Towards untrimmed NURBS: CAD embedded reparameterization of trimmed B-rep geometry using frame-field guided global parameterization


Isogeometric analysis, Model generation, Meshing, Parameterization, Watertight splines


The boundary representation or B-rep is the prevalent geometry description in computer aided design (CAD). It combines aspects from explicit and implicit geometry and is incompatible with many downstream applications such as finite element analysis (FEA) and computer aided manufacturing (CAM). We develop a semi-automatic frame-field guided parameterization approach that converts trimmed B-rep geometry to conforming, watertight analysis-suitable NURBS. The resulting geometry description is simultaneously suitable for design as well as analysis and therefore avoids the need for further meshing and geometry-processing. While existing frame-field based global parameterization methods offer the high quality necessary in our application, they suffer from several robustness issues. Current challenges mainly stem from the lack of integrability of the frame-field which causes the computed parameterization to fold-over, particularly near parameterization singularities. We propose specialized constraints that incorporate properties of an analytical solution that resolve the poor behavior near singularities. Furthermore, we present a convenient and efficient solution framework that directly incorporates such constraints into a reduced basis. Improved behavior around parameterization singularities simplifies the extraction of a quadrilateral layout. This layout is subsequently fitted with C0 NURBS to yield a conforming watertight model that is analysis suitable. The latter is illustrated by performing isogeometric shell modal analysis on several geometric models.

Original Publication Citation

R. R. Hiemstra, K. M. Shepherd, M. J. Johnson, L. Quan, and T. J. R. Hughes. “Towards untrimmed NURBS: CAD embedded reparameterization of trimmed B-rep geometry using frame-field guided global parameterization,” Computer Methods in Applied Engineering and Mathematics, vol. 369, article no. 113227, 2020.

Document Type

Peer-Reviewed Article

Publication Date







Ira A. Fulton College of Engineering


Civil and Environmental Engineering

University Standing at Time of Publication

Graduate Student