Galilei Laguerre Geometry and Rational Circular Ooset Surfaces
نویسندگان
چکیده
In this paper the Laguerre geometry of three-dimensional Galilei space, that is, the geometry of oriented planes and cycles of an aane Cayley-Klein space with absolute line and two conjugate complex absolute points on it, is studied. Several diierent models are presented: A cyclographic model and an isotropic model together with their duals and an interpretation in terms of geometrical optics of Galilei space. We also have a closer look on Laguerre transformations. Galilei geometry arises naturally in the context of rational surfaces which possess rational circular ooset surfaces, and it can also be used for modeling rational circular ooset surfaces, e. g., with Galilei cyclides.
منابع مشابه
A Laguerre geometric approach to rational offsets
Laguerre geometry provides a simple approach to the design of rational curves and surfaces with rational offsets. These so-called PH curves and PN surfaces can be constructed from arbitrary rational curves or surfaces with help of a geometric transformation which describes a change between two models of Laguerre geometry. Closely related to that is their optical interpretation as anticaustics o...
متن کاملBranching blend of natural quadrics based on surfaces with rational offsets
A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed. The blend is a ring shaped patch of a PN surface (surface with rational offset) parametrized by rational bivariant functions of degree (6, 3). General theory of PN surfaces is developed using Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. ...
متن کاملRational Offset Surfaces and Their Modeling Applications
This survey discusses rational surfaces with rational offset surfaces in Euclidean 3-space. These surfaces can be characterized by possessing a field of rational unit normal vectors, and are called Pythagorean normal surfaces. The procedure of offsetting curves and surfaces is present in most modern 3d-modeling tools. Since piecewise polynomial and rational surfaces are the standard representat...
متن کاملPN-surfaces for blending applications
General theory of PN-surfaces (surfaces with rational offsets) is developed using dual Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. This approach allows to construct new PN-blendings between two natural quadrics in many positions, and demostrate improved shape and lower parametrization degree than earlier proposed canal surface solutions. The construction...
متن کاملGenerating Shaded Ooset Surfaces with Distance, Closest-point and Color Volumes
This paper presents a technique for color-shading ooset surfaces of CSG models. The ooset surfaces are generated by rst scan converting the CSG model into a distance volume. A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the object being represented by the volume. Extracting iso-surfaces from the distance volume at various o...
متن کامل