Polygon-to-Object Boundary Clipping in Object Space for Hidden Surface Removal in Computer-Aided Design

1995 ◽  
Vol 117 (3) ◽  
pp. 374-389 ◽  
Author(s):  
Wei-Hua Chieng ◽  
D. A. Hoeltzel
Keyword(s):  
Computer Aided Design ◽  
Geometric Design ◽  
Design System ◽  
Boundary Contour ◽  
Object Boundary ◽  
Computer Aided Geometric Design ◽  
Object Space ◽  
Computer Aided ◽  
Hidden Surface Removal ◽  
Surface Removal

Since techniques for both polygon-to-polygon clipping and polygon-to-object boundary (contour) clipping have been developed, it appears that the visibility problem may exhibit potential for improvement in its time complexity. This paper provides some insight and results concerning the performance of an object-space hidden surface removal algorithm based on polygon-to-object boundary (contour) clipping. The applicability of these results to the graphic rendering of partially visible objects in an incremental computer-aided geometric design system, such as that used in mechanical design, is demonstrated. The polygon-to-object boundary clipping algorithm is compared with the more conventional polygon-to-polygon approach to clipping for hidden surface removal. Examples are included which demonstrate the potential for improving the performance of software-based hidden surface removal algorithms used in computer-aided geometric design applications.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

1999 ◽  
Vol 121 (4) ◽  
pp. 502-506 ◽  
Author(s):  
Q. J. Ge ◽  
M. Sirchia
Keyword(s):  
Computer Aided Design ◽  
Control Structure ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Kinematic Control ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design ◽  
Two Parameter ◽  
And Robotics

This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop methods for computer aided design of two-parameter freeform motions. In particular, a rational Be´zier representation for two-parameter freeform motions is developed. It has been shown that the trajectory surface of such a motion is a tensor-product rational Be´zier surface and that such a kinematically generated surface has a geometric as well as a kinematic control structure. The results have not only theoretical interest in CAGD and kinematics but also applications in CAD/CAM and Robotics.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

1998 ◽  
Author(s):  
Q. J. Ge ◽  
M. Sirchia
Keyword(s):  
Computer Aided Design ◽  
Control Structure ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Computer Aided ◽  
Cad Cam ◽  
Rational Bézier Surface ◽  
Aided Design ◽  
Two Parameter ◽  
And Robotics

Abstract This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop methods for computer aided design of two-parameter freeform motions. In particular, a rational Bézier representation for two-parameter freeform motions is developed. It has been shown that the trajectory surface of such a motion is a tensor-product rational Bézier surface and that such a kinematically generated surface has a geometric as well as a kinematic control structure. The results have not only theoretical interest in CAGD and kinematics but also applications in CAD/CAM and Robotics.

scholarly journals Pembinaan lengkungan peralihan berbentuk C yang memuaskan Data Interpolasi Hermite G2

2020 ◽  
Vol 8 (2) ◽  
pp. 39-50
Author(s):  
Azhar Ahmad
Keyword(s):  
Computer Aided Design ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
B Splines ◽  
Computer Aided ◽  
Aided Design

Makalah ini membincangkan satu kaedah pembinaan lengkungan peralihan berbentuk C yang memenuhi syarat-syarat data interpolasi Hermite Lengkungan peralihan ini dibina berasaskan gabungan dua pilin kuadratik nisbah Bezier atau gabungan bersama satu segmen garis lurus bagi mencapai keselanjaran pada keseluruhan binaan. Kaedah analisis geometri bersama syarat kemonotonan suatu lengkungan kuadratik nisbah Bezier telah digunakan bagi mencapai objektif kajian. Hasil kajian yang dicapai adalah satu teknik pembinaan yang membolehkan kita memperolehi lengkungan peralihan secara terus, mudah diaplikasikan serta tanpa perlu menggunakan sebarang prosedur tranformasi affin. Syarat untuk lengkungan peralihan ini terhasil ditentukan oleh data Hermite yang diberi dan kepelbagaiannya pula dikawal oleh panjang segmen garis lurus yang menghubungkan kedua-dua pilin berkenaan. Keupayaan memenuhi sifat-sifat interpolasi ini memberi banyak kelebihan dan amat sesuai untuk aplikasi tertentu di dalam CAGD (Computer Aided Geometric Design), umpamanya rekabentuk produk industri, trajektori robot non-holonomic, serta rekabentuk mendatar landasan keretapi dan lebuhraya. Oleh kerana kuadratik nisbah Bezier merupakan sebahagian daripada perwakilan NURBS (Nonuniform Rational B-splines) maka adalah mudah bagi kita mengabungjalinkan formulasi lengkungan peralihan yang dicadangkan ini ke dalam kebanyakan sistem pengaturcara CAD (Computer Aided Design).

Structural Analysis of Product and Computer-Aided Assembly Planning in AssemBL Software Package

2018 ◽  
pp. 11-33
Author(s):  
A. N. Bozhko
Keyword(s):  
Computer Aided Design ◽  
State Of The Art ◽  
Graph Model ◽  
Design System ◽  
Assembly Planning ◽  
Complex Products ◽  
Assembly Sequences ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design

Computer-aided design of assembly processes (Computer aided assembly planning, CAAP) of complex products is an important and urgent problem of state-of-the-art information technologies. Intensive research on CAAP has been underway since the 1980s. Meanwhile, specialized design systems were created to provide synthesis of assembly plans and product decompositions into assembly units. Such systems as ASPE, RAPID, XAP / 1, FLAPS, Archimedes, PRELEIDES, HAP, etc. can be given, as an example. These experimental developments did not get widespread use in industry, since they are based on the models of products with limited adequacy and require an expert’s active involvement in preparing initial information. The design tools for the state-of-the-art full-featured CAD/CAM systems (Siemens NX, Dassault CATIA and PTC Creo Elements / Pro), which are designed to provide CAAP, mainly take into account the geometric constraints that the design imposes on design solutions. These systems often synthesize technologically incorrect assembly sequences in which known technological heuristics are violated, for example orderliness in accuracy, consistency with the system of dimension chains, etc.An AssemBL software application package has been developed for a structured analysis of products and a synthesis of assembly plans and decompositions. The AssemBL uses a hyper-graph model of a product that correctly describes coherent and sequential assembly operations and processes. In terms of the hyper-graph model, an assembly operation is described as shrinkage of edge, an assembly plan is a sequence of shrinkages that converts a hyper-graph into the point, and a decomposition of product into assembly units is a hyper-graph partition into sub-graphs.The AssemBL solves the problem of minimizing the number of direct checks for geometric solvability when assembling complex products. This task is posed as a plus-sum two-person game of bicoloured brushing of an ordered set. In the paradigm of this model, the brushing operation is to check a certain structured fragment for solvability by collision detection methods. A rational brushing strategy minimizes the number of such checks.The package is integrated into the Siemens NX 10.0 computer-aided design system. This solution allowed us to combine specialized AssemBL tools with a developed toolkit of one of the most powerful and popular integrated CAD/CAM /CAE systems.

scholarly journals Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Soroosh Tayebi Arasteh ◽  
Adam Kalisz
Keyword(s):  
Computer Graphics ◽  
Geometric Design ◽  
The Other ◽  
Control Points ◽  
Complex Surfaces ◽  
Linear Transformations ◽  
Computer Aided Geometric Design ◽  
Cubic Curves ◽  
Original Curve ◽  
Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

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