Approximation and geometric modeling with simplex B-splines associated with irregular triangles

Bivariate quadratic simplical B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a C1-smooth surface. The generation of triangle vertices is adjusted to the areal distribution of the data in the domain. We emphasize here that the vertices of the triangles initially define the knots of the B-splines and do generally not coincide with the abscissae of the data. Thus, this approach is well suited to process scattered data.\ud \ud With each vertex of a given triangle we associate two additional points which give rise to six configurations of five knots defining six linearly independent bivariate quadratic B-splines supported on the convex hull of the corresponding five knots.\ud \ud If we consider the vertices of the triangulation as threefold knots, the bivariate quadratic B-splines turn into the well known bivariate quadratic Bernstein-Bézier-form polynomials on triangles. Thus we might be led to think of B-splines as of smoothed versions of Bernstein-Bézier polynomials with respect to the entire domain. From the degenerate Bernstein-Bézier situation we deduce rules how to locate the additional points associated with each vertex to establish knot configurations that allow the modeling of discontinuities of the function itself or any of its directional derivatives. We find that four collinear knots out of the set of five defining an individual quadratic B-spline generate a discontinuity in the surface along the line they constitute, and that analogously three collinear knots generate a discontinuity in a first derivative.\ud Finally, the coefficients of the linear combinations of normalized simplicial B-splines are visualized as geometric control points satisfying the convex hull property.\ud Thus, bivariate quadratic B-splines associated with irregular triangles provide a great flexibility to approximate and model fast changing or even functions with any given discontinuities from scattered data.\ud An example for least squares approximation with simplex splines is presented

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

Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)

Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through routing models. The most important input to debris \ufb02ow routing models are the topographic data, usually in the form of Digital Elevation Models (DEMs). The quality of DEMs depends on the accuracy, density, and spatial distribution of the sampled points; on the characteristics of the surface; and on the applied gridding methodology. Therefore, the choice of the interpolation method affects the realistic representation of the channel and fan morphology, and thus potentially the debris \ufb02ow routing modeling outcomes. In this paper, we initially investigate the performance of common interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor, Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging) in building DEMs with the complex topography of a debris \ufb02ow channel located in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full- waveform Light Detection And Ranging (LiDAR) data. The investigation is carried out through a combination of statistical analysis of vertical accuracy, algorithm robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms on the performance of a Geographic Information System (GIS)-based cell model for simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation between the DEMs heights uncertainty resulting from the gridding procedure and that on the corresponding simulated erosion/deposition depths, both the effect of interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid discharges, and channel morphology after the event. The comparison among the tested interpolation methods highlights that the ANUDEM and ordinary kriging algorithms are not suitable for building DEMs with complex topography. Conversely, the linear triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy and shape reliability. Anyway, the evaluation of the effects of gridding techniques on debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does not signi\ufb01cantly affect the model outcomes

An interpolation method of b-spline surface for hull form design

ABSTRACTThis paper addresses the problem of B-spline surface interpolation of scattered points for a hull form design, which are not arbitrarily scattered, but can be arranged in a series of contours permitting variable number of points in the contours. A new approach that allows different parameter value for each point on the same contour has been adopted. The usefulness and quality of the interpolation has been demonstrated with some experimental results

Grid sensitivity for aerodynamic optimization and flow analysis

After reviewing relevant literature, it is apparent that one aspect of aerodynamic sensitivity analysis, namely grid sensitivity, has not been investigated extensively. The grid sensitivity algorithms in most of these studies are based on structural design models. Such models, although sufficient for preliminary or conceptional design, are not acceptable for detailed design analysis. Careless grid sensitivity evaluations, would introduce gradient errors within the sensitivity module, therefore, infecting the overall optimization process. Development of an efficient and reliable grid sensitivity module with special emphasis on aerodynamic applications appear essential. The organization of this study is as follows. The physical and geometric representations of a typical model are derived in chapter 2. The grid generation algorithm and boundary grid distribution are developed in chapter 3. Chapter 4 discusses the theoretical formulation and aerodynamic sensitivity equation. The method of solution is provided in chapter 5. The results are presented and discussed in chapter 6. Finally, some concluding remarks are provided in chapter 7

A computer program for fitting smooth surfaces to three-dimensional aircraft configurations

