Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

An efficient active B-spline/nurbs model for virtual sculpting

This thesis presents an Efficient Active B-Spline/Nurbs Model for Virtual Sculpting. In spite of the on-going rapid development of computer graphics and computer-aided design tools, 3D graphics designers still rely on non-intuitive modelling procedures for the creation and manipulation of freeform virtual content. The ’Virtual Sculpting' paradigm is a well-established mechanism for shielding designers from the complex mathematics that underpin freeform shape design. The premise is to emulate familiar elements of traditional clay sculpting within the virtual design environment. Purely geometric techniques can mimic some physical properties. More exact energy-based approaches struggle to do so at interactive rates. This thesis establishes a unified approach for the representation of physically aware, energy-based, deformable models, across the domains of Computer Graphics, Computer-Aided Design and Computer Vision, and formalises the theoretical relationships between them. A novel reformulation of the computer vision approach of Active Contour Models (ACMs) is proposed for the domain of Virtual Sculpting. The proposed ACM-based model offers novel interaction behaviours and captures a compromise between purely geometric and more exact energy-based approaches, facilitating physically plausible results at interactive rates. Predefined shape primitives provide features of interest, acting like sculpting tools such that the overall deformation of an Active Surface Model is analogous to traditional clay modelling. The thesis develops a custom-approach to provide full support for B-Splines, the de facto standard industry representation of freeform surfaces, which have not previously benefited from the seamless embodiment of a true Virtual Sculpting metaphor. A novel generalised computationally efficient mathematical framework for the energy minimisation of an Active B-Spline Surface is established. The resulting algorithm is shown to significantly reduce computation times and has broader applications across the domains of Computer-Aided Design, Computer Graphics, and Computer Vision. A prototype ’Virtual Sculpting’ environment encapsulating each of the outlined approaches is presented that demonstrates their effectiveness towards addressing the long-standing need for a computationally efficient and intuitive solution to the problem of interactive computer-based freeform shape design

Dynamic skin deformation using finite difference solutions for character animation

We present a new skin deformation method to create dynamic skin deformations in this paper. The core elements of our approach are a dynamic deformation model, an efficient data-driven finite difference solution, and a curve-based representation of 3D models. We first reconstruct skin deformation models at different poses from the taken photos of a male human arm movement to achieve real deformed skin shapes. Then, we extract curves from these reconstructed skin deformation models. A new dynamic deformation model is proposed to describe physics of dynamic curve deformations, and its finite difference solution is developed to determine shape changes of the extracted curves. In order to improve visual realism of skin deformations, we employ data-driven methods and introduce skin shapes at the initial and final poses into our proposed dynamic deformation model. Experimental examples and comparisons made in this paper indicate that our proposed dynamic skin deformation technique can create realistic deformed skin shapes efficiently with a small data size

Virtual sculpting : an investigation of directly manipulated free-form deformation in a virtual environment

This thesis presents a Virtual Sculpting system, which addresses the problem of Free-Form Solid Modelling. The disparate elements of a Polygon-Mesh representation, a Directly Manipulated Free-Form Deformation sculpting tool, and a Virtual Environment are drawn into a cohesive whole under the mantle of a clay-sculpting metaphor. This enables a user to mould and manipulate a synthetic solid interactively as if it were composed of malleable clay. The focus of this study is on the interactivity, intuitivity and versatility of such a system. To this end, a range of improvements is investigated which significantly enhances the efficiency and correctness of Directly Manipulated Free-Form Deformation, both separately and as a seamless component of the Virtual Sculpting system

Real-time hybrid cutting with dynamic fluid visualization for virtual surgery

It is widely accepted that a reform in medical teaching must be made to meet today's high volume training requirements. Virtual simulation offers a potential method of providing such trainings and some current medical training simulations integrate haptic and visual feedback to enhance procedure learning. The purpose of this project is to explore the capability of Virtual Reality (VR) technology to develop a training simulator for surgical cutting and bleeding in a general surgery

Vector offset operators for deformable organic objects.

Many natural materials and most of living tissues exhibit complex deformable behaviours that may be characteriseda s organic. In computer animation, deformable organic material behaviour is needed for the development of characters and scenes based on living creatures and natural phenomena. This study addresses the problem of deformable organic material behaviour in computer animated objects. The focus of this study is concentrated on problems inherent in geometry based deformation techniques, such as non-intuitive interaction and difficulty in achieving realism. Further, the focus is concentrated on problems inherent in physically based deformation techniques, such as inefficiency and difficulty in enforcing spatial and temporal constraints. The main objective in this study is to find a general and efficient solution to interaction and animation of deformable 3D objects with natural organic material properties and constrainable behaviour. The solution must provide an interaction and animation framework suitable for the creation of animated deformable characters. An implementation of physical organic material properties such as plasticity, elasticity and iscoelasticity can provide the basis for an organic deformation model. An efficient approach to stress and strain control is introduced with a deformation tool named Vector Offset Operator. Stress / strain graphs control the elastoplastic behaviour of the model. Strain creep, stress relaxation and hysteresis graphs control the viscoelastic behaviour of the model. External forces may be applied using motion paths equipped with momentum / time graphs. Finally, spatial and temporal constraints are applied directly on vector operators. The suggested generic deformation tool introduces an intermediate layer between user interaction, deformation, elastoplastic and viscoelastic material behaviour and spatial and temporal constraints. This results in an efficient approach to deformation, frees object representation from deformation, facilitates the application of constraints and enables further development

Skin deformation and animation of character models based on static and dynamic ordinary differential equations.

Animated characters play an important role in the field of computer animation, simulation and games. The basic criterion of good character animation is that the animated characters should appear realistic. This can be achieve through proper skin deformations for characters. Although various skin deformation approaches (Joint-based, Example-based, Physics-based, Curve-based and PDE-based) have been developed, the problem of generating realistic skin deformations efficiently with a small data set is a big challenge. In order to address the limitations of skin deformation, this thesis presents a workflow consisting of three main steps. First, the research has developed a new statistical method to determine the positions of joints based on available X-ray images. Second, an effective method for transferring the deformations of the curves to the polygonal model with high accuracy has been developed. Lastly, the research has produced a simple and efficient method to animate skin deformations by introducing a curved-based surface manipulation method combined with physics and data-driven approaches. The novelty of this method depends on a new model of dynamic deformations and an efficient finite difference solution of the model. The application examples indicate that the curve-based dynamic method developed in this thesis can achieve good realism and high computational efficiency with small data sets in the creation of skin deformations