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GSS—A CAD-based graphic sawing simulator for hardwood logs
Comput. & Graphics Vol. 12, Nos. 3/4, pp. 565-578, 1988
0097-8493/88 $3.00 + .00 © 1988 Pergamon Press pie
Printed in Great Britain.
Technical Section GSSmA CAD-BASED GRAPHIC SAWING SIMULATOR FOR HARDWOOD LOGS* LUIS G. OCCEI~IA Department of Industrial Engineering, University of Missouri-Columbia, Columbia, Missouri 6521 I and JOSE M. A. TANCHOCO Wood Technology Center, IIES, and School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907 Abstract--With the objective of studying the breakdown process for hardwood logs, a graphic sawing simulator (GSS) was developed to provide the capability for repeated sawing. Based on polyhedral solid modelling concepts and device-independent graphics, the GSS represents a solid log as a nonregular polyhedron and enables decomposition of the log ("sawing") via regularized CSG Boolean operations. SAWING SIMULATION
Motivation for development of the simulator
Historical review In a market facing serious competition from synthetic wood substitutes, improved productivity through better control of operations at the sawmill level is a genuine concern for hardwood lumber manufacturers. One of the means of studying sawmill operations that has proven to be effective as a nondestructive approach is computer simulation. In the context of lumber production, this means the ability to perform repetitive sawing on the same log. Simulation of both the sawmill system[l] and the sawing operation[2-4] have been done before. However, it was Pnevmaticos et a/.[5-7] who introduced the first graphic simulation of log sawing on a hybrid graphics terminal. The simulated logs were depicted as cylinders or as truncated cones, as were the nongraphic simulation models of log sawing that came before it. Intersections of the log representation with the cutter representation were computed using a linear programming model. The quality and price of hardwood lumber is greatly affected by surface defects (knots, splits, decay, holes, etc.). Mainly used by the furniture industry, hardwood lumber is manufactured with careful attention to the location and distribution of defects. Control of the defect appearance on the lumber surface is performed during log sawing[8]. Researchers are now looking at a design for an automated sawmill that will implement internal defect detection[9-11]. When applied to industrial practice, internal defect detection will provide sawyers with the capability to "see" inside the log and plan for the breakdown pattern more effectively. This capability also paves the way for research into sawmill automation.
A logical consequence of the capability to obtain internal defect information is the question of how to use this kind of information to advantage. A graphic sawing simulator which will enable representation of the log and its detected internal defects can be a useful tool for studying the relation between internal defect configurations and breakdown patterns. A simulator that can depict the log and its defects in more realistic shapes than simplified cylinders or truncated cones and has the capability to simulate sawing will be even more valuable. This paper describes the development of the graphic sawing simulator GSS, its basic structure, capabilities, and use in modelling solid logs and the hardwood log breakdown process.
Role of the GSS The GSS was used as a tool for examining the relation of log and defect profiles to breakdown patterns. The study was based on a sample set of yellow poplar logs. Guidelines on the use of log and internal defect profile information in the determination of a breakdown pattern were extracted from the study. The guidelines were then formalized in a pattern directed inference model for automation of the breakdown decision process[ 12]. Figure 1 shows the position of the GSS in the total system structure. It was a critical component in the determination of guidelines for log sawing. It was also used to verify breakdown patterns generated by the inference model.
* The work reported in this paper was supported in part by a grant from the U.S. Department of Agriculture, administered by the Cooperative State Research Service (CSRS). 565
SIMULATOR DESIGN
Input to the GSS The intended input to the GSS are log and internal defect profile information derived from internal defect detection scanning. This study therefore complements concurrent research on the recognition of internal defects from scan data[10, 11]. The input should ade-
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Fig. 1. System design flowchart. quately describe the log and defect profiles for reproduction on a graphics terminal, and the major defects should already be recognized for grade evaluation. Input data used in the study came from the actual sawing of six yellow poplar logs. For want of real scan data, equivalent information about the log and internal defect profiles were obtained through the physical breakdown and subsequent computer reconstruction of these sample logs.
be defined by the user when the GSS is used on standalone basis, or can come from the pattern directed inference model in the form of a feedback loop for checking the feasibility of computer-generated sawing instructions. Information flows bidirectionally between the GSS and the solid modeller in the course of the simulation. Upon completion of the session, there are several postprocessing options, including lumber grading.
Output from the GSS
Data management
The output of a simulated sawing session using the GSS are data describing the resulting lumber boards and their defects. This stack of data corresponds to a pile of physical lumber. The data can be run through a grading program to determine the individual lumber grades, and ultimately the log yield. The data can also be rendered graphically for visual evaluation of the lumber, or further manipulated as in the case of resawing or log reconstruction.
Under simplified modelling situations where the log is represented as a regular geometric figure (e.g. a cylinder), and the number of defects are few, computational requirements are minimal and even a higherdimensioned array storage performs reasonably well. However, as the number of polygons defining the log and its defects grows in order to render a more realistic profile, data management becomes critical. Higher-dimensioned army variables, for instance, begin to exhibit an increase in computational complexity and storage requirement. External file input/output usage begin to suffer during peak system load. To keep storage requirements and external file transactions to a minimum, a single-dimensioned array is used for primary storage. Other single-dimension arrays are then used to keep track of important parameters, using an address-book approach. This approach allows easy access to stored parameter values and enables the program to operate at reasonable speeds even for complex polyhedral solids. Figure 3 illustrates the use of this .scheme.
