Implicit Blends with an Individual Blending Range Control on Every Primitive´s Subsequent Blend

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,...,f_k) 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 m₁,...,m_k to enable their primitives f ₁,...,f_k to behave like Min(f₁/m₁ ,...,f_k/m_k) on non-blending regions and its original blending surface does not change whatever positive values m₁,...,m_k are set. As a result, in sequential blends, the subsequent blending surfaces of f₁,...,f_k can be adjusted respectively by varying parameters m₁,...,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