Object Extent Determination for Algebraic Solid Models

1992 ◽  
Author(s):  
M. A. Ganter ◽  
D. W. Storti
Keyword(s):  
Spatial Extent ◽  
Polynomial Functions ◽  
Implicit Function ◽  
Profile Function ◽  
Variable Elimination ◽  
Property Evaluation ◽  
Solid Models ◽  
Basis Method ◽  
Implicit Solid

Abstract This paper presents methods for determination of spatial extent of algebraic solid models. Algebraic solid models (ASM) are a variation of implicit solid models defined by implicit polynomial functions with rational coefficients. Spatial extent information, which can be used to enhance the performance of visualization and property evaluation, includes silhouettes, outlines and profiles. Silhouettes are curves on the surface of the solid which separate portions of the surface which face towards or away from a given viewpoint. The projection of the silhouette onto the viewing plane gives the outline of the solid, and the bivariate implicit function which defines the area enclosed by the outline is called the profile. A method for outline determination is demonstrated using concepts from algebraic geometry including polar surfaces and variable elimination via the Gröbner basis method and/or resultants. Examples of outline generation are presented and a sample profile function is constructed.

Object Extent Determination for Algebraic Solid Models

1995 ◽  
Vol 117 (1) ◽  
pp. 20-26 ◽  
Author(s):  
M. A. Ganter ◽  
D. W. Storti
Keyword(s):  
Spatial Extent ◽  
Polynomial Functions ◽  
Profile Function ◽  
Variable Elimination ◽  
Property Evaluation ◽  
Solid Models ◽  
Bner Basis ◽  
Basis Method ◽  
Implicit Solid

This paper presents methods for determination of spatial extent of algebraic solid models. Algebraic solid models are a variation of implicit solid models defined by implicit polynomial functions with rational coefficients. Spatial extent information, which can be used to enhance the performance of visualization and property evaluation, includes silhouettes, outlines and profiles. Silhouettes are curves on the surface of the solid which separate portions of the surface which face towards or away from a given viewpoint. The projection of the silhouette onto the viewing plane gives the outline of the solid, and the bivariate implicit function which defines the area enclosed by the outline is called the profile. A method for outline determination is demonstrated using concepts from algebraic geometry including polar surfaces and variable elimination via the Gro¨bner basis method and/or resultants. Examples of outline generation are presented and a sample profile function is constructed.

Implicit Function Alteration via Radius Mapping and Direct Function Modification

1995 ◽  
Author(s):  
Mark T. Ensz ◽  
Mark A. Ganter ◽  
Duane W. Storti
Keyword(s):  
Generalized Function ◽  
Implicit Function ◽  
Implicit Functions ◽  
Direct Function ◽  
Surface Features ◽  
And Function ◽  
Implicit Solid

Abstract In this paper, we present two closely related techniques, radius mapping, and direct function modification, that allow for the alteration of both the major geometry and surface features of implicit solids. The first technique, radius mapping, is applied to implicit functions generated by swept solid techniques. A more generalized technique, direct function modification, allows for the mapping of generalized function modifiers onto any implicit solid. Both the radius functions and the function modifiers can be either algebraic or non-algebraic in nature. Techniques for generating both algebraic and non-algebraic radius functions and function modifiers are given along with several examples of their use on both swept solids and implicit functions.

Determination of the Whiteside line on femur surface models by fitting high-order polynomial functions to cross-section profiles of the intercondylar fossa

2011 ◽  
Vol 16 (2) ◽  
pp. 71-85 ◽  
Author(s):  
Pietro Cerveri ◽  
Mario Marchente ◽  
Alfonso Manzotti ◽  
Norberto Confalonieri
Keyword(s):  
Cross Section ◽  
High Order ◽  
Polynomial Functions ◽  
Surface Models ◽  
Order Polynomial

Determination of the spatial extent of the focal point of a parabolic dish reflector using a red laser diode

2010 ◽  
Vol 35 (9) ◽  
pp. 1982-1990 ◽  
Author(s):  
J.S.P. Mlatho ◽  
M. McPherson ◽  
A. Mawire ◽  
R.J.J. Van den Heetkamp
Keyword(s):  
Laser Diode ◽  
Focal Point ◽  
Spatial Extent ◽  
Parabolic Dish

