijective between arbitrary polygons, polyhedra, or closed planar curves. We provide theoretical bounds on the bijectivity of the composite mapping related to the norm of the gradient of the coordinates. The fact that the bound depends on the gradient implies that these bounds exist only if the gradient of the coordinates is bounded. We focus on mean value coordinates and analyse the behaviour of their directional derivatives and gradient at the vertices of a polygon. The composition of barycentric mappings for closed planar curves leads to the problem of blending between two planar curves. We suggest to solve it by linearly interpolating the signed curvature and then reconstructing the intermediate curve from the interpolated curvature values. However, when both input curves are closed, this strategy can lead to open intermediate curves. We present a new algorithm for solving this problem, which finds the closed curve whose curvature is closest to the interpolated values. Our method relies on the definition of a suitable metric for measuring the distance between two planar curves and an appropriate discretization of the signed curvature functions. The second method to construct smooth bijective mappings with prescribed behaviour along the domain boundary exploits the properties of harmonic maps. These maps can be approximated in different ways, and we discuss their respective advantages and disadvantages. We further present a simple procedure for reducing their distortion and demonstrate the effectiveness of our approach by providing examples. The last method relies on a reformulation of complex barycentric mappings, which allows us to modify the ``speed'' along the edges to create complex bijective mappings. We provide some initial results and an optimization procedure which creates complex bijective maps. In the second part we provide two main applications of bijective mapping. The first one is in the context of finite elements simulations, where the discretization of the computational domain plays a central role. In the standard discretization, the domain is triangulated with a mesh and its boundary is approximated by a polygon. We present an approach which combines parametric finite elements with smooth bijective mappings, leaving the choice of approximation spaces free. This approach allows to represent arbitrarily complex geometries on coarse meshes with curved edges, regardless of the domain boundary complexity. The main idea is to use a bijective mapping for automatically warping the volume of a simple parametrization domain to the complex computational domain, thus creating a curved mesh of the latter. The second application addresses the meshing problem and the possibility to solve finite element simulations on polygonal meshes. In this context we present several methods to discretize the bijective mapping to create polygonal and piece-wise polynomial meshes

Specifying a hybrid, multiple material CAD system for next-generation prosthetic design

For many years, the biggest issue that causes discomfort and hygiene issues for patients with lower limb amputations have been the interface between body and prosthetic, the socket. Often made of an inflexible, solid polymer that does not allow the residual limb to breathe or perspire and with no consideration for the changes in size and shape of the human body caused by changes in temperature or environment, inflammation, irritation and discomfort often cause reduced usage or outright rejection of the prosthetic by the patient in their day to day lives. To address these issues and move towards a future of improved quality of life for patients who suffer amputations, Loughborough University formed the Next Generation Prosthetics research cluster. This work is one of four multidisciplinary research studies conducted by members of this research cluster, focusing on the area of Computer Aided Design (CAD) for improving the interface with Additive Manufacture (AM) to solve some of the challenges presented with improving prosthetic socket design, with an aim to improve and streamline the process to enable the involvement of clinicians and patients in the design process. The research presented in this thesis is based on three primary studies. The first study involved the conception of a CAD criteria, deciding what features are needed to represent the various properties the future socket outlined by the research cluster needs. These criteria were then used for testing three CAD systems, one each from the Parametric, Non Uniform Rational Basis Spline (NURBS) and Polygon archetypes respectively. The result of these tests led to the creation of a hybrid control workflow, used as the basis for finding improvements. The second study explored emerging CAD solutions, various new systems or plug-ins that had opportunities to improve the control model. These solutions were tested individually in areas where they could improve the workflow, and the successful solutions were added to the hybrid workflow to improve and reduce the workflow further. The final study involved taking the knowledge gained from the literature and the first two studies in order to theorise how an ideal CAD system for producing future prosthetic sockets would work, with considerations for user interface issues as well as background CAD applications. The third study was then used to inform the final deliverable of this research, a software design specification that defines how the system would work. This specification was written as a challenge to the CAD community, hoping to inform and aid future advancements in CAD software. As a final stage of research validation, a number of members of the CAD community were contacted and interviewed about their feelings of the work produced and their feedback was taken in order to inform future research in this area

Blending techniques in Curve and Surface constructions

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A Novel Geometric Theory of On-Machine Tool Measurement and Practical, Optimal Approaches to Highly Accurate and Efficient On-Machine Measurement

Modern industry trends to smart machining that improves productivity at a low cost. The kernel technology of intelligent manufacturing is the automatic on-machine measurement (OMM). When applying OMM technology to computer numerical control (CNC) machines, in-situ measurement takes place in the machining environment without the need of unloading the tool and the part. However, adverse measurement environment, limitations on the efficiency of data capturing and processing, and diversified measured objects render efficient and accurate OMM very difficult. Holistic solutions are needed to advance OMM technology and therefore many scientific topics are involved. This work primarily focuses on geometric modeling of the on-machine cutting tool measurement and kinematic modeling for the calibration process of both the probe and the machine. On-machine cutting tool measurement often takes place on a laser tool setter. However, the geometry principles of the gauging mechanisms of laser tool setters are complicated and had not been studied before. This dissertation modeled such a gauging mechanism and presented virtual simulations of the measurement processes on laser tool setters based on geometry principles. The virtual simulations can predict and compensate the measurement errors, allowing for accurate tool setter calibration processes in practical situations. For cutting tool measurement, the tool length characteristic curve for measurement of round-insert mills is discovered. The derivation of the tool length characteristic curve was carried out by modeling the geometries of tool length measurement processes on a laser tool setter. Based on this characteristic curve, an accurate and efficient approach to measuring lengths of mills with round inserts and bottom cutting edge wear is proposed. Current techniques for probe calibration and machine calibration assume the impractical situations where either the machine is accurate or the location of the probe is accurately known. To address these drawbacks, the actual kinematic model of a six-axis belt grinding CNC machine with a customized add-on probe is built in this dissertation. Using this model along with a specially designed artifact can facilitate the simultaneous calibration of the probe position and the machine geometry error