When another data point is inserted and the Voronoi diagram reconstructed, the newly created region displaces the area that once belonged to the old regions. Those points whose regions were displaced are considered natural neighbours to the new point. The weight of each natural neighbour is given by the area taken from the total area occupied by the new region. In 3D, we measure polyhedral volumes instead of areas.
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Industrial production of kanten (the Japanese name for agar, which translates as “cold weather” or “frozen sky”) began in Japan in the mid-19th century by natural freeze drying, a technique that simultaneously dehydrates and purifies the agar. Seaweed is first washed and boiled to extract the agar, after which the solution is filtered and placed in boxes or trays at room temperature to congeal. The jelly is then cut into slabs called namaten, which can be further processed into noodle-like strips by pushing the slabs through a press. These noodles are finally spread out in layers onto reed mats and exposed to the sun and freezing temperatures for several weeks to yield purified agar. Although this traditional way of producing kanten is disappearing, even today’s industrial-scale manufacturing of agar relies on repeated cycles of boiling, freezing, and thawing.，详情可参考heLLoword翻译官方下载