With many examples and numerous photos, this book explains important geometrical terms and concepts such as multi-view projection and 3D projection, curve bends and surface cambering, the geometry of movement and non-Euclidian space.
Introduction.- An idealized world out of simple elements: Points,
straight lines and circles in the drawing plane. Special points inside the
triangle. Elemental building blocks in space. Euclidean space. Polarity,
duality and inversion. Projective and non-euclidean geometry.- Projections
and shadows - Reduction of the dimension: The principle of the central
projection. Through restrictions to parallel projection and normal
projection. Assigned normal projections. The difference about technical
drawing.- Polyhedra: Multiple faced and multi-sided: Congruence
transformations. Convex polyhedral. Platonic solids. Other special classes of
polyhedral. Planar sections of prisms and pyramids.- Curved but simple:
Planar and spatial curves. The sphere. Cylinder surfaces. The ellipse as a
planar section of a cylinder of revolution.- More about conic sections and
developable surfaces: Cone surfaces. Conic sections. General developables
(torses). About maps and "sphere developments". The "physical" reflection in
a circle, a sphere and a cylinder of revolution.- Prototypes: Second-order
surfaces. Three types of spatial points. Surfaces of revolution. The torus as
a prototype for all other surfaces of revolution. Pipe and duct surfaces.-
Further remarkable classes of surfaces: Ruled surfaces. Helical surfaces.
Different types of spiral surfaces. Minimal surfaces.- The endless variety of
curved surfaces: Mathematical surfaces and free-form surfaces. Interpolating
surfaces. Bézier- and B-spline-curves. Bézier- and B-spline-surfaces. Surface
design, only differently.- Photographic image and individual perception: The
human eye and the pinhole camera. Different techniques of perspective.
Reconstruction of spatial objects. Other perspectives. Geometry at the water
surface.- Everything is moving - Kinematics: The pole, about which everything
revolves. Different mechanisms. Ellipse movement. Trochoid motion.- Movement
in space: Movement on the sphere. Genmeral spatial movements. Where is the
sun? About sundials.- A: The variety of tessellations.- B: A course in free
hand drawing.- C: A geometrical course about photography.- D Nature of
geometry and geometry of nature.
Georg Glaeser ( born in 1955 in St. Johann im Pongau, Austria) is an Austrian mathematician and has been a professor of mathematics and geometry at the University of Applied Arts, Vienna since 1998. He studied mathematics and geometry at the University of Vienna from 1973 to 1978 before completing his doctorate and habilitation. Glaeser was also a visiting professor at Princeton University between 1986 and 1987 and has written a number of books on computational geometry and computer graphics.