Processing control The main program for the GSS is written in FORTRAN77 and implemented on a DEC VAX 11/780 running under the UNIX operating system. Through system calls, the program interfaces with two predefined programs, a C-based polyhedral solid modeller[13] and a Lisp-based grading program[14]. All other functions are internal to the program and are represented as callable FORTRAN subroutines. The block diagram in Fig. 2 summarizes the information flow structure for the GSS. External input can
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Fig. 2. Graphic sawing simulator information flowchart. INPUT
PRE-PROCESSING
The input data passes through a preprocessor routine which performs the conversion to the format required by the program. This process is represented in Fig. 2 by the Syntax Converter block. The input format conforms to a boundary representation polygon standard[13] which represents any solid object as a set of connected polygons, or faces ft. The polygons in turn are sets of connected lines, or edges ej, which are decomposable into sets of connected vertices Vk. These parameters are related by Euler's formula num(v) - hum(e) + n u m ( f ) = 2 (where num is the cardinality)[ 15]. The solid representation therefore consists of a polyhedral approximation of the original solid profile. In the current implementation, a wire-frame graphics image is used. The polygons are formed according to the topological relations of the data points. Figure 4 illustrates the transformation of the raw flitch data into closed planar loops, and subsequently into polygon standard format. GRAPHICS
RENDERING
The GSS was designed to enable interactive, graphic analysis of the hardwood log breakdown process. The
graphics rendering of the GSS was implemented using DI-3000[ 17], a library of ANSI FORTRAN-based, device-independent graphics tools. Like most other general-purpose graphics packages, DI-3000 has several modelling capabilities including standard transformations, windowing and clipping, color, shading, line and text font control, retained segments, 2D and 3D modes, and external file communications. Hidden line removal and animation are not standard features of DI3000 but can be incorporated using established algorithms. Work with the GSS was primarily done on a Tektronix 4105 raster graphics terminal.
THE
SOLID
MODELLING
CONCEPT
Solid modelling originated in the design of machinable metal parts for the manufacturing industry[16, 18]. It has evolved from physical models of solid objects using clay and splines, to computer-aided design representations. There are currently two schools of thought: Constructive Solid Geometry (CSG) which supports the use of primitive solids such as spheres, cubes, and cylinders, and regularized Boolean operations in the representation of solid parts; and Boundary Representation (BRep) which supports the idea of a
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more explicit topological data structure using faces, edges and vertices to represent solid parts. Solid modelling enables both formation and decomposition of more complex solids through the interaction of simpler solids. This interaction is accomplished by regularized Boolean operations of union, intersection, and difference. To give an example, a cube with a horizontal through-hole can be produced by subtracting a cylinder (with the same diameter as the hole) from the cube (at the specified location). Figure 5 illustrates this example. The solid modeller used in the GSS has a BRep structure. A BRep modeller is more appropriate for nonregular geometric solids such as logs, than a CSG structure. Furthermore, this solid modeller is polyhedral-based, enabling both a computationally simpler representation and a more realistic approximation of hardwood logs than was available with the cylindrical or conical representations used the past. SOLID LOG RECONSTRUCTION
Available data The input data for the log profile included both whole log measurements prior to sawing and flitchslab measurements after sawing. A slab, which contains bark on one side, is the first piece removed from each log face. Flitches, which may have bark on the edges,
are the subsequent pieces removed and later finished into lumber. The flitch-slab measurements were used to rebuild a solid representation of the log in a "reversesawing" sense. This procedure was used after it was found that the whole log measurements allowed too much play in the diameter placements to provide an accurate reconstruction. The flitch-slab measurements did not have that problem.
Polygon formation To conform with the polygon standard, three types of polygons were generated: wide faces, edges, and ends. The resulting flitch representation has two wide faces, two edges (sometimes with wane, i.e. bark), and two ends. The resulting slab representation has one wide face, a waney face, and two ends. These are illustrated in Figs. 6 and 7 . The wide faces on which lumber grading is performed were generally assumed to be fiat, having been cut straight by the saw blade. They were described quite simply by a quadrilateral face. Ends were similarly assumed to be flat and straight, having been cut by a straight saw blade in the preliminary operations of bucking and topping. Though the ends may not always be planar as the wide faces in practice, such an assumption is valid in the light of subsequent finishing operations.
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Edges were the most difficult of the faces to represent because of wane, which is nonplanar. If wane is eventually removed from the edges in the resulting log breakdown pattern, an edge can be represented by a single face. If wane is present, however, the edge is essentially multifaceted. To simplify polygonal representation of waney edges, triangulation was used. The price to pay for this simplification, however, is the proliferation of triangulated faces. Similar treatment was given to the waney face of a slab, with the increase in width towards the longitudinal ends of the slab as the only distinction. Sectional reconstruction To facilitate log reconstruction, whole log sections were built up at a time. This sectional reconstruction approach saved an entire step in the reconstruction process, because eventually the flitches had to be CAG 12: 3/4-R
merged with adjacent flitches according to the breakdown pattern. This procedure also ensured control over face generation, because the number of resulting faces could then be predicted. In the case of around-sawed logs, the flat side on the sawn faces provided an excellent reference face for alignment in sectional reconstruction. Figure 8 illustrates sectional reconstruction, and Fig. 9 shows a completed section of a sample log.
CAD-based log unification Unification of log sections was performed using the regularized Boolean union operation. The first step in the unification was to use the GSS to position one log section s~, relative to an adjacent log section, s2, so that the two sections were separated only by the kerf width, wk. One of the two opposing faces from either section was then extended by an increment ~, such that the extended face crossed over into the opposite
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Fig. 5. Composite part formation using CSG Boolean subtraction. face. The log sections were then unified in this intersected state by a regularized Boolean union operation, to form bigger log sections. Figure l0 provides an illustration. This procedure is repeated for the rest of the log sections. The end result is a whole log, as shown in Fig. 11. SOLID DEFECT RECONSTRUCTION Available data Log defect information collected for the study consisted of defects found on the surface of the log samples prior to sawing and defects found on the wide faces of the flitches and slabs after sawing.
