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Constructing Curvature-continuous Surfaces by Blending
[article]
2006
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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In this paper we describe an approach to the 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. ...
doi:10.2312/sgp/sgp06/031-040
fatcat:fl4pvsxoffdandnq3tqgnyidem
Rapid Generation of C 2 Continuous Blending Surfaces
[chapter]
2002
Lecture Notes in Computer Science
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Most 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. ...
doi:10.1007/3-540-46080-2_10
fatcat:5xozlocfqvbgnago2ckp3x6hva
Curvature Computation for Triangular Meshes based on Local Parametrization
2008
Computer-Aided Design and Applications
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A 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. ...
doi:10.3722/cadaps.2008.220-227
fatcat:i2vx5jddr5etdmwl7o5mj4yoh4
An Introduction to Guided and Polar Surfacing
[chapter]
2010
Lecture Notes in Computer Science
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We demonstrate the challenge of high-quality 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. ...
doi:10.1007/978-3-642-11620-9_20
fatcat:d7ou4xj4sbhoraouioiw2sagdi
G1 surface modelling using fourth order geometric flows
2006
Computer-Aided Design
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We use two fourth order geometric partial differential equations to efficiently solve several 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. ...
doi:10.1016/j.cad.2005.11.002
fatcat:souh5r7tibdrvhgibzkuar344i
Rational fixed radius rolling ball blends between natural quadrics
2012
Computer Aided Geometric Design
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In particular, G 1 or G 2 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. ...
doi:10.1016/j.cagd.2012.06.008
fatcat:k4yeed77ene5bj5zpnur3pzbmu
Modified subdivision surfaces with continuous curvature
2006
ACM Transactions on Graphics
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(b) Circular regions around the extraordinary points, in which we modify the Catmull-Clark limit 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. ...
doi:10.1145/1141911.1141990
fatcat:cadvn4cz6fe6xnx423mragujum
Discrete surface modelling using partial differential equations
2006
Computer Aided Geometric Design
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We use various nonlinear partial differential equations to efficiently solve several 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. ...
doi:10.1016/j.cagd.2005.05.004
pmid:19830268
pmcid:PMC2760856
fatcat:74ryy3jcwzeipa6tizdjk6kpm4
Minimal Mean-Curvature-Variation Surfaces and Their Applications in Surface Modeling
[chapter]
2006
Lecture Notes in Computer Science
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Using this Euler-Lagrange equation, we 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. ...
doi:10.1007/11802914_25
fatcat:j7rawjw2azbdvgqnm27ga3geka
Constructing G2 Continuous Curve on Freeform Surface with Normal Projection
2010
Chinese Journal of Aeronautics
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First, a G 2 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 , ...
doi:10.1016/s1000-9361(09)60197-7
fatcat:u2szuawb35d6dfs3f6os4yqqmq
Streamline Modeling
[chapter]
2001
Geometric Modelling
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The popular conventional 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. ...
doi:10.1007/978-0-387-35490-3_16
fatcat:6opli4cl2fh7fargtcnfexocpm
surface modeling using minimal mean-curvature-variation flow
2007
Computer-Aided Design
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We apply our equation to solving several 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. ...
doi:10.1016/j.cad.2007.02.007
fatcat:zrwo2r6ozjea3mgf4wspbtg5pi
Semi-structured B-spline for blending two B-spline surfaces
2014
Computers and Mathematics with Applications
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We formulated the B-spline 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). ...
doi:10.1016/j.camwa.2014.07.013
fatcat:buxe3b2su5hojmg7fvywse37l4
Intuitive procedure for constructing geometrically complex objects using cyclides
1994
Computer-Aided Design
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In the past, cyclide 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. ...
doi:10.1016/0010-4485(94)90078-7
fatcat:6ultcr6bbrexdfjzfbtayyxwrm
Curvature continuous blend surfaces
[chapter]
1993
Modeling in Computer Graphics
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We describe a method to generate 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. ...
doi:10.1007/978-3-642-78114-8_19
dblp:conf/ifip5-10/GreinerS93
fatcat:z7r7mzujjjhstk3nocahtwtkfm
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