Constructive G1 connection of multiple freeform pipes in arbitrary poses

This paper expands the application scope of pipe connection to multiple pipes having freeform cross sections and arbitrary poses. Starting with a typical case - bifurcation, we first connect every two pipe ends of totally three using side patches. Inside them appear two holes. Usually the 6 sides of each hole are short (on the pipe edges) and long (on the side patch edges) alternately. Then in each hole draw three optimized geometric Hermite (OGH) curves connecting two long edges and roughly parallel to a short edge, thus splitting the hole into 4 regions: three 4-sided and a more regular 6-sided. The former are interpolated by three setback patches, while the latter by hole-filling patches using the well-known central split. As illustrated with several practical examples, the above three building blocks can build miscellaneous multiple pipe blending, guaranteed to be G1-continuous and twist compatible. Highlights? The initial pipes can be multiple with freeform cross sections in arbitrary poses. ? Present 3 building blocks, used sequentially to connect the pipes. ? Being the crux of this approach, compatibility is well coped with. ? Four smart practical examples illustrate the general applicability.

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