Although there were isolated cases of decay, knots and bumps left by former branches comprised the predominant defects detected on the log surface. The defect profiles were recorded in photographs. The defect locations were measured, with reference to the log small-end and eight rotational sections. Internal defects were detected only after the log had been sawn. Detected defects included both tight and loose round knots, pin knots, worm holes, bird pecks, splits, and pith decay. The defect profiles were recorded in their actual size on transparent overlays using quickdrying permanent marker pens. Each defect location was measured with reference to the small end of the 1-90ME'fRIC
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-i Fig. 7. Slab polygonal representation. flitch and the bottom face-side edge of the flitch. As the flitches were sawn from the log, the side on which the decision to cut was based (open log face) was labelled the face side. These conventions were adopted to aid in reconstruction.
Polygonformation Defect to log correspondence in solid form would be direct if internal defect detection, using either Industrial Photon Tomography (IPT) or Nuclear Magnetic Resonance (NMR) scan data, were used. When collected from sawn logs, however, the only way to visualize the solid defects was to rebuild three-dimen-
sional representations from the two-dimensional defect data. The reconstruction was performed using the GSS and a procedure similar to log reconstruction. Internal defect data were collected in the form of curvilinear tracings. To satisfy the standard polygon requirements of the GSS, the tracings were converted into polygon format by an approximate point-to-point linear fit.
Graphics-aided reconstruction Following formation, the defect polygons were then matched with defect polygons from flitches adjacent in the breakdown pattern. Thus the polygons were
SECTIONAL
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Fig. 8. Sectional and individual reconstruction.
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Fig. 9. Completed sectional log reconstruction.
treated as slices from a solid defect. Referenced to a common point (the flitch small end), the defect polygons of adjacent flitches appeared graphically as opposing faces. A convenient way of showing the alignment of opposing faces was through the GSS. The GSS made it possible to perform relative positioning of the defect
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polygons, using translational and rotational transformations. This relative positioning was done two polygons at a time for defect polygons resident in flitches that were known to be adjacent in the breakdown pattern. As the number of positioned defect polygons increased, the defect solids begin to take shape. To form
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Fig. 11. Completed whole log reconstruction.
The reconstructed defects were restored inside the reconstructed log using the GSS as a graphic aid. Restoration was performed using relative positioning and the original log breakdown pattern. The result was a "see-through" image of the solid log, as would be generated by imaging devices such as IPT or N M R scannet's. Color was used to distinguish the log from its defects.
the defect solid, aligned polygons were "stitched" together by triangulation of the corresponding data points. The reconstructed solid defects therefore consisted of at least two opposing polygonal faces with multifaceted edges. This procedure was in keeping with the sectional reconstruction approach for log reconstruction. Figure 12 shows a reconstructed defect configuration.
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SOLID LOG DECOMPOSITION Using regularized CSG Boolean operations, a flitch or slab can be extracted from a solid log representation by performing an intersection operation between the log representation and the saw representation. Conversely, the remaining log can be obtained by performing a difference operation of the cutter representation from the solid log representation. Figure 13 shows a sample remaining log. Among the design issues in the decomposition process were: • positioning of the log representation relative to the cutter representation; • setting up of the input file for the batch mode interaction with the solid modeller; • allowing for kerf, i.e., sawdust; • routing the piece removed for further processing; • sequencing the execution of the operations and supporting processes. MODEL OPERATION Getting started To begin a sawing session, the following files are required: * vwply.x--the compiled sawing simulation program; • origlsd--the data file containing the log and defect description in polygon file standard; • poly.x--the compiled polyhedral solid modelling program; • zero--end-of-file character file used in input and output; • grade--grading program.
The GSS is initialized by entering the compiled simulator name, vwply.x. The solid log and its defects are then graphically rendered. Main menu The main menu comes up on the screen soon after the initial log and defect representations are drawn. The Tektronix 4105 supports separation of alphanumeric and graphic displays, so the textual input/output via menus are superimposed on the graphics image. The main menu consists of the following entries: Exit, Rescaling, Decomposition, and Postprocessing. Exit is the escape option to use when the session is completed, or when strictly viewing and no processing is desired. Rescaling is a utility option for resizing the image. Decomposition leads to a submenu for sawing the log, and Postprocessing leads to a submenu for evaluating the outcome of a sawing session. Decomposition submenu The decomposition category comprises the simulated sawing activity. It introduces the saw representation, enables the user to position the log representation relative to the saw representation via translation or rotation, actuates the sawing, and terminates sawing. Upon entering this mode, a saw representation is generated based on the size of the log representation. Figure 14 shows a saw representation, in the form of a rectangular block, intersected with the log representation. Parameter settings are indicated alongside with the option to change the kerf allowance, initially set at 0.125 inches. The simulated sawing is actuated by the Cut command which is invoked after the log representation has
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been positioned relative to the saw representation. The two representations must be intersected (overlapped) for the operation to succeed. When the Cut command is given, the log and cutter representations are written out to a file in polygon file standard. A Boolean intersection operation is specified, and then the file is submitted as a batch job to the solid modeller. Diagnostics are printed on the left side of the screen, serving as indicators for successful cutting. Upon completion, the user is prompted for the flitch (or slab) routing. If cutting was unsuccessful due to solid modeller restrictions, the previous operation can be aborted. Otherwise, a piece is removed which can be either a slab, a flitch, or a piece intended for resawing. While the piece is being processed in the background, the program once again writes the log and saw representations to a file, but this time offsetting the log representation toward the saw representation by the kerf width, Wk. A Boolean subtraction operation is specified to extract the remaining log. After the remaining log representation is rendered on the screen, the user has the option to continue sawing, or to terminate the session.
