When using the circumcision method, the tool's path is composed of closed loops that are equidistant from the contour. These rings are also called windows. The distance between the ring and the ring is called the line spacing. In the past, many automatic generation of the circumcision path was a method of continuously shrinking the contour curve inward. The main problem with this approach is the need to continually eliminate some extra intersections. In addition, it is a very difficult problem to connect these equidistant lines into a complete ring.
In order to solve the above problem, the Voronoi diagram is first used for the calculation of the tool path of the circumcision method. The method of equidistant line regions (polygons) is used to construct the tool path. After the equidistant line areas are obtained, the equidistant lines in each zone can be connected to generate a tool path. Later, LEE proposed a recursive algorithm for calculating the medial-axis in a polygon. Since then, the Voronoi diagram-based loop cutting method has been further developed, and most of them have adopted the recursive algorithm proposed by LEE.
A new method for constructing a closed pattern of Voronoi diagrams is proposed, which is called a fast growth method. The main idea is to calculate only the bisectors present in the final Voronoi diagram. This method can also be extended to include grooves in the island.
Definitions related to the Voronoi diagram:
(1) A boundary is a closed figure composed of a straight line segment or an arc.
(2) Every point on the Voronoi diagram is at least equidistant from the two lines.
(3) The bisector is the trajectory of a point equidistant from the two boundary lines defined by it.
(4) A polygon is a closed figure composed of a boundary line and a bisector associated with this boundary line. This boundary line is also known as the possession line of this closed figure.
(5) Area of ​​Interest (AOI). Since we are only interested in the area inside the groove, we can determine the area of ​​interest for various boundary curves. The area of ​​interest for lines and arcs is shown in Figure 1.
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