Shape computations with NURB curves

2018 ◽  
Vol 32 (3) ◽  
pp. 282-294
Author(s):  
Elif Ensari ◽  
Mine Özkar
Keyword(s):  
Practical Approach ◽  
Control Points ◽  
Two Dimensional ◽  
Rational Basis ◽  
Modeling Tools ◽  
Initial Shape ◽  
Digital Modeling ◽  
Additional Control ◽  
Sample Set ◽  
Adjustment Of Parameters

AbstractFreeform curves are commonly used in contemporary design practices, especially with digital modeling tools. We investigate facilitating shape subtraction and addition with two-dimensional (planar) non-uniform rational basis-spline (NURB) curves with the codes and conventions of modeling while preserving the visual continuity of curved shapes. Our proposed tool, developed in a common digital modeling environment, automates the adjustment of parameters for tangential continuity of curves in shape rule applications. When the user designates a curve range to subtract from an initial shape and provides a new curved shape to add to it, the tool splits the initial shape, scales and aligns the curve to be added to fit into this range, introduces additional control points at the joining ends of the new curve to preserve continuity and redraws the new curve. We present a sample set of design variations produced using this practical approach which can be utilized as a method or become part of an automated NURB curve manipulation tool for designers.

scholarly journals Cultural heritage conservation and communication by digital modeling tools. Case studies: minor architectures of the Thirties in the Turin area

2015 ◽  
Vol II-5/W3 ◽  
pp. 25-32 ◽  
Author(s):  
A. Bruno Jr. ◽  
R. Spallone
Keyword(s):  
Three Dimensional ◽  
Le Corbusier ◽  
World War ◽  
Cultural Goods ◽  
Modeling Tools ◽  
Representation Systems ◽  
Digital Modeling ◽  
The Relationship ◽  
New Buildings ◽  
Guide Lines

Between the end of the twenties and the beginning of the World war two Turin, as the most of the Italian cities, was endowed by the fascist regime of many new buildings to guarantee its visibility and to control the territory: the fascist party main houses and the local ones. <br><br> The style that was adopted for these constructions was inspired by the guide lines of the Modern movement which were spreading by a generation of architects as Le Corbusier, Gropius, Mendelsohn. <br><br> At the end of the war many buildings were reconverted to several functions that led heavy transformations not respectful of the original worth, other were demolished. <br><br> Today it's possible to rebuild those lost architectures in their primal format as it was created by their architects on paper (and in their mind). This process can guarantee the three-dimensional perception, the authenticity of the materials and the placement into the Turin urban tissue, using static and dynamic digital representation systems. The “three-dimensional re-drawing” of the projects, thought as an heuristic practice devoted to reveal the original idea of the project, inserts itself in a digital model of the urban and natural context as we can live it today, to simulate the perceptive effects that the building could stir up today. The modeling skills are the basis to product videos able to explore the relationship between the environment and “re-built architectures”, describing with the synthetic movie techniques, the main formal and perceptive roots. The model represents a scientific product that can be involved in a virtual archive of cultural goods to preserve the collective memory of the architectural and urban past image of Turin.

Analysis of Flood and Dry Threshold Definition in Two-Dimensional Hydrodynamic Flood Modeling Tools

2018 ◽  
pp. 675-687
Author(s):  
Leslie Salvan ◽  
Elodie Zavattero ◽  
Olivier Delestre ◽  
Philippe Gourbesville
Keyword(s):  
Two Dimensional ◽  
Flood Modeling ◽  
Modeling Tools

Parametric Modeling as a Tool of Analysis and Interpretation of Built Heritage

2019 ◽  
pp. 366-402
Author(s):  
Marco Vitali ◽  
Roberta Spallone ◽  
Francesco Carota
Keyword(s):  
Parametric Modeling ◽  
Design Criteria ◽  
Architectural Heritage ◽  
Modeling Tools ◽  
The Past ◽  
Built Heritage ◽  
Digital Modeling ◽  
Modeling Software

In this chapter are developed some considerations about the heuristic potentialities of parametric digital modeling as a tool for analyzing and interpreting architectural heritage. Observed that the parametric thinking in architecture could be recognized almost from the origin, new parametric modeling software allows to verify the design criteria of the past. On the basis of previous studies on Baroque vaulted atria, this chapter develops, using parametric modeling tools, a real vocabulary of shapes and their possible combinations, suggested by the architectural literature of the time and the survey of about seventy atria in Turin. This method has been tested on the case study of the lunettes dome in the atrium of Palazzo Carignano.