Board routing submenu Board routing determines the treatment of the removed piece. The piece can be a slab, a flitch, or a piece to be saved for further resawing. There is also an option for aborting the piece due to unsuccessful sawing. If the piece is a slab, it is stored in the file recbrds for eventual reconstruction to its initial position in the whole log. This reconstruction is done by reverse transformation, using a homogeneous matrix saved
from earlier transformations. The piece is then saved in the file stack. Specifying the piece as aflitch precipitates a number of postprocessing activities which includes saving a copy of the flitch data in recbrds for eventual log reconstruction purposes, face extraction for eventual grading purposes, and finishing operations (i.e. edging at the sides and trimming at the ends to produce a rectangular lumber board). By processing only the faces on which grading is performed (wide faces), instead of the entire flitch description, considerable computational effort is saved. A search is conducted through the flitch data for two polygons which have outward normals parallel to the X-axis in opposite directions. Edging is performed by resetting the edges of the extracted faces by a prescribed displacement 6~(wf, wt), which is a function of the face width wI and the desired lumber width wt. Trimming is likewise performed by resetting the face ends by a prescribed displacement trt(lf, lt), which is a function of the face length If and the desired lumber length It. Specifying a piece for resawing allows later processing on that piece. This option is a provision for sawing patterns that are executed by first sectioning the log into quarters, then treating each quarter separately. An example of this is quarter-sawing, which produces edgegrained lumber. When a sawing instruction is unsuccessful, as indicated by program diagnostics, the user has the option to abort the instruction. This action restores the state before the unsuccessful sawing instruction, and discards the data associated with that instruction. Diagnostics are generated by the solid modeUer whenever violations
LUIS G. OCCEf~Aand JOSE M. A. TANCHOCO
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to the polygon file standard, solid modelling conventions, or the current version of the modeller are detected. An example of the latter is a solid completely enveloped by another solid, a case which defies traditional manufacturing practices with respect to tool approach.
Postprocessing The postprocessing submenu provides the options for evaluating the outcome of the simulated sawing. The sawed-up log can be put together to show the breakdown pattern, saved log quarters can be retrieved for further sawing, or the resulting lumber can be graded. Reconstruct reads the stack in recbrds and renders the stack graphically. The image is a concatenation of the flitches and slabs, and serves as a quick check of the breakdown pattern. Figure 15 shows a sample reconstruction. Resaw retrieves stored log pieces for further sawing. Once chosen, it puts the user in an environment similar to the original sawing environment. Each log piece retrieved for resawing is treated as a completely new log. Upon completion of the sawing, the user is returned to the original sawing environment. The sawed pieces are added to the rest of the stack. Grading submits the extracted lumber face pairs for evaluation. The grading program requires a specific input format. Thus the face data has to be searched for the end vertices of the lumber diagonal, the end vertices of the "boxed" defects, and the defect types. The end vertices of the lumber are easily obtained as the minimum and maximum coordinate points of the data set. The end vertices of the defects are deter-
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mined by bounding each defect orthogonally, to form a "box". Obtaining the end vertices then becomes a similar task to that of lumber. The defect types are identified by associating their end vertices with the bounding planes of the original solid defects. If the end vertices are within a particular set of bounding planes, the defect type is identified. Note that the end vertices still correspond to data from extracted faces. SIMULATED SAWING METHODOLOGY
Simulated sawing sequence The GSS was used to examine a variety of log breakdown patterns. The simulated sawing proceeded in the following sequence:
1. Bring up log representation on the screen. The startup procedure required that the log data be assigned to the input file origsld. Once the program vwply.x was called, the log representation was automatically booted up as the initial display. The image was of the log alone, without defects yet.
2. Superimpose defect representations on log representation. The defects were then rendered on the screen to provide a reference for making breakdown decisions (i.e. saw placements). The log was therefore decomposed with reference to defect locations, although the solid defects were not embedded in the log per se. Instead, the defects were embedded in the resulting flitches, and subsequently in the pair of grading faces. This procedure was done to circumvent the modelling limitations of the current version of the solid modeller as described earlier (the section on unsuccessful cutting).
3. Visually evaluate the defect configuration inside the
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Graphic sawing simulator
log, and determine a breakdown pattern. This step constitutes the decision process in hardwood log sawing. Foreknowledge of defect location and distribution inside the log represented new information which the sawyer now has to consider.
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Table 1. Comparison of actual and simulated sawing of original pattern.
Aggregate Re~ndts for Six Logs Surface Meas~Lre, (Number of Botrds)
4. Position the log representation relative to the saw representation and perform the breakdown. 5. Postprocess the extracted flitches. (5.1) For eachflitch, subtract the corresponding defects using Boolean difference. Actual defect
Grade
embedding occurs here. To save time, selective subtraction was done, i.e. only those defects that lay in the same region as the flitch were considered. (5.2) Extract flitch faces. From this step onwards, the information pertinent to subsequent operations were limited to parameters found in the wide faces. To capitalize on this knowledge, wide faces were extracted and retained. Other information were discarded. (5.3) Edge and trim faces according to preassigned procedure. There are several sawmill practices on edging and trimming. Severe edging and trimming were used in the study.
