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K-ary Implicit Blends with Increasing or Decreasing Blend Ranges for Level Blend Surfaces

Pi-Chung Hsu
Department of Information Management, Shu-Te University, Taiwan
Abstract—This paper develops four new families of C1 continuous k-ary boolean set blends, which can blend more than 2 objects in a single blend operation and furthermore can also be used as a new primitive in sequential blends, i.e. blend on blend, for implicit surface modeling. Especially, two of them have increasing and decreasing blend ranges for level blend surfaces in Zero implicit surface f(x,y,z)0 and the other two have increasing and decreasing blend ranges in Function Representation f(x,y,z)0. In addition, they can also simulate constant blend ranges. By applying the proposed blends into sequential blends, shape control on the transition of a blend’s subsequent blend surface is offered, and a blend with a sharp transition is also allowed to have a smooth subsequent blend surface.
 
Index Terms—implicit surface, implicit blend, CSG

Cite: Pi-Chung Hsu, "K-ary Implicit Blends with Increasing or Decreasing Blend Ranges for Level Blend Surfaces," Vol. 9, No. 2, pp. 25-32, May 2018. doi: 10.12720/jait.9.2.25-32
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