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Volume Modeling for Rapid Prototyping
The expanding workspace of Rapid Prototyping will draw on the new developments
in geometric modeling. Volume modeling has substantial advantages over other modeling
schemes to meet the emerging requirements of Rapid Prototyping technology. It provides us with
a new approach to design complex geometry and topology. The integration of the volume
modeling and Rapid Prototyping technology will help us to fully exploit RP's ability to fabricate
objects with complex structures. This paper addresses our research and practice in a volume
modeling system toward Rapid Prototyping. Novel techniques in volumetric data manipulation,
NURBS volume models and triangular facet generation over solid models are presented.
Computer models designed by this system and their corresponding DTM products are also
shown atthe end of this paper.Mechanical Engineerin
Boundary-Conforming Free-Surface Flow Computations: Interface Tracking for Linear, Higher-Order and Isogeometric Finite Elements
The simulation of certain flow problems requires a means for modeling a free
fluid surface; examples being viscoelastic die swell or fluid sloshing in
tanks. In a finite-element context, this type of problem can, among many other
options, be dealt with using an interface-tracking approach with the
Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A
difficult issue that is connected with this type of approach is the
determination of a suitable coupling mechanism between the fluid velocity at
the boundary and the displacement of the boundary mesh nodes. In order to avoid
large mesh distortions, one goal is to keep the nodal movements as small as
possible; but of course still compliant with the no-penetration boundary
condition. Standard displacement techniques are full velocity, velocity in a
specific coordinate direction, and velocity in normal direction. In this work,
we investigate how the interface-tracking approach can be combined with
isogeometric analysis for the spatial discretization. If NURBS basis functions
of sufficient order are used for both the geometry and the solution, both a
continuous normal vector as well as the velocity are available on the entire
boundary. This circumstance allows the weak imposition of the no-penetration
boundary condition. We compare this option with an alternative that relies on
strong imposition at discrete points. Furthermore, we examine several coupling
methods between the fluid equations, boundary conditions, and equations for the
adjustment of interior control point positions.Comment: 20 pages, 16 figure
A survey of partial differential equations in geometric design
YesComputer aided geometric design is an area
where the improvement of surface generation techniques
is an everlasting demand since faster and more accurate
geometric models are required. Traditional methods
for generating surfaces were initially mainly based
upon interpolation algorithms. Recently, partial differential
equations (PDE) were introduced as a valuable
tool for geometric modelling since they offer a number
of features from which these areas can benefit. This work
summarises the uses given to PDE surfaces as a surface
generation technique togethe
A discrete methodology for controlling the sign of curvature and torsion for NURBS
This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial BĆ©zier configuration
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