Sawmill*
Original*
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74 (9) S (1) 33 (S) 207 (31) 111 (17) 70 (10) 6 (7)
88 (12) 7 (1) 46 (6) 214 (32) 149 (20) 71 (10) 2 (1)
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not resawed.
exhibit a similar trend for high and low yields. More on the use of the GSS are reported in [12].
SAWING RESULTS
Several sawing patterns were examined using the GSS, which included the original sawing pattern (from the sawmill), live-sawing, cant-sawing, around-sawing, and pattern-directed sawing. Figure 16 shows some of the sawing patterns, and Table 1 gives a comparison of the simulated sawing results and the actual sawing results from the sawmill. Despite the use of different grading standards (human grader for the actual sawing and a grading program for the simulation), the results
SUMMARY A graphic simulator for modelling hardwood logs and the log breakdown process was described, including a discussion on its development, data structure, configuration, capabilities, and usage. The GSS has the potential for use as a sawyer training tool and more significantly as a verification tool for computer-generated sawing instructions in the presence of internal defect information. REFERENCES 1. E. L. Adams, DESIM: A system for designing and sim-
2. a) Live-Sawing
b) Cant-Sawing
3. 4. 5. 6.
7. 8. c) Taper-Sawing
d) Around-Sawing
Fig. 16. Typical sawing pattern.
ulating hardwood sawmill systems. Gen. Tech. Report NE-89, p. 10, USDA Forest Service Northeastern Forest Expt. Stn., Broomall, PA (1984). R.K. Peter, Influence of sawing methods o n . . . lumber grade yield from yellow poplar. ForestProductsJournal, 17(1 l), 19-24, (1967). J. A. Tsolakides, A simulation model for log yield study. Forest ProductsJournal, 19(7), 21-26 (1969). D. B. Richards, Hardwood lumber yield by various simulated sawing methods. ForestProductsJournal, 23(10), 49-58 (1973). S. M. Pnevmaticos, P. E. Dress and F. R. Stocker, Log and sawing simulation through computer graphics. Forest Products Journal, 24(3), 53-55 (1974). S. M. Pnevmaticos, U. G. Lama and M. Milot, Applications of computer graphics in simulating sawmilling operations. 9th Annual Simulation Symposium Proceedings, 1-13 (1976). S. M. Pnevmaticos and P. Mouland, Hardwood sawing simulation techniques. Forest Products Journal, 28(4) (1978). L.G. Occefia and J. M. A. Tanchoco, Review of hardwood lumber production research. Technical Report, School of Industrial Engineering, Purdue University, West Lafayette, IN 47907 (1986).
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LUlS G. OCCEI~Aand JOSE M. A. TANCHOCO
9. C. W. McMillin, R. W. Conners and H. A. Huber, ALPS---A potential new automated lumber processing system. Forest Products Journal, 34(1), 13-20 (1984). 10. F. W. Taylor, F. G. Wagner, Jr., C. W. McMiilin, I. U Morgan and F. F. Hopkins, Locating knots by industrial tomography--A feasibility study. Forest Products Journal, 34(5), 42-46 (1984). 11. S. J. Chang, P. C. Wang and J. R. Olson, NMR imaging of white oak logs. Technical Forum, 41st Annual Meeting of the FPRS, Louisville, KY (1987). 12. L. G. Occefia, A pattern directed inference approach to hardwood log breakdown decision automation. Unpublished Ph.D. Dissertation, Purdue University, West Lafayette, IN (1987). 13. T. A. Mashburn and D. C. Anderson, TIAM polygonal
14.
15. 16. 17. 18.
modeler user's overview. Purdue University CADLAB, West Lafayette, IN (1986). S. L. Huang and F. T. Sparrow, Wood engineering--An expert system for grading hardwood lumber. Technical Forum Presentation, 41st Annual Meeting, Forest Products Research Society, Louisville, KY (1987). F. P. Preparata and M. I. Shamos, Computational Geometry, Springer-Vedag, New York, NY (1985). A. A. G. Requicha, Representations for rigid solids: theory, methods, and systems. ACM Computing Surveys, 12(4), 437-464 (1980). DI-3000 User's Guide, Precision Visuals, Inc., Boulder, CO (1984). M. E. Mortenson, Geometric Modelling, John Wiley & Sons (1985).
0097-8493/88 $3.00 + .00 © 1988 Pergamon Press pie
Printed in Great Britain.
Technical Section GSSmA CAD-BASED GRAPHIC SAWING SIMULATOR FOR HARDWOOD LOGS* LUIS G. OCCEI~IA Department of Industrial Engineering, University of Missouri-Columbia, Columbia, Missouri 6521 I and JOSE M. A. TANCHOCO Wood Technology Center, IIES, and School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907 Abstract--With the objective of studying the breakdown process for hardwood logs, a graphic sawing simulator (GSS) was developed to provide the capability for repeated sawing. Based on polyhedral solid modelling concepts and device-independent graphics, the GSS represents a solid log as a nonregular polyhedron and enables decomposition of the log ("sawing") via regularized CSG Boolean operations. SAWING SIMULATION
Motivation for development of the simulator
Historical review In a market facing serious competition from synthetic wood substitutes, improved productivity through better control of operations at the sawmill level is a genuine concern for hardwood lumber manufacturers. One of the means of studying sawmill operations that has proven to be effective as a nondestructive approach is computer simulation. In the context of lumber production, this means the ability to perform repetitive sawing on the same log. Simulation of both the sawmill system[l] and the sawing operation[2-4] have been done before. However, it was Pnevmaticos et a/.[5-7] who introduced the first graphic simulation of log sawing on a hybrid graphics terminal. The simulated logs were depicted as cylinders or as truncated cones, as were the nongraphic simulation models of log sawing that came before it. Intersections of the log representation with the cutter representation were computed using a linear programming model. The quality and price of hardwood lumber is greatly affected by surface defects (knots, splits, decay, holes, etc.). Mainly used by the furniture industry, hardwood lumber is manufactured with careful attention to the location and distribution of defects. Control of the defect appearance on the lumber surface is performed during log sawing[8]. Researchers are now looking at a design for an automated sawmill that will implement internal defect detection[9-11]. When applied to industrial practice, internal defect detection will provide sawyers with the capability to "see" inside the log and plan for the breakdown pattern more effectively. This capability also paves the way for research into sawmill automation.
