Geometrically exact dynamic splines
In this paper, we propose a complete model handling the physical simulation of deformable
1D objects. We formulate continuous expressions for stretching, bending and twisting …
1D objects. We formulate continuous expressions for stretching, bending and twisting …
[PDF][PDF] The Bernstein Basis and its Applications in Solving Geometric Constraint Systems.
S Foufou, D Michelucci - Reliab. Comput., 2012 - reliable-computing.org
This article reviews the properties of Tensorial Bernstein Basis (TBB) and its usage, with
interval analysis, for solving systems of nonlinear, univariate or multivariate equations …
interval analysis, for solving systems of nonlinear, univariate or multivariate equations …
Geometric over-constraints detection: a survey
Currently, geometric over-constraints detection is of major interest in several different fields.
In terms of product development process (PDP), many approaches exist to compare and …
In terms of product development process (PDP), many approaches exist to compare and …
Defining tools to address over-constrained geometric problems in Computer Aided Design
This paper proposes a new tool for decision support to address geometric over-constrained
problems in Computer Aided Design (CAD). It concerns the declarative modeling of …
problems in Computer Aided Design (CAD). It concerns the declarative modeling of …
Formalizing projective plane geometry in Coq
We investigate how projective plane geometry can be formalized in a proof assistant such as
Coq. Such a formalization increases the reliability of textbook proofs whose details and …
Coq. Such a formalization increases the reliability of textbook proofs whose details and …
Bounding polynomials and rational functions in the tensorial and simplicial Bernstein forms
T Hamadneh - 2018 - kops.uni-konstanz.de
This thesis considers bounding functions for multivariate polynomials and rational functions
over boxes and simplices. It also considers the synthesis of polynomial Lyapunov functions …
over boxes and simplices. It also considers the synthesis of polynomial Lyapunov functions …
[HTML][HTML] A case study in formalizing projective geometry in Coq: Desargues theorem
Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized
in the literature, the non-degeneracy conditions lead to long technical proofs. In addition …
in the literature, the non-degeneracy conditions lead to long technical proofs. In addition …
Formalizing Desargues' theorem in Coq using ranks
Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized
in the literature, the non-degeneracy conditions leads to technical proofs. In addition, when …
in the literature, the non-degeneracy conditions leads to technical proofs. In addition, when …
[HTML][HTML] Interrogating witnesses for geometric constraint solving
S Foufou, D Michelucci - Information and Computation, 2012 - Elsevier
Classically, geometric constraint solvers use graph-based methods to decompose systems
of geometric constraints. These methods have intrinsic limitations, which the witness method …
of geometric constraints. These methods have intrinsic limitations, which the witness method …
Two cryptomorphic formalizations of projective incidence geometry
Incidence geometry is a well-established theory which captures the very basic properties of
all geometries in terms of points belonging to lines, planes, etc. Moreover, projective …
all geometries in terms of points belonging to lines, planes, etc. Moreover, projective …