2D Straight Skeleton and Polygon Offsetting

1. 2D Straight Skeleton and Polygon Offsetting Overview

A straight skeleton of a polygon [SSPO] is a geometric structure representing the inward deformation of the polygon until it reduces to a point, akin to a simplified "medial axis" of the polygon.

simple skeleton 0

Constructing the straight skeleton involves moving the polygon’s edges inward at a constant speed. The edges move parallel to themselves, and the vertices move at the same speed until they meet and form new vertices.

sls progress

2. Extrusion:

Extrusion is a process of transforming a 2D outline into a 3D object by adding a third dimension. In the context of straight skeletons, extrusion allows the creation complex 3D shapes from 2D polygons.

  • Extrusion Procedure:

    • Define the 2D Outline: This is the base shape from which the extrusion starts.

    • Calculate the Straight Skeleton: This involves computing the internal structure of the polygon that guides the extrusion.

    • Apply the Extrusion: Following the straight skeleton, the edges of the 2D outline are extended in the chosen direction , creating a 3D object.

  • Advantages of Extrusion Using the Straight Skeleton:

    • Geometric Precision: Extrusion based on the straight skeleton ensures that the resulting shapes are geometrically accurate and aesthetically pleasing.

    • Flexibility: This method can handle complex and irregular shapes, unlike simpler extrusion methods that might only work with regular polygons.

  • Application:

    • Extrude roof from our inputted polygon

3. Other tools:

Polygon Mesh Processing
3d Mesh Generation



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