A logical consequence of the capability to obtain internal defect information is the question of how to use this kind of information to advantage. A graphic sawing simulator which will enable representation of the log and its detected internal defects can be a useful tool for studying the relation between internal defect configurations and breakdown patterns. A simulator that can depict the log and its defects in more realistic shapes than simplified cylinders or truncated cones and has the capability to simulate sawing will be even more valuable. This paper describes the development of the graphic sawing simulator GSS, its basic structure, capabilities, and use in modelling solid logs and the hardwood log breakdown process.
Role of the GSS The GSS was used as a tool for examining the relation of log and defect profiles to breakdown patterns. The study was based on a sample set of yellow poplar logs. Guidelines on the use of log and internal defect profile information in the determination of a breakdown pattern were extracted from the study. The guidelines were then formalized in a pattern directed inference model for automation of the breakdown decision process[ 12]. Figure 1 shows the position of the GSS in the total system structure. It was a critical component in the determination of guidelines for log sawing. It was also used to verify breakdown patterns generated by the inference model.
* The work reported in this paper was supported in part by a grant from the U.S. Department of Agriculture, administered by the Cooperative State Research Service (CSRS). 565
SIMULATOR DESIGN
Input to the GSS The intended input to the GSS are log and internal defect profile information derived from internal defect detection scanning. This study therefore complements concurrent research on the recognition of internal defects from scan data[10, 11]. The input should ade-
566
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be defined by the user when the GSS is used on standalone basis, or can come from the pattern directed inference model in the form of a feedback loop for checking the feasibility of computer-generated sawing instructions. Information flows bidirectionally between the GSS and the solid modeller in the course of the simulation. Upon completion of the session, there are several postprocessing options, including lumber grading.
Output from the GSS
Data management
The output of a simulated sawing session using the GSS are data describing the resulting lumber boards and their defects. This stack of data corresponds to a pile of physical lumber. The data can be run through a grading program to determine the individual lumber grades, and ultimately the log yield. The data can also be rendered graphically for visual evaluation of the lumber, or further manipulated as in the case of resawing or log reconstruction.
Under simplified modelling situations where the log is represented as a regular geometric figure (e.g. a cylinder), and the number of defects are few, computational requirements are minimal and even a higherdimensioned array storage performs reasonably well. However, as the number of polygons defining the log and its defects grows in order to render a more realistic profile, data management becomes critical. Higher-dimensioned army variables, for instance, begin to exhibit an increase in computational complexity and storage requirement. External file input/output usage begin to suffer during peak system load. To keep storage requirements and external file transactions to a minimum, a single-dimensioned array is used for primary storage. Other single-dimension arrays are then used to keep track of important parameters, using an address-book approach. This approach allows easy access to stored parameter values and enables the program to operate at reasonable speeds even for complex polyhedral solids. Figure 3 illustrates the use of this .scheme.
Processing control The main program for the GSS is written in FORTRAN77 and implemented on a DEC VAX 11/780 running under the UNIX operating system. Through system calls, the program interfaces with two predefined programs, a C-based polyhedral solid modeller[13] and a Lisp-based grading program[14]. All other functions are internal to the program and are represented as callable FORTRAN subroutines. The block diagram in Fig. 2 summarizes the information flow structure for the GSS. External input can
Graphic sawing simulator
567
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PRE-PROCESSING
The input data passes through a preprocessor routine which performs the conversion to the format required by the program. This process is represented in Fig. 2 by the Syntax Converter block. The input format conforms to a boundary representation polygon standard[13] which represents any solid object as a set of connected polygons, or faces ft. The polygons in turn are sets of connected lines, or edges ej, which are decomposable into sets of connected vertices Vk. These parameters are related by Euler's formula num(v) - hum(e) + n u m ( f ) = 2 (where num is the cardinality)[ 15]. The solid representation therefore consists of a polyhedral approximation of the original solid profile. In the current implementation, a wire-frame graphics image is used. The polygons are formed according to the topological relations of the data points. Figure 4 illustrates the transformation of the raw flitch data into closed planar loops, and subsequently into polygon standard format. GRAPHICS
RENDERING
The GSS was designed to enable interactive, graphic analysis of the hardwood log breakdown process. The
graphics rendering of the GSS was implemented using DI-3000[ 17], a library of ANSI FORTRAN-based, device-independent graphics tools. Like most other general-purpose graphics packages, DI-3000 has several modelling capabilities including standard transformations, windowing and clipping, color, shading, line and text font control, retained segments, 2D and 3D modes, and external file communications. Hidden line removal and animation are not standard features of DI3000 but can be incorporated using established algorithms. Work with the GSS was primarily done on a Tektronix 4105 raster graphics terminal.
