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Asked: 2026-06-13T06:54:46+00:00

In Loop’s Subdivision, I don’t understand what is often written as Choose locations for

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In Loop’s Subdivision, I don’t understand what is often written as “Choose locations for new vertices as weighted average of original vertices in local neighbourhood“.

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The new vertices are derived from adding new points in the middle of each edge. How is this related to a “weighted average” of the original vertices? How do the

In the first place, what is “weighted average of original vertices”? Where is the “weight” seen in the mesh?

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1 Answer

  1. Editorial Team

    Adding a point in the middle of an edge is actually just a first phase of the process. Subdivision algorithms usually have two:

    1. Topology phase – adding new vertices and edges
    2. Geometry phase – adjusting the newly added vertices so that they “form a smoother surface” with their neighbors

    The following slides give some more details on the weight scheme (the beta parameter).

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