1,180 research outputs found
Assessment criteria for 2D shape transformations in animation
The assessment of 2D shape transformations (or morphing) for animation is a difficult task because it is a multi-dimensional problem. Existing morphing techniques pay most attention to shape information interactive control and mathematical simplicity. This paper shows that it is not enough to use shape information alone, and we should consider other factors such as structure, dynamics, timing, etc. The paper also shows that an overall objective assessment of morphing is impossible because factors such as timing are related to subjective judgement, yet local objective assessment criteria, e.g. based on shape, are available. We propose using “area preservation” as the shape criterion for the 2D case as an acceptable approximation to “volume preservation” in reality, and use it to establish cases in which a number of existing techniques give clearly incorrect results. The possibility of deriving objective assessment criteria for dynamics simulations and timing under certain conditions is discussed
Boundary-Conforming Finite Element Methods for Twin-Screw Extruders using Spline-Based Parameterization Techniques
This paper presents a novel spline-based meshing technique that allows for
usage of boundary-conforming meshes for unsteady flow and temperature
simulations in co-rotating twin-screw extruders. Spline-based descriptions of
arbitrary screw geometries are generated using Elliptic Grid Generation. They
are evaluated in a number of discrete points to yield a coarse classical mesh.
The use of a special control mapping allows to fine-tune properties of the
coarse mesh like orthogonality at the boundaries. The coarse mesh is used as a
'scaffolding' to generate a boundary-conforming mesh out of a fine background
mesh at run-time. Storing only a coarse mesh makes the method cheap in terms of
memory storage. Additionally, the adaptation at run-time is extremely cheap
compared to computing the flow solution. Furthermore, this method circumvents
the need for expensive re-meshing and projections of solutions making it
efficient and accurate. It is incorporated into a space-time finite element
framework. We present time-dependent test cases of non-Newtonian fluids in 2D
and 3D for complex screw designs. They demonstrate the potential of the method
also for arbitrarily complex industrial applications
Probabilistic Matching of Planar Regions
We analyze a probabilistic algorithm for matching shapes modeled by planar
regions under translations and rigid motions (rotation and translation). Given
shapes and , the algorithm computes a transformation such that with
high probability the area of overlap of and is close to maximal. In
the case of polygons, we give a time bound that does not depend significantly
on the number of vertices
matching, interpolation, and approximation ; a survey
In this survey we consider geometric techniques which have been used to
measure the similarity or distance between shapes, as well as to approximate
shapes, or interpolate between shapes. Shape is a modality which plays a key
role in many disciplines, ranging from computer vision to molecular biology.
We focus on algorithmic techniques based on computational geometry that have
been developed for shape matching, simplification, and morphing
Fast character modeling with sketch-based PDE surfaces
© 2020, The Author(s). Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly
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