Combining task and motion planning requires to interleave causal and geometric reasoning, in order to guarantee the plan to be executable in the real world. The resulting search space, which is the cross product of the symbolic search space and the geometric search space, is huge. Systematically calling a geometric reasoner while evaluating symbolic actions is costly. On the other hand, geometr...

Introduction Various methods for symbolic melodic search have been proposed, from string matching based approaches to geometric models [3]. A study on melodies in the Dutch Song Database (www.liederenbank.nl) has shown that sequence alignment methods are quite powerful at dealing with melodic variability [2]. We investigate the potential of such methods for retrieving RISM incipits, comparing 2...

This paper introduces a novel technique to create digital potteries using certain number-theoretic techniques of digital geometry. Given a digital generatrix, the proposed wheel-throwing procedure works with a few primitive integer computations only, wherein lies its strength and novelty. The digital surface created out of the digital wheel-throwing is digitally connected and irreducible when t...

Various geometric and algebraic computations (e.g., of the convex hulls, Voronoi diagrams, and scalar, univariate and multivariate resultants) boil down to computing the sign or the value of the determinant of a matrix. For these tasks numerical factorizations of the input matrix is the most attractive approach under the present day computer environment provided the rounding errors are controll...

On the walls of the Museum there hangs a picture symbolic of one of the strangest phenomena in the history of modern art. It shows five painters gathered in a studio. One is commenting on a drawing by a second, while the other three look up from their work to listen. Painted in London during 1765 by the Pennsylvaniaborn portraitist Matthew Pratt, the canvas was exhibited a year later at the Soc...

Nativists have postulated fundamental geometric knowledge that predates linguistic and symbolic thought. Central to these claims is the proposal for an isolated cognitive system dedicated to processing geometric information. Testing such hypotheses presents challenges due to difficulties in eliminating the combination of geometric and non-geometric information through language. We present evide...

For robots to solve real world tasks, they often require the ability to reason about both symbolic and geometric knowledge. We present a framework, called KABouM, for integrating knowledge-level task planning and motion planning in a bounding geometry. By representing symbolic information at the knowledge level, we can model incomplete information, sensing actions and information gain; by repre...

Many (2D) Dynamic Geometry Systems (DGSs) are able to export numeric coordinates and equations with numeric coefficients to Computer Algebra Systems (CASs). Moreover, different approaches and systems that link (2D) DGSs with CASs, so that symbolic coordinates and equations with symbolic coefficients can be exported from the DGS to the CAS, already exist. Although the 3D DGS Calques3D can export...