Geometry is a privileged field of investigation for various domains of computer science from image processing to geometric modeling via artificial intelligence in education and automated proof in geometry or semantic indexation of multimedia databases, and so on.

This special issue of AMAI is devoted to formal computational aspects of geometry. Computer supported geometry can be investigated in several different ways. At the beginning of the 1960s, the seminal work of Gelernter in the domain of automated proof was about synthetic geometry as taught in school. Then, in the late 1970s, a kind of revolution occurred with the work of Wu consisting in translating geometry into algebra and in using pseudo-division to perform proofs of a high-level theorem in both Euclidean and hyperbolic geometries. Subsequently, much work has been done continuing that geometry/algebra relation by considering other aspects of geometry, like differential geometry, distance geometry, discovering geometric theorems in figures with dynamic geometry software or from graphical figures, etc.

Moreover, several researchers studied the foundations of geometry through various sets of axioms; this way, the classical axiomatic approaches of Hilbert and Tarski have been formalized, as well as computational origami or incidence geometry. Outside the domain of automated and formalized proof, computer supported geometry is also encountered almost everywhere in geometric modeling – for instance with geometric constraint solving, declarative modeling or topological modeling – and also in computational geometry or combinatorial geometry.

For this special issue of AMAI, we are seeking original contributions on various aspects of computer supported geometry. Relevant topics include (but are not limited to):

• probabilistic, synthetic, and logical approaches for automated geometric reasoning;
• polynomial algebra, invariant and coordinate-free methods;
• interactive theorem proving in geometry;
• symbolic and numeric methods for geometric computation, geometric constraint solving, automated generation/reasoning and manipulation with diagrams;
• design and implementation of geometry software, special-purpose tools, experimental studies;
• applications of formalization of geometry to mechanics, geometric modeling, CAGD/CAD, computer vision, robotics and education.