Special Issue of CAGD
on
Geometric Constraint Solving and Reasoning

Description

This special issue follows the fifth edition of the Technical Track:

GCR: Geometric Constraints and Reasoning

of the 25th Annual ACM Symposium on Applied Computing, which took place March 22-26, 2010, in Sierre, Switzerland.

GCR is devoted to the recent trends in the domain of geometric constraint solving (GCS) and automated, or computer-aided, deduction in geometry (ADG). Geometric problems lie at the core of many theoretical and applied studies and engineering applications. For instance, many problems from geometric modeling, computer graphics, computer vision, computer aided design, and robotics can be reduced to either geometric constraint solving or geometric reasoning. Conversely, a great variety of methods following very different approaches have been used for solving geometric constraints and for proving geometric theorems.

GCR offers a great opportunity to bring together researchers coming from diverse communities concerned with subjects as different as constraint programming, numerical analysis, interval analysis, CAD-CAM, theorem proving and computer graphics.

The topics for GCR, and for this special issue in CAGD include, but are not limited to:

• resolution of geometric constraints, with computer algebra, numerical analysis, interval analysis, logical approaches (e.g. provers), or new methods,
  
• geometric theorem proving,
  
• decomposition of systems of geometric constraints,
  
• mixing geometric and non geometric constraints, white boxes, black boxes, geometric constraints and constraints programming,
  
• detection of dependencies between constraints, debugging geometric constraints,
  
• constrained curves, surfaces, blends,
  
• "exotic" formulations of geometric constraints,
  
• comparison of resolution methods or constraints formulations for the same problems,
  
• mathematical foundations: combinatorial rigidity, graph theory, matroid theory, computer algebra,
  
• broad applications, in Computer Graphics, CAD-CAM, robotics, mechanism design, chemistry , photogrammetry, virtual reality,
  
• sensitivity to value parameters, and other robustness issues,
  
• choice of "good" or "intended" solutions,
  
• dynamic geometry, pedagogical purposes, generating explanations, examples, counter examples,
• computer-human interfaces for geometric constraints,
• geometric constraints and data exchange,
• topological constraints, eg optimal curves or surfaces with prescribed, topology (homology, homotopy, isotopy), shape optimization,
• geometric constraints and geometric representations (boundary representation, constructive solid geometry, features),
  
• integration of geometric solvers into modelers, geometric solver industrial/market solutions
  
• constraints versus features,
  
• reverse engineering, capturing design intent,
  
• definition of new kinds of constraints (i.e.: topological constraints; ergonomic constraints; aesthetic constraints; kinematic constraints; physical constraints; assembly-disassembly constraints) and how to manage them,
  
• persistent naming problem and geometric modeling by constraints.