This paper addresses the problem of automated registration of multi-view point clouds generated by a 3D scanner using sphere targets. First, sphere targets are detected from each point cloud. The centroids of the detected targets in each point cloud are then used for rough registration. Congruent triangles are computed from the centroids for the correspondence among them, with which a rigid bod...

In [3], in my argument for the primacy of Euclidean geometry on the basis of rigid motions and the existence of similar but non-congruent triangles, I wrote the following: A: “The mobility of rigid objects is now recognized as one of the things every normal human child learns in infancy, and this learning appears to be part of our biological progaramming.” B. “. . . we are all used to thinking ...

A famous theorem due to E. Steinitz states, in one of its formulations, that every planar (or, equivalently, every spherical) graph can be realized as the graph of edges and vertices of a convex polyhedron in Euclidean 3-space (see, for example, Grünbaum [1, Section 13.1] or Ziegler [3, Chapter 4]). This representation is possible in many different ways, but in all of them the circuits that bou...

Vocabulary is one of the essential components of language and learning phrasal verbs as part of vocabulary is quite challenging for foreign language learners. The present study aimed at investigating the effects of visual and auditory input enhancement on learning non-congruent phrasal verbs. The participants of the study were 90 intermediate English language learners who were divided into two ...