01-08-2012, 02:37 PM
Boundary extraction algorithm for cutting area detection
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Abstract
In sculptured surface machining, many machining operations require cutting areas to be expressed in terms of a boundary representation.
To extract cutting areas from a sculptured surface, this paper employs a regular grid model (Z-map model) and presents a procedure
extracting areas from a Z-map model. The extracted areas may correspond to various machining features, depending on what the Z-map
stores, such as curvature (®llet, uncut area), slope (wall, ¯oor) and Z-values (contour). The core of the procedure is a `boundary extraction
algorithm' extracting boundaries and identifying the inclusion relationships among the boundaries from a binary image. The time complexity
of the boundary extraction algorithm is O(n), where n is the number of runs. In terms of its time complexity and simplicity, the proposed
algorithm has advantages over the prior ones. Empirical tests show the performance of the proposed algorithm. q 2001 Elsevier Science Ltd.
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Introduction
NC-data generation for sculptured surface machining is
usually handled by NC-programmers with commercial
CAM systems. Generally, NC-data generation involves
three steps: (1) process planning by NC-programmers, splitting
the sculptured surface into several cutting areas according
to the machining features and assigning cutting
parameters (tool, tool-path topology) to each cutting area;
(2) modeling boundary curves to represent the cutting areas
in terms of a boundary representation and (3) NC-data
generation from a CAM system with the boundary curves
and the cutting parameters. Many researchers have studied
CAPP (computer-automated process planning) to replace
the ®rst and second steps of the NC-data generation;
however, there remain many obstacles to be overcome for
the implementation of a practical CAPP system [3]. Especially,
the second step, modeling boundary curves, has
rarely been brought into focus even though it is essential
for the implementation of a CAPP system.
Connectivity-net construction
This section gives a detailed explanation of the algorithm
completing an initial connectivity-net by extracting the
connectivity information (N.link) of all the nodes. Before
the formal description of the algorithm, some de®nitions are
addressed.
Empirical performance tests
The proposed algorithm was implemented in C language
and test runs were made on an engineering workstation. Fig.
12a shows an injection molding-die for the front mask of a
TV monitor. The boundary curves of the wall areas are
extracted from the model as shown in Fig. 12b.
Another example shown in Fig. 13a is a stamping-die for the
fuel tank of a passenger car. At 10 different heights, contour
curves are extracted from the model as shown in Fig. 13b.
Fig. 14 shows the execution times plotted against the
number of the runs for the contour curves in Fig. 13. We
observe that the algorithm more or less behaves linearly
with respect to the number (n) of runs.
Discussion and conclusions
This paper presents a procedure to extract cutting areas
from a Z-map for sculptured surface machining. Cutting
areas, corresponding to machining features (®llet/uncut
area, wall/¯oor, contour curve), can be extracted from a
Z-map storing a speci®c attribute of a sculptured surface,
such as curvature, slope and Z-values. The core of the procedure
is a `boundary extraction algorithm' to extract boundaries
and identify the inclusion relationships among the
boundaries from a run-length coded binary image. The
time complexity of the boundary extraction algorithm is
O(n), where n is the number of runs.