THE
SOLID
MODELLING
CONCEPT
Solid modelling originated in the design of machinable metal parts for the manufacturing industry[16, 18]. It has evolved from physical models of solid objects using clay and splines, to computer-aided design representations. There are currently two schools of thought: Constructive Solid Geometry (CSG) which supports the use of primitive solids such as spheres, cubes, and cylinders, and regularized Boolean operations in the representation of solid parts; and Boundary Representation (BRep) which supports the idea of a
Luls G. OCCEI~Aand JOSE M. A. TANCHOCO
568
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more explicit topological data structure using faces, edges and vertices to represent solid parts. Solid modelling enables both formation and decomposition of more complex solids through the interaction of simpler solids. This interaction is accomplished by regularized Boolean operations of union, intersection, and difference. To give an example, a cube with a horizontal through-hole can be produced by subtracting a cylinder (with the same diameter as the hole) from the cube (at the specified location). Figure 5 illustrates this example. The solid modeller used in the GSS has a BRep structure. A BRep modeller is more appropriate for nonregular geometric solids such as logs, than a CSG structure. Furthermore, this solid modeller is polyhedral-based, enabling both a computationally simpler representation and a more realistic approximation of hardwood logs than was available with the cylindrical or conical representations used the past. SOLID LOG RECONSTRUCTION
Available data The input data for the log profile included both whole log measurements prior to sawing and flitchslab measurements after sawing. A slab, which contains bark on one side, is the first piece removed from each log face. Flitches, which may have bark on the edges,
are the subsequent pieces removed and later finished into lumber. The flitch-slab measurements were used to rebuild a solid representation of the log in a "reversesawing" sense. This procedure was used after it was found that the whole log measurements allowed too much play in the diameter placements to provide an accurate reconstruction. The flitch-slab measurements did not have that problem.
Polygon formation To conform with the polygon standard, three types of polygons were generated: wide faces, edges, and ends. The resulting flitch representation has two wide faces, two edges (sometimes with wane, i.e. bark), and two ends. The resulting slab representation has one wide face, a waney face, and two ends. These are illustrated in Figs. 6 and 7 . The wide faces on which lumber grading is performed were generally assumed to be fiat, having been cut straight by the saw blade. They were described quite simply by a quadrilateral face. Ends were similarly assumed to be flat and straight, having been cut by a straight saw blade in the preliminary operations of bucking and topping. Though the ends may not always be planar as the wide faces in practice, such an assumption is valid in the light of subsequent finishing operations.
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Edges were the most difficult of the faces to represent because of wane, which is nonplanar. If wane is eventually removed from the edges in the resulting log breakdown pattern, an edge can be represented by a single face. If wane is present, however, the edge is essentially multifaceted. To simplify polygonal representation of waney edges, triangulation was used. The price to pay for this simplification, however, is the proliferation of triangulated faces. Similar treatment was given to the waney face of a slab, with the increase in width towards the longitudinal ends of the slab as the only distinction. Sectional reconstruction To facilitate log reconstruction, whole log sections were built up at a time. This sectional reconstruction approach saved an entire step in the reconstruction process, because eventually the flitches had to be CAG 12: 3/4-R
merged with adjacent flitches according to the breakdown pattern. This procedure also ensured control over face generation, because the number of resulting faces could then be predicted. In the case of around-sawed logs, the flat side on the sawn faces provided an excellent reference face for alignment in sectional reconstruction. Figure 8 illustrates sectional reconstruction, and Fig. 9 shows a completed section of a sample log.
CAD-based log unification Unification of log sections was performed using the regularized Boolean union operation. The first step in the unification was to use the GSS to position one log section s~, relative to an adjacent log section, s2, so that the two sections were separated only by the kerf width, wk. One of the two opposing faces from either section was then extended by an increment ~, such that the extended face crossed over into the opposite
570
Lu]s G. OCCERAand JOSE M. A. TANCHOCO
Fig. 5. Composite part formation using CSG Boolean subtraction. face. The log sections were then unified in this intersected state by a regularized Boolean union operation, to form bigger log sections. Figure l0 provides an illustration. This procedure is repeated for the rest of the log sections. The end result is a whole log, as shown in Fig. 11. SOLID DEFECT RECONSTRUCTION Available data Log defect information collected for the study consisted of defects found on the surface of the log samples prior to sawing and defects found on the wide faces of the flitches and slabs after sawing.
Although there were isolated cases of decay, knots and bumps left by former branches comprised the predominant defects detected on the log surface. The defect profiles were recorded in photographs. The defect locations were measured, with reference to the log small-end and eight rotational sections. Internal defects were detected only after the log had been sawn. Detected defects included both tight and loose round knots, pin knots, worm holes, bird pecks, splits, and pith decay. The defect profiles were recorded in their actual size on transparent overlays using quickdrying permanent marker pens. Each defect location was measured with reference to the small end of the 1-90ME'fRIC
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-i Fig. 7. Slab polygonal representation. flitch and the bottom face-side edge of the flitch. As the flitches were sawn from the log, the side on which the decision to cut was based (open log face) was labelled the face side. These conventions were adopted to aid in reconstruction.
Polygonformation Defect to log correspondence in solid form would be direct if internal defect detection, using either Industrial Photon Tomography (IPT) or Nuclear Magnetic Resonance (NMR) scan data, were used. When collected from sawn logs, however, the only way to visualize the solid defects was to rebuild three-dimen-
sional representations from the two-dimensional defect data. The reconstruction was performed using the GSS and a procedure similar to log reconstruction. Internal defect data were collected in the form of curvilinear tracings. To satisfy the standard polygon requirements of the GSS, the tracings were converted into polygon format by an approximate point-to-point linear fit.
