Implicit Blends with an Individual Blending Range Control on Every Primitives Subsequent Blend
Pi-Chung Hsu · 2006
In implicit surfaces, implicit blends are important because they can be used to construct a complex surface from primitive surfaces. Among existing blends, blends with a blending range control are applied very wide because they can deform blended primitives locally after blending. However, this kind of blends usually behaves like a pure union blend Min(f1,...,fk) on non-blending regions. Hence, when they are used as a new primitive in other blends, their primitives always have similar subsequent blending surfaces with the primitives in their subsequent blends. To solve this problem, this paper proposes new implicit blends that can provide parameters to individually adjust their primitives’ subsequent blending surfaces, without deforming the original blending surfaces. The proposed blends can provide parameters m_1,...,m_k, to enable their primitives f1,...,fk, to behave like Min (f_1/m_1,...,f_k/m_k) on non-blending regions and its original blending surface does not change whatever positive values m_1,...,m_k, are set. As a result, in sequential blends, the subsequent blending surfaces of f_1,...,f_k, can be adjusted respectively by varying parameters m_1,..,m_k. Furthermore, this paper also proposes a generalized method that can transform some of existing blends into a new blend with the ability stated above.