Browsing by Author "Hwang, WC"

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Adaptive polygonization of geometrically constrained surfaces
(1998-01-01)
Chuang, JH
;
Hoffmann, CM
;
Ko, KM
;
Hwang, WC
;
資訊工程學系
Many surfaces in geometric and solid modeling, including offsets and blends, are naturally defined from given surfaces subject to geometric constraints. Surfaces that are geometrically constrained can be uniformly defined as the projection of two-dimensional manifolds (2-surfaces) in n-dimensional space, where n>3. This definition can be used for given surfaces that are implicit or parametric. This paper presents a robust, adaptive polygonization algorithm for evaluating and visualizing geometrically constrained surfaces. Let F be the constrained surface, a 2-surface in n-space, and let pi(F) be its projection into the subspace spanned by the first three coordinates. Our polygonization algorithm computes pi(F). The method works directly with the n-space representation, but performs all major computations in 3-space. Techniques for triangulation, polygon decimation, and local refinement are also presented.
Adaptive polygonization of geometrically constrained surfaces
(1998-01-01)
Chuang, JH
;
Hoffmann, CM
;
Ko, KM
;
Hwang, WC
;
資訊工程學系
Many surfaces in geometric and solid modeling, including offsets and blends, are naturally defined from given surfaces subject to geometric constraints. Surfaces that are geometrically constrained can be uniformly defined as the projection of two-dimensional manifolds (2-surfaces) in n-dimensional space, where n>3. This definition can be used for given surfaces that are implicit or parametric. This paper presents a robust, adaptive polygonization algorithm for evaluating and visualizing geometrically constrained surfaces. Let F be the constrained surface, a 2-surface in n-space, and let pi(F) be its projection into the subspace spanned by the first three coordinates. Our polygonization algorithm computes pi(F). The method works directly with the n-space representation, but performs all major computations in 3-space. Techniques for triangulation, polygon decimation, and local refinement are also presented.
Boundary control of subdivision surfaces using an open uniform quadratic subdivision scheme
(2003-09-01)
Hwang, WC
;
Chuang, JH
;
資訊工程學系
;
Department of Computer Science
The ability to control boundary behaviors is critical for the subdivision surface to become a useful representation in computer aided geometric design. Previous methods achieve boundary control by extending the boundary vertices of the control mesh, or by applying different subdivision rules to the boundary edges and vertices. This paper presents an open uniform quadratic subdivision scheme derived from the subdivision of open uniform B-spline surfaces. For meshes with 4-sided boundary and corner faces, the cross-tangent along the boundary curves can also be derived. The proposed scheme leads to a straightforward boundary control that enables two subdivision surfaces to be joined with C-0 and C-1-continuity.
N-sided hole filling and vertex blending using subdivision surfaces
(2003-09-01)
Hwang, WC
;
Chuang, JH
;
資訊工程學系
;
Department of Computer Science
To fill an N-sided hole on a NURBS surface and to blend a corner formed by NURBS surfaces, we propose a regular N-sided open uniform quadratic subdivision surface derived by applying the open uniform quadratic subdivision scheme to a regular N-sided control mesh which is confined to the hole or to the region of the vertex blend. Boundary conditions such as C(0) and G(1)-continuity required for the hole filling and vertex blending, are ensured by certain refinement steps performed in the course of the subdivision. The shape of the filling or blending surface is controlled by using fullness parameters. Methods are also proposed to represent the resulting regular N-sided open uniform quadratic subdivision surface using non-uniform rational B-spline surfaces.
Variable-radius blending by constrained spine generation
(1997)
Chuang, JH
;
Hwang, WC
;
交大名義發表
;
資訊工程學系
;
National Chiao Tung University
Radius blends, very important in geometric and solid modeling, can be seen as the trimmed envelope of a rolling sphere or a sweeping circle with a constant or variable radius that centers on a spine curve and touches the surfaces to be blended along the linkage curves. Usually, in variable-radius blending, the radius is difficult to specify, and the spine curve is hard to trace. We propose several geometric constraints to specify the variable radius, which we then translate to a nonlinear system to represent the spine curve exactly. This is finally traced numerically in a high-dimensional space. We also propose a paradigm that implements the constraints while tracing along the spine curve in 3D space. We represent the result in parametric form.
Variable-radius blending of parametric surfaces
(1995)
Chuang, JH
;
Lin, CH
;
Hwang, WC
;
交大名義發表
;
資訊工程學系
The radius blend is a popular surface blending because of its geometric simplicity. A radius blend can be seen as the envelope of a rolling sphere or sweeping circle that centers on a spine curve and touches the surface to be blended along the linkage curves. For a given pair of base surfaces in parametric form, a reference curve, and a radius function of the rolling sphere, we present an exact representation for the variable-radius spine curve and propose a marching procedure. We describe methods that use the derived spine curve and linkage curves to compute a parametric form of the variable-radius sphearical and circular blends.