ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Gn-1-functional splines for interpolation and approximation of curves, surfaces and solids
Computer Aided Geometric Design
Blending of implicit surfaces with functional splines
Computer-Aided Design
Computer Aided Geometric Design
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Using Geometric Distance Fits for 3-D Object Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The NURBS book
Pipe surfaces with rational spine curve are rational
Computer Aided Geometric Design
On blending of several quadratic algebraic surfaces
Computer Aided Geometric Design
Gn-continous connections between normal ringed surfaces
Computer Aided Geometric Design
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Blending quadric surfaces with piecewise algebraic surfaces
Graphical Models
Constructive modeling of G1 bifurcation
Computer Aided Geometric Design
Bounded Blending for Function-Based Shape Modeling
IEEE Computer Graphics and Applications
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
G1-smooth branching surface construction from cross sections
Computer-Aided Design
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
Functional splines with different degrees of smoothness and their applications
Computer-Aided Design
Technical Section: Locally restricted blending of Blobtrees
Computers and Graphics
Gn blending multiple surfaces in polar coordinates
Computer-Aided Design
Constructive G1 connection of multiple freeform pipes in arbitrary poses
Computer Aided Geometric Design
| Hi-index | 0.00 |
The functional spline is a highly effective tool for blending multiple implicit surfaces, but the pipes to be blended are generally defined as parametric normal ringed surfaces. To bridge the gap between the equation forms, Hartmann presented a closing-based algorithm (constructing a closing for each pipe and blending the closings), where a closing is an implicit surface sealing a pipe end (inlet or outlet). So far, however, the closing construction remains imperfect: the initial normal ringed surfaces must satisfy a certain geometric requirement and the obtained closings are only G^1-continuous with these surfaces (as is the resulting blending surface). This paper proposes a new algorithm that finds the desired closings without restricting its scope of application. The procedure involves the rational parametrization of the initial surfaces and seeking the closings, interpolating rational surfaces with higher-order continuity through constrained optimization. Three practical examples illustrate the strong performance of this algorithm. In particular, the last example addresses the normal elliptic surfaces.