Journal Article10.1007/BF01901583
Computational methods for evaluating swept object boundaries
Laxmi Parida,Sudhir P. Mudur +1 more
19
TL;DR: This paper identifies a sufficiently general class of swept objects and classify the sweep rules, and presents computational methods for directly evaluating the boundary representation which implicitly simulate the sweep process.
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Abstract: Many systems support the design of two-dimensional (2D) regions and three-dimensional (3D) volumes by sweeping a generator contour over a spine Well-established and widely used rendering systems accept high-level boundary descriptions of regions and solids but not in the contour-spine form Hence the swept object design specification must be such as to lend itself to efficient evaluation of a compact and high-level boundary description In this paper, we identify a sufficiently general class of swept objects and classify the sweep rules We also present computational methods for directly evaluating the boundary representation which implicitly simulate the sweep process The boundary is generated as a set of piecewise curves/surfaces in a compact form suitable for direct input to rendering systems like Post-Script(R) in 2D and Renderman(R) in 3D
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Citations
The sweep-envelope differential equation algorithm and its application to NC machining verification
TL;DR: This method is used as the theoretical foundation of an algorithm for computing swept volumes using the trajectories of the sweep-envelope differential equation which start at the initial grazing points of the moving object.
168
Geometric representation of the swept volume using Jacobian rank-deficiency conditions
Karim Abdel-Malek,Harn-Jou Yeh +1 more
TL;DR: A broadly applicable formulation for representing the boundary of swept geometric entities is presented, applicable to entities of any dimension and applications to NC part geometry verification, robotic manipulators, and computer modeling are discussed.
124
Swept volumes: fundation, perspectives, and applications
TL;DR: A survey of swept volume concepts and methods consolidates and relates seemingly different terminology and methods and demonstrates the applicability of this seemingly simple formulation to the fields of solid modeling, robotics, manufacturing automation, and visualization.
123
Trimming swept volumes
TL;DR: Efficient methods for both local and global trimming of swept volume are developed and are shown to be computationally cost effective when combined with the sweep-envelope differential equation algorithm for the approximate calculation and graphical rendering of swept volumes for quite general objects and sweeps.
49
Multiple sweeping using the Denavit–Hartenberg representation method
Karim Abdel-Malek,Saeb Othman +1 more
TL;DR: The Denavit–Hartenberg (DH) method, first introduced in 1955 in the field of kinematics to mathematically relate motion between two coordinate frames, provides an effective formulation for characterizing the resulting solid model.
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