Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

Modeling of multifunctional porous tissue scaffolds with continuous deposition path plan

A novel modeling technique for porous tissue scaffolds with targeting the functionally gradient variational porosity with continuous material deposition planning has been proposed. To vary the porosity of the designed scaffold functionally, medial axis transformation is used. The medial axis of each layers of the scaffold is calculated and used as an internal feature. The medial axis is then used connected to the outer contour using an optimum matching. The desired pore size and hence the porosity have been achieved by discretizing the sub-regions along its peripheral direction based on the pore size while meeting the tissue scaffold design constraints. This would ensure the truly porous nature of the structure in every direction as well as controllable porosity with interconnected pores. Thus the desired controlled variational porosity along the scaffold architecture has been achieved with the combination of two geometrically oriented consecutive layers. A continuous, interconnected and optimized tool-path has been generated for successive layers for additive-manufacturing or solid free form fabrication process. The proposed methodology has been computationally implemented with illustrative examples. Furthermore, the designed example scaffolds with the desired pore size and porosity has been fabricated with an extrusion based bio-fabrication process

Smooth Subdivision Surfaces: Mesh Blending and Local Interpolation

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

Vector Geometry and Applications to Three-Dimensional Computer Graphics

The mathematics behind algorithms involved in generating three-dimensional images on a computer has stemmed from the analysis of the processes of sight and vision. These processes have been modeled to provide methods of visualising three-dimensional data sets. The applications of such visualisations are varied. This project will study some of the mathematics that IS used in three-dimensional graphics application

Analysis and construction of rational curve parametrizations with non-ordinary singularities

In this paper, we provide a method that allows to construct parametric curves having (or not) non-ordinary singularities and having (or not) neighboring points. This method is based on a characterization of the non-ordinary singularities and neighboring points by means of linear equations involving the given parametrization. As a consequence, we obtain an algorithm that constructs a parametrization which contains a given point, P, as a singularity as well as some additional information as for instance, the order of P, parameters corresponding to P, multiplicity of each parameter and the singularities in the first neighborhood of the singularity P.Ministerio de Economía y Competitivida

Hybrid Rugosity Mesostructures (HRMs) for fast and accurate rendering of fine haptic detail

The haptic rendering of surface mesostructure (fine relief features) in dense triangle meshes requires special structures, equipment, and high sampling rates for detailed perception of rugged models. Low cost approaches render haptic texture at the expense of fidelity of perception. We propose a faster method for surface haptic rendering using image-based Hybrid Rugosity Mesostructures (HRMs), paired maps with per-face heightfield displacements and normal maps, which are layered on top of a much decimated mesh, effectively adding greater surface detail than actually present in the geometry. The haptic probe’s force response algorithm is modulated using the blended HRM coat to render dense surface features at much lower costs. The proposed method solves typical problems at edge crossings, concave foldings and texture transitions. To prove the wellness of the approach, a usability testbed framework was built to measure and compare experimental results of haptic rendering approaches in a common set of specially devised meshes, HRMs, and performance tests. Trial results of user testing evaluations show the goodness of the proposed HRM technique, rendering accurate 3D surface detail at high sampling rates, deriving useful modeling and perception thresholds for this technique.Peer ReviewedPostprint (published version

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

Designing heterogeneous porous tissue scaffolds for additive manufacturing processes

A novel tissue scaffold design technique has been proposed with controllable heterogeneous architecture design suitable for additive manufacturing processes. The proposed layer-based design uses a bi-layer pattern of radial and spiral layers consecutively to generate functionally gradient porosity, which follows the geometry of the scaffold. The proposed approach constructs the medial region from the medial axis of each corresponding layer, which represents the geometric internal feature or the spine. The radial layers of the scaffold are then generated by connecting the boundaries of the medial region and the layer's outer contour. To avoid the twisting of the internal channels, reorientation and relaxation techniques are introduced to establish the point matching of ruling lines. An optimization algorithm is developed to construct sub-regions from these ruling lines. Gradient porosity is changed between the medial region and the layer's outer contour. Iso-porosity regions are determined by dividing the subregions peripherally into pore cells and consecutive iso-porosity curves are generated using the isopoints from those pore cells. The combination of consecutive layers generates the pore cells with desired pore sizes. To ensure the fabrication of the designed scaffolds, the generated contours are optimized for a continuous, interconnected, and smooth deposition path-planning. A continuous zig-zag pattern deposition path crossing through the medial region is used for the initial layer and a biarc fitted isoporosity curve is generated for the consecutive layer with C-1 continuity. The proposed methodologies can generate the structure with gradient (linear or non-linear), variational or constant porosity that can provide localized control of variational porosity along the scaffold architecture. The designed porous structures can be fabricated using additive manufacturing processes