Blending Operations with Blending Range Controls in Implicit Surfaces

• Main Authors: Pi-Chung Hsu, 許丕忠
• Other Authors: Chungnan Lee
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/70619750840809599682

博士 === 國立中山大學 === 資訊工程學系研究所 === 91 === Implicit surface modeling is attracting attention, because a complex object can be constructed easily and intuitively from some simple primitive objects, defined by primitive defining functions, using successive compositions of blending operations. Blending operations play a major role in implicit surfaces, because they can join intersecting primitive objects (operands) smoothly with transitions generated automatically by blending operators. Hence, this dissertation proposes three new methods: (1) the scale method, (2) field functions with adjustable inner and outer radii, and (3) the translation method, for developing blending operations that have blending range controls. That is, the proposed blending operations provide blending range parameters to adjust the size and shape of the transition of the blending surface freely, without deforming the shapes of blended primitives totally. The first and the third methods offer blending range controls by developing new blending operators, whereas the second method does the similar things by developing new primitive defining functions. The scale method is a generalized method. It provides a framework to transform any existing blending operators or arc-shaped curves into the blending operator that has the following properties: (1) Provides blending range and curvature parameters to adjust the size and shape of the transition of the blending surface, without deforming the shapes of blended primitives totally. (2) Behaves like Max/Min(x1,…,xk) operators in non-blending regions in the entire domain. As a result, it gives a more intuitive shape control on modeling its subsequent blends. (3) Possesses C1 continuity in the entire domain except the origin. As a result, it can prevent from generating non-smooth surfaces on sequential blends with overlapped blending regions. (4) Works to blend both non-zero and zero implicit surfaces. (5) Can be a new primitive in other blends, especially in Soft blending. (6) Applies for bulge elimination. Field functions with adjustable inner and outer radii provide parameters to adjust the inner and the outer radii of influence, respectively. This dissertation proposes four different transforms to develop this kind of field functions. Thus, using the proposed field functions as the new primitive defining functions of soft object modeling, Soft blending, R-functions, Ricci’s super-ellipsoid blends and Perlin’s set operations: (1) Can retain their low computing complexity. (2) Can perform the blending range controls, by adjusting the inner and the outer radii of influence of the proposed field functions. The translation method is also a generalized method. It offers a framework to transform any existing blending operators or arc-shaped curves into controllable blending operators for blending zero implicit surfaces. A controllable blending operator has the following properties: (1) Offers blending range and curvature parameters to adjust the size and shape of transition of the blending surface, without deforming the shapes of blended primitives completely. (2) Provides parameters mi, i=1,2,…,k, to behave like Max/Min(x1/m1,…,xk/mk) operators on non-blending regions in the entire domain, and its zero level blending surface remains unchanged, whatever mi, i=1,2,…,k, are set. As a result, by adjusting mi, i=1,2,…,k, a controllable blending operator has the following abilities to control its primitives’ subsequent blends: �� The ability to individually adjust its primitives’ subsequent blending surfaces, without deforming its zero blending surface. �� The ability to avoid unwanted subsequent blending surfaces of its primitives with the primitives in its subsequent blend. (3) Has C1 continuity in the entire domain. Consequently, they can avoid from generating non-smooth surfaces on sequential blends possessing overlapped blending regions. (4) Can be a new primitive in other blends. (5) Works for bulge elimination. For the theoretical soundness, twenty theorems and four propositions are proposed to guarantee the correctness and reliability of all the applications and the properties of the above three methods, and to help develop blending operators with C1 continuity in the entire domain. For the practical applications, many new blending operators and field functions, developed from the above methods, are also presented in this dissertation.