Geometry. Application orientated basics and examples for engineers (Q2877561)

This is a textbook (in German language) on typical topics of engineering geometry. The content is divided into four major chapters, titled ``Ties to geometry in high-school'', ``Matrices, vectors, coordinates'', ``Curves, surfaces, solids'', and ``Projections and basics of descriptive geometry''.NEWLINENEWLINEThe first chapter discusses polygons with emphasis on triangles, length and area computations, and selected solids (cuboids, cylinders and prisms, pyramids and cones, rotation and translation solids, and polyhedra).NEWLINENEWLINEThe second chapter is concerned with basic linear algebra in two and three dimensions. As a specialty, homogeneous coordinates are used for describing rotations and other spatial transformations.NEWLINENEWLINEChapter~3 presents parametric and algebraic equations for curves and surfaces and discusses conic sections and quadrics in more detail. One section is dedicated to the computation of distances and intersections between curves and surfaces.NEWLINENEWLINEFinally, Chapter~4 deals with basic aspects of descriptive geometry: Orthographic projection and in particular 2-view projection, the construction of surfaces of constant slope and roofs (important in civil engineering and architecture), and axonometric projection.NEWLINENEWLINEThe book aims at an engineering audience. The presentation strives for exactness and precision whenever this is possible with reasonable effort. The same is true for proofs or, at least, motivating calculations. Usually, the presented topics are accompanied by applied examples, often from spherical geometry and roof constructions. Instead of using a variety of different examples, the author often considers identical or similar examples in different context or presents an alternative solution by different methods.NEWLINENEWLINEShort solutions to the (mostly numeric) exercises are given in the book. They are complemented by more detailed solutions that can also be downloaded from an accompanying web-page. There, one can also find the Matlab source for some numeric and symbolic calculations and for the numerous illustrations in this book.