Issue 1Regular Issuehttps://diglib.eg.org:443/handle/10.2312/1092024-03-19T06:17:49Z2024-03-19T06:17:49ZInterpolating an Unlimited Number of Curves Meeting at Extraordinary Points on Subdivision Surfaces*Nasri, Ahmed H.https://diglib.eg.org:443/handle/10.2312/87302017-03-16T14:56:58Z2003-01-01T00:00:00ZInterpolating an Unlimited Number of Curves Meeting at Extraordinary Points on Subdivision Surfaces*
Nasri, Ahmed H.
Interpolating curves by subdivision surfaces is one of the major constraints that is partially addressed in the literature. So far, no more than two intersecting curves can be interpolated by a subdivision surface such as Doo-Sabin or Catmull-Clark surfaces. One approach that has been used in both of theses surfaces is the polygonal complex approach where a curve can be defined by a control mesh rather than a control polygon. Such a definition allows a curve to carry with it cross derivative information which can be naturally embodied in the mesh of a subdivision surface. This paper extends the use of this approach to interpolate an unlimited number of curves meeting at an extraordinary point on a subdivision surface. At that point, the curves can all meet with eitherC0orC1continuity, yet still have common tangent plane. A straight forward application is the generation of subdivision surfaces through 3-regular meshes of curves for which an easy interface can be used.
2003-01-01T00:00:00ZQuad/Triangle SubdivisionStam, JosLoop, Charleshttps://diglib.eg.org:443/handle/10.2312/87292017-03-16T15:09:57Z2003-01-01T00:00:00ZQuad/Triangle Subdivision
Stam, Jos; Loop, Charles
In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad-only meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known Catmull-Clark and Loop subdivision algorithms. We show that our surfaces areC1everywhere and provide a proof that it is impossible to construct such aC2scheme at the quad/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples.ACM CSS: I.3.5 Computer Graphics-Curve, surface, solid, and object representations
2003-01-01T00:00:00ZCreation and Control of Real-time Continuous Level of Detail on Programmable Graphics HardwareSouthern, RichardGain, Jameshttps://diglib.eg.org:443/handle/10.2312/87262017-03-16T14:56:57Z2003-01-01T00:00:00ZCreation and Control of Real-time Continuous Level of Detail on Programmable Graphics Hardware
Southern, Richard; Gain, James
Continuity in level of detail sequences is essential in hiding visual artefacts that occur when switching between discrete levels of detail. However, construction and implementation of these sequences is prohibitively complex. We present a new structure, the g-mesh, which greatly simplifies the implementation of continuous level of detail in large scenes. We also introduce a novel greedy predictive level of detail control system suited to the g-mesh. Finally we achieve a dramatic improvement in the rendering of morphing sequences by exploiting current graphics hardware.ACM CSS: I.3.5 Computational Geometry and Object Modeling-Geometric Transformations, Object Hierarchies, I.3.6 Methodology and Techniques-Graphics Data Structures
2003-01-01T00:00:00ZTwo-dimensional Potential Fields for Advanced Implicit Modeling OperatorsBarthe, L.Dodgson, N. A.Sabin, M. A.Wyvill, B.Gaildrat, V.https://diglib.eg.org:443/handle/10.2312/87252017-03-16T14:56:56Z2003-01-01T00:00:00ZTwo-dimensional Potential Fields for Advanced Implicit Modeling Operators
Barthe, L.; Dodgson, N. A.; Sabin, M. A.; Wyvill, B.; Gaildrat, V.
Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free-form curve to define the profile of the blend region between implicit primitives.The use of a free-form implicit curve, controlled point-by-point in the Euclidean user space, allows us to group boolean composition operators with sharp transitions or smooth free-form transitions in a single modeling metaphor. This idea is generalized for the creation, sculpting and manipulation of volume objects, while providing the user with simplicity, controllability and freedom in implicit modeling.ACM CSS: I.3.5 Computational Gemoetry and Object Modeling-Curve, surface, solid, and object representations
2003-01-01T00:00:00Z