Interval Method for Interrogation of Implicit Solid Models

2000 ◽  
Author(s):  
Jack Chang ◽  
Mark Ganter ◽  
Duane Storti
Keyword(s):  
Computer Aided Design ◽  
Boundary Representation ◽  
Free Form ◽  
Solid Models ◽  
Cad Cam ◽  
Implicit Modeling ◽  
Manufacturing Applications ◽  
Determine Surface Area ◽  
Implicit Solid ◽  
Aided Design

Abstract Computer-aided design/manufacturing (CAD/CAM) systems intended to support automated design and manufacturing applications such as shape generation and solid free-form fabrication (SFF) must provide not only methods for creating and editing models of objects to be manufactured, but also methods for interrogating the models. Interrogation refers to any process that derives information from the model. Typical interrogation tasks include determine surface area, volume or inertial properties, computing surface points and normals for rendering, and computing slice descriptions for SFF. While currently available commercial modeling systems generally employ a boundary representation (B-rep) implementation of solid modeling, research efforts have considered implicit modeling schemes as a potential source of improved robustness. Implicit implementations are available for a broad range of modeling operations, but interrogation operations have been widely considered too costly for many applications. This paper describes a method based on interval analysis for interrogating implicit solid models that aims at achieving both robustness and efficiency.

Effects of Internal Standards and Peak Profile Functions on Quantitative XRD Phase Analysis of Cement and its Hydrates

2011 ◽  
Vol 492 ◽  
pp. 424-428
Author(s):  
Yong Qi Wei ◽  
Wu Yao ◽  
Wei Wang
Keyword(s):  
Phase Analysis ◽  
Internal Standard ◽  
Direct Determination ◽  
Quantitative Phase Analysis ◽  
X Ray Diffraction ◽  
Profile Function ◽  
Internal Standards ◽  
Refinement Method ◽  
Xrd Phase Analysis

Quantitative X-Ray diffraction (QXRD) combined with the Rietveld refinement method allows direct determination of crystalline phase content of cement and its hydrates. However, relatively precise results need the correction of proper internal standards and the use of matched peak profile functions with masterly refinement strategies. The aim of this paper is to research and discuss effects of these factors on the quantitative phase analysis results. For this purpose, different internal standards and peak profile functions with corresponding refinement strategies were attempted in experiments and refinements. The results indicate that Al2O3as internal standard is more suitable for cement and its hydrates than ZnO, and the better peak profile function is CW function 2 rather than function 3 in GSAS.

scholarly journals Trajectory Determination of Chang’E-5 during Landing and Ascending

2021 ◽  
Vol 13 (23) ◽  
pp. 4837
Author(s):  
Peng Yang ◽  
Yong Huang ◽  
Peijia Li ◽  
Siyu Liu ◽  
Quan Shan ◽  
...  
Keyword(s):  
Image Data ◽  
Landing Site ◽  
Polynomial Functions ◽  
The Moon ◽  
B Spline ◽  
Lunar Reconnaissance Orbiter ◽  
Orbiter Image ◽  
Positioning Method ◽  
Trajectory Determination

Chang’E-5 (CE-5) is China’s first lunar sample return mission. This paper focuses on the trajectory determination of the CE-5 lander and ascender during the landing and ascending phases, and the positioning of the CE-5 lander on the Moon. Based on the kinematic statistical orbit determination method using B-spline and polynomial functions, the descent and ascent trajectories of the lander and ascender are determined by using ground-based radiometric ranging, Doppler and interferometry data. The results show that a B-spline function is suitable for a trajectory with complex maneuvers. For a smooth trajectory, B-spline and polynomial functions can reach almost the same solutions. The positioning of the CE-5 lander on the Moon is also investigated here. Using the kinematic statistical positioning method, the landing site of the lander is 43.0590°N, 51.9208°W with an elevation of −2480.26 m, which is less than 200 m different from the LRO (Lunar Reconnaissance Orbiter) image data.

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