Branching blend of natural quadrics based on surfaces with rational offsets

نویسنده

  • Rimvydas Krasauskas
چکیده

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. The construction is extended via inversion to a PN branching blend of degree (8, 4) between Dupin cyclide and a natural quadric.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

PN-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 کامل

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 کامل

Parameterizing surfaces with certain special support functions, including offsets of quadrics and rationally supported surfaces

We discuss rational parameterizations of surfaces whose support functions are rational functions of the coordinates specifying the normal vector and of a given non-degenerate quadratic form. The class of these surfaces is closed under offsetting. It comprises surfaces with rational support functions and non-developable quadric surfaces, and it is a subset of the class of rational surfaces with ...

متن کامل

Improved Blends between Primitive Surfaces

By applying results on canal surfaces, we study exact rational parametrizations of fixed radius rolling ball blends of pairs of natural quadrics. We classify all configurations where this kind of rational parametrization is possible, and describe a general algorithm for parametrizing fixed radius rolling ball blends. The algorithm is then applied to parametrize the fixed radius rolling ball ble...

متن کامل

Rational blending surfaces between quadrics

Using tools from classical line geometry and the theory of kinematic mappings, it is possible to define an intrinsic control structure for NURBS curves and surfaces on the sphere, the cylinder and on any projectively equivalent quadratic surface. These methods are further used to construct exact C blends between these surfaces, such that interactive design of trim lines and surface tension is p...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Computer Aided Geometric Design

دوره 25  شماره 

صفحات  -

تاریخ انتشار 2008