Descriptive geometry

Abstract: John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD and other areas of computer graphics in this updated and expanded fourth edition. The first four chapters revise number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, transforms, interpolation, 3D curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, and the last two chapters provide an introduction to differential and integral calculus, with an emphasis on geometry. Mathematics for Computer Graphics covers all of the key areas of the subject, including:Number setsAlgebraTrigonometryCoordinate systemsTransformsQuaternionsInterpolationCurves and surfacesAnalytic geometryBarycentric coordinatesGeometric algebraDifferential calculusIntegral calculusThis fourth edition contains over 120 worked examples and over 270 illustrations, which are central to the authors descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics, giving a fascinating insight into the design of computer graphics software and setting the scene for further reading of more advanced books and technical research papers.

Abstract: This article presents a mobile Augmented Reality system, called DiedricAR, aimed at the learning of Descriptive Geometry. Thanks to its ability to recreate virtual models in real space, Augmented Reality is a technology suitable for making Descriptive Geometry comprehension and interpretation easier. The DiedricAR application allows students to learn in autonomously way by using their own mobile devices (smartphones and tablets), that work as Augmented Reality displays over training material (DiedricAR exercise workbook) specially designed for the new learning model defined by the European Higher Education System. Compared to some of the existing Augmented Reality systems used to learn Descriptive Geometry, DiedricAR offers the advantage of being specifically developed for mobile devices giving the students the possibility of using ubiquitous learning to its ultimate extent by interacting with the didactical content (i.e. showing the desired intermediate step when solving dihedral exercises). The presentation of DiedricAR is completed by exploring some key items such as the potential benefits for students' spatial ability, the relationship between application design and user experience, and software performance on several mobile devices.

Abstract: An important question in educational research is whether the im- parting of knowledge and skills also improves pupils' intelligence This aspect of transfer of learning is di-cult to study within the framework of educational re- search The longitudinal study presented hereshows, based on sophisticated test materialsandmethodsofanalysis,thatcoursesinDescriptiveGeometryimprove pupils' spatial ability, a primary dimension of intelligence Also, sex difierences thatwereclearlypresentattheflrsttestingdisappearedduring\training"inDe- scriptiveGeometry

Abstract: We review traditional and novel paradigms for representing solids and interrogating them. The traditional paradigms reviewed are the boundary, constructive, and spatial subdivision representations. The novel representation paradigms are the B-rep index, the dimensionality paradigm, and the skeleton (medial-axis transform). The B-rep index is a polyhedral representation that integrates boundary and subdivision representation. We show how to construct it and explain some of the advantages this representation offers for operations such as point/solid and line/solid classification. We also discuss how it can account for the robustness problem. The dimensionality paradigm is a technique for representing exactly complex surfaces that satisfy prescribed constraints, and we discuss some of the algorithmic infrastructure available to manipulate and interrogate this surface representation. This paradigm generalizes both implicit and parametric representations, and can deal with surfaces that otherwise could be obtained exactly only through elimination computations of forbidding complexity. The skeleton is a solid representation originally proposed in computer vision. It is an informationally-complete solid representation, and seems to facilitate operations such as automatic mesh generation for finiteelement computations, and geometric tolerancing. We show how the skeleton relates to the cyclographic map, a concept from classical descriptive geometry, and also explain the relationship between the skeleton and the Hamilton-Jacobi equation. Finally, we review some algorithms for two-dimensional mesh generation based on the skeleton. ITo appear in Advance.!! in Conlroland Dynamic!, C. T. Leondes, ed., Academic Press.