Authors
C. Blanc, C. Schlick
Keywords
Computer Aided Geometric Design, Curves and Surfaces,
Splines, Intuitive Modelling.
Abstract
This paper presents a new model of spline curves and
surfaces. The main characteristic of this model is that it has been
created from scratch by using a kind of mathematical engineering
process. In a first step, a list of specifications was
established. This list groups all the properties that a spline model
should contain in order to appear intuitive to a non-mathematician
end-user. In a second step, a new family of blending functions was
derived, trying to fulfill as many items as possible of the previous
list. Finally, the degrees of freedom offered by the model have been
reduced to provide only shape parameters that have a visual
interpretation on the screen. The resulting model includes many
classical properties such as affine and perspective invariance, convex
hull, variation diminution, local control and C2/G2 or C2/G0
continuity. But it also includes original features such as a continuum
between B-splines and Catmull-Rom splines, or the ability to define
approximation zones and interpolation zones in the same curve or
surface.
Document
sig95.ps (5.6 MB)
Extended Field Functions for Soft Objects
Authors
C. Blanc, C. Schlick
Keywords
Implicit Surfaces, Soft Objects, Blobs, Metaballs, Convolution
Surfaces, Field Functions.
Abstract
In the field of geometric design, the generic term "soft object"
embeds several implicit models (blobs, metaballs, distance surfaces,
convolution surfaces) proposed over the years for modelling and
animating free-form 3D objects. All these models share the property
that curved surfaces are defined by computing isosurfaces of a set of
potential fields. The topic of this paper is to presents some
innovative ways for defining these potential fields. First, it
proposes a set of ready-to-use functions and second describes an
environment which allows the user to design interactively his own
functions.
Document
Part 1 (6.7 MB)
Part 2 (5.8 MB)
Generic Implementation of Axial
Deformation Techniques
Author
C. Blanc
Keywords
Geometric Modeling, Deformation Techniques, Implementation
Abstract
Global deformation techniques were first introduced to extend the set
of primitives that may be used in constructive solid modeling. In
fact, these techniques are more general and have been consequently
adapted to tessellated surfaces or parametric patches as well. This
paper proposes a generic implementation of several of these global
deformation techniques. The term "generic" focuses on the fact that
the implementation depends neither on a given geometric model for
surfaces nor on a specific data structures for internal
representation.
Document
gem.V.ps
More Accurate Representation of Conics by
NURBS
Authors
C. Blanc, C Schlick
Keywords
Conic Sections, NURBS, Reparametrization, Rational Polynomials,
Continuity.
Abstract
One of the argument usually given to explain the popularity of NURBS
is the fact that they allow to define free-form curves and surfaces
(as almost every spline model) and provide also an exact
representation of conic sections and thus of a large set of curves and
surfaces that are intensively used in CAD : circular arcs, circles,
cylinders, cones, spheres, surfaces of revolution, etc. This paper
deals with the two following problems :
- All the known representations by NURBS of curves and
surfaces based on conics have only a C1 continuity. Moreover, there
does not exist any technique which would eventually allow to find a
parametrization with a higher level of continuity.
- The parametrization resulting from the representation of
conics by NURBS can deviate significantly from the ideal arc length
parametrization. The only known solution to reduce this deviation is
to increase the number of control points of the spline (using
refinement algorithms, for instance), but such a process converges
quite slowly to the ideal parametrization.
The solution that we propose in this paper uses an original
reparametrization process, that we have called zigzag
reparametrization, which is based on a particular family of rational
polynomials. This techniques allows to get a higher order continuity
as well as a more uniform parametrization.
Document
cga1.ps
Ratioquadrics: An Alternative Model for
Superquadrics
Authors
C. Blanc, C Schlick
Keywords
Superconics, Superquadrics, Ratioconics,
Ratioquadrics, Rational Polynomials.
Abstract
This paper presents a new family of 2D curves and its extension to 3D
surfaces, respectively called ratioconics and ratioquadrics, that have
been designed as alternatives to the well-known superconics and
superquadrics. This new model is intended to improve the original one
on three main points : first it is several times faster to compute,
second it provides higher order continuities (C1/G2 or C2/G2 instead
of C0/G0), and third it provides a greater variety of shapes for the
resulting curves and surfaces. All these improvements are obtained by
replacing the signed power function involved in the formulation of
superconics and superquadrics by linear or quadratic rational
polynomials.
Document
tvc1.ps
tvc1-pic.ps
Easy Transformations between Cartesian,
Cylindrical and Spherical Coordinates
Authors
C. Blanc, C Schlick
Keywords
Geometrical Transformations, Implementation.
Abstract
This paper proposes a set of functions that realize all possible
transformations of a point in a threedimensional euclidian space
between global and local frames using either cartesian, cylindrical or
spherical coordinates.
Document
coord.ps
A Generic Implementation of Free Form
Deformation Techniques
Authors
C. Blanc, C. Schlick
Keywords
Geometric Modeling, Deformation Techniques, FFD, EFFD, Implementation.
Abstract
The present paper proposes a generic implementation of FFD and EFFD
techniques. The term "generic" focuses on the fact that the
implementation depends neither on a given geometric model for surfaces
nor on a specific data structures for internal representation. Each
deformation routine acts only on points : it takes the coordinates of
a point on the original object, computes its displacement according to
the deformed lattice, and finally returns the new coordinates of the
point.
Document
gen_ffd.ps