Formal grammar methodology for digital visualization of Islamic geometric patterns

2021 ◽  
pp. 147807712110390
Author(s):  
Ghazal Refalian ◽  
Eloi Coloma ◽  
Joaquim N Moya
Keyword(s):  
Computer Science ◽  
New Technologies ◽  
Applied Mathematics ◽  
Digital Fabrication ◽  
Formal Grammar ◽  
Modeling Tools ◽  
Flat Surfaces ◽  
Geometric Patterns ◽  
Digital Modeling ◽  
Cad Cam

In the oriental practice of art and architecture, and among the regions under their influence, Islamic geometric patterns (IGPs) have been widely used, not only due to aesthetics and decoration but also to make it possible to cover wide flat surfaces, curved surface of domes, and perforated surfaces of window and partitions, with perfectly tessellated shapes. However, with advances in time and technology, these techniques could not connect to the new technologies and benefit from the capacities of digitalization. Recent progress in science and technology tends to open new doors to study geometrical patterns by digitalizing the old ones and developing new variations. This study looks at formal grammar and computer science to introduce a new approach to digital visualization of available IGPs, particularly, star patterns. We investigate the potentials of developing a re-writing system for simulation of IGPs to provide a flexible platform, which allows introducing IGP to CAD/CAM software without previous knowledge on their design or drawing techniques. This methodology allows designers to directly develop various scenarios of IGP applications and implement them on related CAD/CAM tools. Formal language and grammar theories, based on applied mathematics are contributing to the advancements of computer science and digital modeling. They can provide an opportunity to express relational definition and written equivalents of the geometries by using strings and symbols. It is supposed that by using the formal grammar frameworks, certain languages could be developed to visualize IGPs in a machine-friendly way, and consequently, this computational interpretation of IGPs facilitates their application and further developments, for example, regards to digital fabrication. The presented method of IGP visualization is developed as a C#-based add-on for Grasshopper in Rhino3D, one of the main modeling tools used by architects and product designers.

A Two Dimensional Rule-Based Shape Synthesis Method

1989 ◽  
Author(s):  
D. M. Russell ◽  
S. P. Manoochehri
Keyword(s):  
Finite Element ◽  
Minimum Weight ◽  
Synthesis Method ◽  
Element Model ◽  
Optimization Methods ◽  
Two Dimensional ◽  
Shape Modification ◽  
Allowable Limit ◽  
Initial Shape ◽  
Optimal Configurations

Abstract The objective of this study is to form two-dimensional structural/mechanical parts under general loading and restraint conditions. The designs created are of minimum weight with the stresses throughout the parts as close to the allowable limit as possible. The study uses a thresholding approach with minimal designer intervention for generating optimal configurations. The process begins with the user creating an initial design which encompasses all the specified loads and restraints. Finite element techniques are employed to discretize the part geometry. Then a set of heuristics are utilized for shape modification, by removing elements from the finite element model. A Bi-Directional Thresholding technique, BDT, is developed that determines which elements ought to be removed. After BDT is performed element connectivity is checked and maintained. A two-step connectivity check algorithm is implemented which locates and resolves major (complete) as well as minor (partial) losses in connectivity. This procedure, unlike most common shape optimization methods, is capable of quickly making very large changes in the geometry of the part. It is able to create holes in the geometry, where none existed in the initial shape, in order to produce a better design.

Release of a viscous power-law fluid over an inviscid ocean

2012 ◽  
Vol 700 ◽  
pp. 63-76 ◽  
Author(s):  
Samuel S. Pegler ◽  
John R. Lister ◽  
M. Grae Worster
Keyword(s):  
Power Law ◽  
Large Time ◽  
Three Dimensional ◽  
Shear Thinning ◽  
Capillary Forces ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Initial Shape ◽  
Algebraic Decay

AbstractWe consider the two- and three-dimensional spreading of a finite volume of viscous power-law fluid released over a denser inviscid fluid and subject to gravitational and capillary forces. In the case of gravity-driven spreading, with a power-law fluid having strain rate proportional to stress to the power $n$, there are similarity solutions with the extent of the current being proportional to ${t}^{1/ n} $ in the two-dimensional case and ${t}^{1/ 2n} $ in the three-dimensional case. Perturbations from these asymptotic states are shown to retain their initial shape but to decay relatively as ${t}^{\ensuremath{-} 1} $ in the two-dimensional case and ${t}^{\ensuremath{-} 3/ (n+ 3)} $ in the three-dimensional case. The former is independent of $n$, whereas the latter gives a slower rate of relative decay for fluids that are more shear-thinning. In cases where the layer is subject to a constraining surface tension, we determine the evolution of the layer towards a static state of uniform thickness in which the gravitational and capillary forces balance. The asymptotic form of this convergence is shown to depend strongly on $n$, with rapid finite-time algebraic decay in shear-thickening cases, large-time exponential decay in the Newtonian case and slow large-time algebraic decay in shear-thinning cases.

Establishment of High Precision Horizontal and Vertical Control Network in Zoucheng City

2013 ◽  
Vol 864-867 ◽  
pp. 2787-2791
Author(s):  
De Bao Wang ◽  
Yong Xiang Liu ◽  
Wen Jing Yang
Keyword(s):  
Fourth Order ◽  
Function Method ◽  
Three Dimensional ◽  
Geodetic Network ◽  
Control Network ◽  
Control Points ◽  
Two Dimensional ◽  
Level Control ◽  
Vertical Control ◽  
Free Network

The paper uses D level, E level and the level of GPS control network establishment satellite space geodetic network in Zoucheng city, through the baseline calculating, classic adjustment of free network, three-dimensional unconstrained adjustment and two-dimensional constraint adjustment to get the WGS-84 three dimensional coordinates and 1980 xi 'an horizontal coordinates of control points; then using the fourth-order levelling connection survey all D-level and part E-level control points to build vertical control network, for the remaining GPS control points we utilize quadric function method using GPS elevation fitting given its elevation seek to obtain three-dimensional coordinates of all the basic control points.

Sign in / Sign up

Export Citation Format

Share Document