Surface Reconstruction From Dexel Data for Virtual Sculpting

2004 ◽  
Author(s):  
Xiaobo Peng ◽  
Weihan Zhang ◽  
Sai-Gowthami Asam ◽  
Ming C. Leu
Keyword(s):  
Surface Reconstruction ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Ray Casting ◽  
Virtual Sculpting ◽  
Shortest Distance ◽  
Branching Problem ◽  
Volume Ray Casting ◽  
Swept Volume ◽  
Differential Equation Method

This paper presents a new method for surface reconstruction from dexel data for virtual sculpting. We are in the midst of developing a dexel model based sculpting system having the capability of interactive solid modeling with haptics interface. The geometric modeling of our sculpting system is based on the Sweep Differential Equation method to compute the boundary of the tool swept volume. Ray casting is used to perform Boolean operations between the tool swept volume and the virtual stock in dexel models to simulate the sculpting process. The dexel data are converted to a series of planar contours in parallel slices (i.e. cross sections). The overlapping ratio between two contour areas is used as the criterion for deciding on the corresponding contours in two adjacent slices. The tiling problem is tackled by using the rule of the shortest distance between points on two corresponding contours. The branching problem is solved by adding one line segment between two contours to form one composite contour. Examples are given to demonstrate the ability of the developed code to convert from dexel data to triangular meshes for the viewing of a sculpted model in different directions.

Surface Reconstruction From Triple Dexel Model for Virtual Sculpting

2007 ◽  
Author(s):  
Weihan Zhang ◽  
Ming C. Leu
Keyword(s):  
Differential Equation ◽  
Surface Reconstruction ◽  
Boundary Surface ◽  
Solid Modeling ◽  
Haptic Interface ◽  
Solid Model ◽  
Virtual Sculpting ◽  
Novel Method ◽  
Swept Volume ◽  
Differential Equation Method

This paper presents a novel method for surface reconstruction from triple dexel data for virtual sculpting. A triple dexel based virtual sculpting system is developed to provide the capability of interactive solid modeling with haptic interface. A solid model is converted to triple dexel data, which depicts the intersections of the solid with rays cast in three orthogonal directions, and modified during the virtual sculpting process. The boundary of the tool swept volume is computed based on the Sweep Differential Equation method. Contour generation and combination algorithms convert the triple dexel data to three sets of orthogonal slices of contours. A tiling algorithm then generates the solid’s boundary surface in triangular facets from these contours. Examples are given to demonstrate the ability of the developed method and software to realistically simulate the physical sculpting process and to allow viewing the sculpted models in any directions.

Geometric Modeling of a Moving Object With Self-Intersection

1995 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Cross Sections ◽  
Time Domain ◽  
Geometric Modeling ◽  
Moving Object ◽  
The Self ◽  
Graphical Solution ◽  
Simple Polygons ◽  
Swept Volume ◽  
Facet Model

Abstract The solution to the self-intersection of a swept volume is the bottleneck to the geometric modeling of a moving object. Self-intersection of a swept volume is the result of an object, which is called a generator here, moving into a space which it previously occupied. A graphical solution is devised in this study. It consists of following steps. First of all, a candidate swept volume is created by warping a series of characteristics curves on the boundary of the generator in a given time domain. The result is the facet model of a swept volume. Secondly, a series of sectioning operations to the candidate swept volume are performed where the sectioning planes are parallel. If self-intersection exists for a given candidate swept volume, some of the resulting polygons (cross-sections) after the sectioning operations are complex polygons. Thirdly, an algorithm is proposed here to convert these polygons into sweep contours, which are simple polygons. A well defined facet model of the swept volume is then obtained by fitting the corresponding sweep contours with a surface.

scholarly journals Template-based surface reconstruction from cross-sections

2016 ◽  
Vol 58 ◽  
pp. 84-91 ◽  
Author(s):  
Michelle Holloway ◽  
Cindy Grimm ◽  
Tao Ju
Keyword(s):  
Surface Reconstruction ◽  
Cross Sections

scholarly journals GEOMETRIC MODELING OF A SHAPE OF PARALLELOGRAM PLATES IN A PROBLEM OF FREE VIBRATIONS USING CONFORMAL RADII

2021 ◽  
pp. 143-159
Author(s):  
A.A. Chernyaev ◽  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Interpolation Method ◽  
Geometric Characteristic ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Basic Frequency ◽  
Plate Vibrations ◽  
The Subject

The paper considers a method of geometric modeling applied when solving basic twodimensional problems of the theory of elasticity and structural mechanics, in particular the applied problems of engineering. The subject of this study is vibrations of thin elastic parallelogram plates of constant thickness. To determine a basic frequency of vibrations, the interpolation method based on the geometric characteristic of the shape of plates (membrane, cross sections of a rod) is proposed. This characteristic represents a ratio of interior and exterior conformal radii of the plate. As is known from the theory of conformal mappings, conformal radii are those obtained by mapping of a plate onto the interior and exterior of a unit disk. The paper presents basic terms, tables, and formulas related to the considered geometric method with a comparative analysis of the curve diagrams obtained using various interpolation formulas. The original computer program is also developed. The main advantage of the proposed method of determining the basic frequency of plate vibrations is a graphic representation of results that allows one to accurately determine the required solution on the graph among the other solutions corresponding to the considered case of parallelogram plates. Although there are many known approximate approaches, which are used to solve the considered problems, only geometric modeling technique based on the conformal radii ratio gives such an opportunity.

scholarly journals Geometric modeling of surfaces dependent cross sections in the tasks of spinning and laying

2019 ◽  
Vol 110 ◽  
pp. 01057
Author(s):  
Yuri Deniskin ◽  
Pavel Miroshnichenko ◽  
Andrew Smolyaninov
Keyword(s):  
Composite Materials ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Solid Modeling ◽  
Uniform Method ◽  
Calculation Methods ◽  
Related Process

The article is devoted to the development of a geometric model of surfaces of dependent sections to solve the problems of winding by continuous fibers in the direction of the force and its related process of automated winding of composite materials. A uniform method for specifying the surfaces of dependent sections with a curvilinear generator and a method for solid modeling of the shell obtained by winding or calculation methods are described.

Minimal area for surface reconstruction from cross sections

2002 ◽  
Vol 18 (7) ◽  
pp. 437-444 ◽  
Author(s):  
Dmitrii Berzin ◽  
Ichiro Hagiwara
Keyword(s):  
Surface Reconstruction ◽  
Cross Sections ◽  
Minimal Area
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