Abstract

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

Highlights

  • NURBS are the standard mechanism for modelling in CAD

  • For decades [1], there has been interest in producing hierarchical NURBS, NURBS with T-junctions, and other NURBS variants that allow for local refinement of a NURBS patch (Section 3)

  • Our motivation is that providing local refinement through the user interface alone would allow CAD software providers to add the extra functionality without the need to make expensive additions and changes to the underlying NURBS engine

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Summary

Introduction

For decades [1], there has been interest in producing hierarchical NURBS, NURBS with T-junctions, and other NURBS variants that allow for local refinement of a NURBS patch (Section 3). None of these solutions, has yet been widely adopted in the CAD industry. Our investigation shows that our method does deliver such functionality but that it suffers from inescapable limitations (Section 8). This idea provides an interesting intermediate option between the status quo and adoption of a new engine

The challenge
Related work
The mathematical framework
Outline of the method
Algorithm
Algorithm for the insertion of a new control point
Algorithm for generating the user-interface view
The generating system
Discussion
Limitations
Conclusion
Challenges in parallel insertion
Potential solutions in parallel insertion
Challenges in perpendicular insertion
Full Text
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