A computer program developed to fit smooth surfaces to the component parts of three-dimensional aircraft configurations was described. The resulting equation definition of an aircraft numerical model is useful in obtaining continuous two-dimensional cross section plots in arbitrarily defined planes, local tangents, enriched surface plots and other pertinent geometric information; the geometry organization used as input to the program has become known as the Harris Wave Drag Geometry

An investigation on the framework of dressing virtual humans

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Realistic human models are widely used in variety of applications. Much research has been carried out on improving realism of virtual humans from various aspects, such as body shapes, hair, and facial expressions and so on. In most occasions, these virtual humans need to wear garments. However, it is time-consuming and tedious to dress a human model using current software packages [Maya2004]. Several methods for dressing virtual humans have been proposed recently [Bourguignon2001, Turquin2004, Turquin2007 and Wang2003B]. The method proposed by Bourguignon et al [Bourguignon2001] can only generate 3D garment contour instead of 3D surface. The method presented by Turquin et al. [Turquin2004, Turquin2007] could generate various kinds of garments from sketches but their garments followed the shape of the body and the side of a garment looked not convincing because of using simple linear interpolation. The method proposed by Wang et al. [Wang2003B] lacked interactivity from users, so users had very limited control on the garment shape.This thesis proposes a framework for dressing virtual humans to obtain convincing dressing results, which overcomes problems existing in previous papers mentioned above by using nonlinear interpolation, level set-based shape modification, feature constraints and so on. Human models used in this thesis are reconstructed from real human body data obtained using a body scanning system. Semantic information is then extracted from human models to assist in generation of 3 dimensional (3D) garments. The proposed framework allows users to dress virtual humans using garment patterns and sketches. The proposed dressing method is based on semantic virtual humans. A semantic human model is a human body with semantic information represented by certain of structure and body features. The semantic human body is reconstructed from body scanned data from a real human body. After segmenting the human model into six parts some key features are extracted. These key features are used as constraints for garment construction.Simple 3D garment patterns are generated using the techniques of sweep and offset. To dress a virtual human, users just choose a garment pattern, which is put on the human body at the default position with a default size automatically. Users are allowed to change simple parameters to specify some sizes of a garment by sketching the desired position on the human body.To enable users to dress virtual humans by their own design styles in an intuitive way, this thesis proposes an approach for garment generation from user-drawn sketches. Users can directly draw sketches around reconstructed human bodies and then generates 3D garments based on user-drawn strokes. Some techniques for generating 3D garments and dressing virtual humans are proposed. The specific focus of the research lies in generation of 3D geometric garments, garment shape modification, local shape modification, garment surface processing and decoration creation. A sketch-based interface has been developed allowing users to draw garment contour representing the front-view shape of a garment, and the system can generate a 3D geometric garment surface accordingly. To improve realism of a garment surface, this thesis presents three methods as follows. Firstly, the procedure of garment vertices generation takes key body features as constraints. Secondly, an optimisation algorithm is carried out after generation of garment vertices to optimise positions of garment vertices. Finally, some mesh processing schemes are applied to further process the garment surface. Then, an elaborate 3D geometric garment surface can be obtained through this series of processing. Finally, this thesis proposes some modification and editing methods. The user-drawn sketches are processed into spline curves, which allow users to modify the existing garment shape by dragging the control points into desired positions. This makes it easy for users to obtain a more satisfactory garment shape compared with the existing one. Three decoration tools including a 3D pen, a brush and an embroidery tool, are provided letting users decorate the garment surface by adding some small 3D details such as brand names, symbols and so on. The prototype of the framework is developed using Microsoft Visual Studio C++,OpenGL and GPU programming

DATAMAP upgrade version 4.0

The changes made on the data analysis and management program DATAMAP (Data from Aeromechanics Test and Analytics - Management and Analysis Package) are detailed. These changes are made to Version 3.07 (released February, 1981) and are called Version 4.0. Version 4.0 improvements were performed by Sterling Software under contract to NASA Ames Research Center. The increased capabilities instituted in this version include the breakout of the source code into modules for ease of modification, addition of a more accurate curve fit routine, ability to handle higher frequency data, additional data analysis features, and improvements in the functionality of existing features. These modification will allow DATAMAP to be used on more data sets and will make future modifications and additions easier to implement