Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T10:11:26.957Z Has data issue: false hasContentIssue false
  • English
  • Français

Shape computations with NURB curves

Published online by Cambridge University Press:  28 May 2018

Elif Ensari  and
Mine Özkar
Elif Ensari*
Affiliation:
Istanbul Technical University, Faculty of Architecture, Taskisla, Taksim, Istanbul34437
Mine Özkar
Affiliation:
Istanbul Technical University, Faculty of Architecture, Taskisla, Taksim, Istanbul34437
*
Author for correspondence: Elif Ensari, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Freeform 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.

Keywords

Computer implementationcurve implementationNURB curve grammarsshape grammars
Type
Research Article
Information
AI EDAM , Volume 32 , Issue 3 , August 2018 , pp. 282 - 294
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chau, HH (2002) Preserving brand identity in engineering design using a grammatical approach (Doctoral dissertation). University of Leeds, Leeds, United Kingdom.Google Scholar
Jowers, I and Earl, C (2009) The construction of curved shapes. Environment and Planning B: Planning and Design 37, 42–58.CrossRefGoogle Scholar
Jowers, I and Earl, C (2011) Implementation of curved shape grammars. Environment and Planning B: Planning and Design 38, 616–635.CrossRefGoogle Scholar
Jowers, I and Earl, C (2015) Extending the algebras of design. Nexus Network Journal 17(3).CrossRefGoogle Scholar
Jowers, I, Hogg, DC, McKay, A, Chau, HH and de Pennington, A (2010) Shape detection with vision: implementing shape grammars in conceptual design. Research in Engineering Design 21, 235–247.CrossRefGoogle Scholar
Jowers, I, Prats, M, Earl, C and Garner, S (2004) On curves and computation with shapes. In Akin, O, Krishnamurti, R and Lam, KP (eds). Generative CAD Systems Symposium: G-CADS 2004. Pittsburgh: Carnegie Mellon University, pp. 439–457.Google Scholar
Keles, HY, Özkar, M and Tari, S (2012) Weighted shapes for embedding perceived wholes. Environment and Planning B: Planning and Design 39, 360–375.Google Scholar
Krishnamurti, R (1992) The maximal representation of a shape. Environment and Planning B: Planning and Design 19, 267–288.CrossRefGoogle Scholar
McCormack, JP and Cagan, J (2003). Increasing the scope of implemented shape grammars: a shape grammar interpreter for curved shapes. In Proc. ASME 2003 Int. Design Engineering Technical Conf. & Computers and Information in Engineering Conf., Paper No. DETC2003/DTM-48643, Chicago, IL, September 2–6.Google Scholar
McCormack, JP and Cagan, J (2006) Curve-based shape matching: supporting designers’ hierarchies through parametric shape recognition of arbitrary geometry. Environment and Planning B: Planning and Design 33, 523–540.CrossRefGoogle Scholar
Piegl, L and Tiller, W (1997) The NURBS Book, 2nd edn. New York: Springer-Verleg.Google Scholar
Stiny, G (2006) Shape: Talking About Seeing and Doing. Cambridge, Massachusetts: MIT Press.Google Scholar