124 research outputs found
Surface discretisation with rectifying strips on Geodesics
The use of geodesic curves of surfaces has enormous potential in architecture due to their multiple properties and easy geometric control using digital graphic tools. Among their numerous properties, the geodesic curves of a surface are the paths along which straight strips can be placed tangentially to the surface. On this basis, a graphical method is proposed to discretize surfaces using straight strips, which optimizes material consumption since rectangular straight strips take advantage of 100% of the material in the cutting process. The contribution of the article consists of presenting the geometric constraints that characterize this type of panelling from the idea of ârectifying surfaceâ, considering the material inextensible. Experimental prototypes that have been part of the research are also described and the final theoretical results are presented
Smooth quasi-developable surfaces bounded by smooth curves
Computing a quasi-developable strip surface bounded by design curves finds
wide industrial applications. Existing methods compute discrete surfaces
composed of developable lines connecting sampling points on input curves which
are not adequate for generating smooth quasi-developable surfaces. We propose
the first method which is capable of exploring the full solution space of
continuous input curves to compute a smooth quasi-developable ruled surface
with as large developability as possible. The resulting surface is exactly
bounded by the input smooth curves and is guaranteed to have no
self-intersections. The main contribution is a variational approach to compute
a continuous mapping of parameters of input curves by minimizing a function
evaluating surface developability. Moreover, we also present an algorithm to
represent a resulting surface as a B-spline surface when input curves are
B-spline curves.Comment: 18 page
Equilibrium Shapes with Stress Localisation for Inextensible Elastic Mobius and Other Strips
We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order one-dimensional problem posed on the centreline of the strip. We derive EulerâLagrange equations for this problem in EulerâPoincarĂ© form and formulate boundary-value problems for closed symmetric one- and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami
A Survey of Developable Surfaces: From Shape Modeling to Manufacturing
Developable surfaces are commonly observed in various applications such as
architecture, product design, manufacturing, and mechanical materials, as well
as in the development of tangible interaction and deformable robots, with the
characteristics of easy-to-product, low-cost, transport-friendly, and
deformable. Transforming shapes into developable surfaces is a complex and
comprehensive task, which forms a variety of methods of segmentation,
unfolding, and manufacturing for shapes with different geometry and topology,
resulting in the complexity of developable surfaces. In this paper, we reviewed
relevant methods and techniques for the study of developable surfaces,
characterize them with our proposed pipeline, and categorize them based on
digital modeling, physical modeling, interaction, and application. Through the
analysis to the relevant literature, we also discussed some of the research
challenges and future research opportunities.Comment: 20 pages, 24 figures, Author submitted manuscrip
Non-smooth developable geometry for interactively animating paper crumpling
International audienceWe present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations
Developable Quad Meshes
There are different ways to capture the property of a surface being
developable, i.e., it can be mapped to a planar domain without stretching or
tearing. Contributions range from special parametrizations to
discrete-isometric mappings. So far, a local criterion expressing the
developability of general quad meshes has been lacking. In this paper, we
propose a new and efficient discrete developability criterion that is based on
a property well-known from differential geometry, namely a rank-deficient
second fundamental form. This criterion is expressed in terms of the canonical
checkerboard patterns inscribed in a quad mesh which already was successful in
describing discrete-isometric mappings. In combination with standard global
optimization procedures, we are able to perform developable lofting,
approximation, and design. The meshes we employ are combinatorially regular
quad meshes with isolated singularities but are otherwise not required to
follow any special curves. They are thus easily embedded into a design workflow
involving standard operations like re-meshing, trimming, and merging
operations
Continuous Surface Rendering, Passing from CAD to Physical Representation
This paper describes a desktopâmechatronic interface that has been conceived to support designers in the evaluation of aesthetic virtual shapes. This device allows a continuous and smooth free hand contact interaction on a real and developable plastic tape actuated by a servoâcontrolled mechanism. The objective in designing this device is to reproduce a virtual surface with a consistent physical rendering well adapted to designers' needs. The desktopâmechatronic interface consists in a servoâactuated plastic strip that has been devised and implemented using seven interpolation points. In fact, by using the MEC (Minimal Energy Curve) Spline approach, a developable real surface is rendered taking into account the CAD geometry of the virtual shapes. In this paper, we describe the working principles of the interface by using both absolute and relative approaches to control the position on each single control point on the MEC spline. Then, we describe the methodology that has been implemented, passing from the CAD geometry, linked to VisualNastran in order to maintain the parametric properties of the virtual shape. Then, we present the coâ simulation between VisualNastran and MATLAB/Simulink used for achieving this goal and controlling the system and finally, we present the results of the subsequent testing session specifically carried out to evaluate the accuracy and the effectiveness of the mechatronic device
Equilibrium shapes with stress localisation for inextensible elastic möbius and other strips
© Springer Science+Business Media Dordrecht 2015. We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order onedimensional problem posed on the centreline of the strip. We derive Euler-Lagrange equations for this problem in Euler-Poincaré form and formulate boundary-value problems for closed symmetric one-and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami
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