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Constructing Curvature-continuous Surfaces by Blending
[article]

2006
*
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
*

In this paper we describe an approach to the

doi:10.2312/sgp/sgp06/031-040
fatcat:fl4pvsxoffdandnq3tqgnyidem
*construction*of*curvature*-*continuous**surfaces*with arbitrary control meshes using subdivision. ... spots or*curvature*singularities at extraordinary vertices. ... The*blending*function B 2 k • Φ −1 k is C 2 -*continuous**by**construction*. ...##
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Rapid Generation of C 2 Continuous Blending Surfaces
[chapter]

2002
*
Lecture Notes in Computer Science
*

Most

doi:10.1007/3-540-46080-2_10
fatcat:5xozlocfqvbgnago2ckp3x6hva
*surface*-*blending*methods are able to*blend**surfaces*with tangent*continuity*. ... However,*curvature**continuity*has become increasingly important in geometric modelling and its applications, such as computer animation, computer-aided design and virtual reality. ... This method was first proposed*by*Bloor and Wilson [5] . In the reported literature, however, the PDE based approach has only been used to*construct*a C 1*continuous**blending**surface*. ...##
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Curvature Computation for Triangular Meshes based on Local Parametrization

2008
*
Computer-Aided Design and Applications
*

A

doi:10.3722/cadaps.2008.220-227
fatcat:i2vx5jddr5etdmwl7o5mj4yoh4
*blending*technique is then applied to vicinities of extra-ordinary vertices to ensure*continuity*and boundedness of*curvature*at each extra-ordinary vertex. ... This*blending*process does not change the value of the*surface*at the extra-ordinary points. ... The*construction*of the locally*blended*Loop*surface*requires two steps. ...##
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An Introduction to Guided and Polar Surfacing
[chapter]

2010
*
Lecture Notes in Computer Science
*

We demonstrate the challenge of high-quality

doi:10.1007/978-3-642-11620-9_20
fatcat:d7ou4xj4sbhoraouioiw2sagdi
*surface**construction**by*examples since the notion of*surface*quality lacks an overarching theory. ... A second ingredient is separation of shape design from*surface*representation*by*creating an initial guide shape and leveraging classical approximation-theoretic tools to*construct*a final*surface*compatible ... The images were generated with the*surface*analysis tool BezierView. This work was supported*by*the National Science Foundation Grant 0728797. ...##
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G1 surface modelling using fourth order geometric flows

2006
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Computer-Aided Design
*

We use two fourth order geometric partial differential equations to efficiently solve several

doi:10.1016/j.cad.2005.11.002
fatcat:souh5r7tibdrvhgibzkuar344i
*surface*modelling problems, including the*surface**blending*, the N -sided hole filling and the free-form*surface*... fitting with the G 1 boundary*continuity*. ...*Surface**Blending*Given a collection of*surface*meshes with boundaries, we*construct*a fair*surface*to*blend*the meshes with the specified G 1*continuity*at the boundaries. ...##
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Rational fixed radius rolling ball blends between natural quadrics

2012
*
Computer Aided Geometric Design
*

In particular, G 1 or G 2

doi:10.1016/j.cagd.2012.06.008
fatcat:k4yeed77ene5bj5zpnur3pzbmu
*continuity*of the curve is inherited*by*the corresponding canal*surface*. ... The above results are applied in the*construction*of composite rolling ball*blends*with internal G 1 or G 2*continuity*. ... Acknowledgements This paper has been partially financed*by*the Marie-Curie Initial Training Network SAGA (ShApes, Geometry, Algebra), FP7-PEOPLE contract PITN-GA-2008-214584. ...##
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Modified subdivision surfaces with continuous curvature

2006
*
ACM Transactions on Graphics
*

(b) Circular regions around the extraordinary points, in which we modify the Catmull-Clark limit

doi:10.1145/1141911.1141990
fatcat:cadvn4cz6fe6xnx423mragujum
*surface*for*curvature**continuity*. (c) Isophotes of the modified C 2*surface*. ... The idea is to*blend*the limit*surface*with a low degree polynomial defined over the characteristic map, in the vicinity of each extraordinary point. ... Acknowledgement This paper was inspired*by*a conversation with my father, David Levin. ...##
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Discrete surface modelling using partial differential equations

2006
*
Computer Aided Geometric Design
*

We use various nonlinear partial differential equations to efficiently solve several

doi:10.1016/j.cagd.2005.05.004
pmid:19830268
pmcid:PMC2760856
fatcat:74ryy3jcwzeipa6tizdjk6kpm4
*surface*modelling problems, including*surface**blending*, N -sided hole filling and free-form*surface*fitting. ... The proposed approach is simple, efficient and gives very desirable results, for a range of*surface*models, possibly having sharp creases and corners. ... Given a collection*surface*mesh with boundaries, we*construct*a fair*surface*to*blend*the meshes at the boundaries with specified geometric*continuity*. ...##
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Minimal Mean-Curvature-Variation Surfaces and Their Applications in Surface Modeling
[chapter]

2006
*
Lecture Notes in Computer Science
*

Using this Euler-Lagrange equation, we

doi:10.1007/11802914_25
fatcat:j7rawjw2azbdvgqnm27ga3geka
*construct*a sixth-order geometric flow (named as minimal mean-*curvature*-variation flow), which is solved numerically*by*a divided-difference-like method. ... We apply our equation to solving several*surface*modeling problems, including*surface**blending*, N-sided hole filling and point interpolating. ... From these figures, we can observe that the*surface*produced*by*MMCVF is mean-*curvature**continuous*at the*blending*boundaries, while the*surfaces*produced*by*SDF and WF are not. ...##
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Constructing G2 Continuous Curve on Freeform Surface with Normal Projection

2010
*
Chinese Journal of Aeronautics
*

First, a G 2

doi:10.1016/s1000-9361(09)60197-7
fatcat:u2szuawb35d6dfs3f6os4yqqmq
*continuous*curve is*constructed*in three-dimensional space. Then the curve is projected normally onto the given*surface*. ... This article presents a new method for G 2*continuous*interpolation of an arbitrary sequence of points on an implicit or parametric*surface*with prescribed tangent direction and*curvature*vector, respectively ... Fig.3 illustrates the G 2*continuous**blending*curve of two curves on*surface*S, i.e., the*blending*curve segment 01 and curves 0 have common tangent direction and common*curvature*vectors at P 0 , 1 , ...##
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Streamline Modeling
[chapter]

2001
*
Geometric Modelling
*

The popular conventional

doi:10.1007/978-0-387-35490-3_16
fatcat:6opli4cl2fh7fargtcnfexocpm
*surface**construction*method is to generate free-form*surfaces**by*determining positions of their control points for Bezier, NURBS and other free-form*surface*formulations. ...*blend*the tangent vectors of these streamlines to generate isoparametric lines of a free-form*surface*. ... The main idea of their*surface**construction*shceme is to*blend*positions of points called control ones to define*surface*shapes. ...##
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surface modeling using minimal mean-curvature-variation flow

2007
*
Computer-Aided Design
*

We apply our equation to solving several

doi:10.1016/j.cad.2007.02.007
fatcat:zrwo2r6ozjea3mgf4wspbtg5pi
*surface*modeling problems, including*surface**blending*, N-sided hole filling and point interpolating, with G 2*continuity*. ... Using this Euler-Lagrange equation, we*construct*a sixthorder geometric flow, which is solved numerically*by*a divided-difference-like method. ... From these figures, we can observe that the*surface*produced*by*MMCVF is mean-*curvature**continuous*at the*blending*boundaries, while the*surfaces*produced*by*SDF and WF are not. ...##
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Semi-structured B-spline for blending two B-spline surfaces

2014
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Computers and Mathematics with Applications
*

We formulated the B-spline

doi:10.1016/j.camwa.2014.07.013
fatcat:buxe3b2su5hojmg7fvywse37l4
*surface**blending*problem as an optimization problem with*continuity*constraints, and the*continuity*between the base and*blending**surfaces*can reach G 2 or C 2 . ...*By*assigning suitable knot vectors to the head and tail skinned curves, the semi-structured B-spline*surface*can*blend*two B-spline*surfaces*smoothly without disturbing them at all. ... Acknowledgment This paper is supported*by*Natural Science Foundation of China (Nos. 61379072, 60970150, 60933008). ...##
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Intuitive procedure for constructing geometrically complex objects using cyclides

1994
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Computer-Aided Design
*

In the past, cyclide

doi:10.1016/0010-4485(94)90078-7
fatcat:6ultcr6bbrexdfjzfbtayyxwrm
*surfaces*have been used effectively for the variable radius*blending*of natural quadric intersections. ... However, attempts to use cyclides for*constructing*realistic, freeform composite*surfaces*met with rather limited success. ... In fact, *A double-cyclide*blend*is a*blending*technique in which two pieces from (different) cyclides, joined in a tangent-*continuous*manner, are used to produce a smooth*blending**surface*. ...##
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Curvature continuous blend surfaces
[chapter]

1993
*
Modeling in Computer Graphics
*

We describe a method to generate

doi:10.1007/978-3-642-78114-8_19
dblp:conf/ifip5-10/GreinerS93
fatcat:z7r7mzujjjhstk3nocahtwtkfm
*blend**surfaces*which t with*continuous**curvature*to the primary*surfaces*. ... Among all the bicubic tensor splines which give a*curvature**continuous**blend**surface*, the one is chosen which minimizes a bilinear functional. ... In this case, one can only prescribe the boundary values not the normal or even the*curvature*. Thus, generating*blend**surfaces**by*this method will only yield*continuous**surfaces*. ...
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