Graphics-aided reconstruction Following formation, the defect polygons were then matched with defect polygons from flitches adjacent in the breakdown pattern. Thus the polygons were
SECTIONAL
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Fig. 8. Sectional and individual reconstruction.
572
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Fig. 9. Completed sectional log reconstruction.
treated as slices from a solid defect. Referenced to a common point (the flitch small end), the defect polygons of adjacent flitches appeared graphically as opposing faces. A convenient way of showing the alignment of opposing faces was through the GSS. The GSS made it possible to perform relative positioning of the defect
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polygons, using translational and rotational transformations. This relative positioning was done two polygons at a time for defect polygons resident in flitches that were known to be adjacent in the breakdown pattern. As the number of positioned defect polygons increased, the defect solids begin to take shape. To form
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Fig. 11. Completed whole log reconstruction.
The reconstructed defects were restored inside the reconstructed log using the GSS as a graphic aid. Restoration was performed using relative positioning and the original log breakdown pattern. The result was a "see-through" image of the solid log, as would be generated by imaging devices such as IPT or N M R scannet's. Color was used to distinguish the log from its defects.
the defect solid, aligned polygons were "stitched" together by triangulation of the corresponding data points. The reconstructed solid defects therefore consisted of at least two opposing polygonal faces with multifaceted edges. This procedure was in keeping with the sectional reconstruction approach for log reconstruction. Figure 12 shows a reconstructed defect configuration.
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Luis G. OCCElqlAand JOSEM. A. TANCHOCO
574
SOLID LOG DECOMPOSITION Using regularized CSG Boolean operations, a flitch or slab can be extracted from a solid log representation by performing an intersection operation between the log representation and the saw representation. Conversely, the remaining log can be obtained by performing a difference operation of the cutter representation from the solid log representation. Figure 13 shows a sample remaining log. Among the design issues in the decomposition process were: • positioning of the log representation relative to the cutter representation; • setting up of the input file for the batch mode interaction with the solid modeller; • allowing for kerf, i.e., sawdust; • routing the piece removed for further processing; • sequencing the execution of the operations and supporting processes. MODEL OPERATION Getting started To begin a sawing session, the following files are required: * vwply.x--the compiled sawing simulation program; • origlsd--the data file containing the log and defect description in polygon file standard; • poly.x--the compiled polyhedral solid modelling program; • zero--end-of-file character file used in input and output; • grade--grading program.
The GSS is initialized by entering the compiled simulator name, vwply.x. The solid log and its defects are then graphically rendered. Main menu The main menu comes up on the screen soon after the initial log and defect representations are drawn. The Tektronix 4105 supports separation of alphanumeric and graphic displays, so the textual input/output via menus are superimposed on the graphics image. The main menu consists of the following entries: Exit, Rescaling, Decomposition, and Postprocessing. Exit is the escape option to use when the session is completed, or when strictly viewing and no processing is desired. Rescaling is a utility option for resizing the image. Decomposition leads to a submenu for sawing the log, and Postprocessing leads to a submenu for evaluating the outcome of a sawing session. Decomposition submenu The decomposition category comprises the simulated sawing activity. It introduces the saw representation, enables the user to position the log representation relative to the saw representation via translation or rotation, actuates the sawing, and terminates sawing. Upon entering this mode, a saw representation is generated based on the size of the log representation. Figure 14 shows a saw representation, in the form of a rectangular block, intersected with the log representation. Parameter settings are indicated alongside with the option to change the kerf allowance, initially set at 0.125 inches. The simulated sawing is actuated by the Cut command which is invoked after the log representation has
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Graphic sawing simulator "rc)P
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been positioned relative to the saw representation. The two representations must be intersected (overlapped) for the operation to succeed. When the Cut command is given, the log and cutter representations are written out to a file in polygon file standard. A Boolean intersection operation is specified, and then the file is submitted as a batch job to the solid modeller. Diagnostics are printed on the left side of the screen, serving as indicators for successful cutting. Upon completion, the user is prompted for the flitch (or slab) routing. If cutting was unsuccessful due to solid modeller restrictions, the previous operation can be aborted. Otherwise, a piece is removed which can be either a slab, a flitch, or a piece intended for resawing. While the piece is being processed in the background, the program once again writes the log and saw representations to a file, but this time offsetting the log representation toward the saw representation by the kerf width, Wk. A Boolean subtraction operation is specified to extract the remaining log. After the remaining log representation is rendered on the screen, the user has the option to continue sawing, or to terminate the session.
Board routing submenu Board routing determines the treatment of the removed piece. The piece can be a slab, a flitch, or a piece to be saved for further resawing. There is also an option for aborting the piece due to unsuccessful sawing. If the piece is a slab, it is stored in the file recbrds for eventual reconstruction to its initial position in the whole log. This reconstruction is done by reverse transformation, using a homogeneous matrix saved
from earlier transformations. The piece is then saved in the file stack. Specifying the piece as aflitch precipitates a number of postprocessing activities which includes saving a copy of the flitch data in recbrds for eventual log reconstruction purposes, face extraction for eventual grading purposes, and finishing operations (i.e. edging at the sides and trimming at the ends to produce a rectangular lumber board). By processing only the faces on which grading is performed (wide faces), instead of the entire flitch description, considerable computational effort is saved. A search is conducted through the flitch data for two polygons which have outward normals parallel to the X-axis in opposite directions. Edging is performed by resetting the edges of the extracted faces by a prescribed displacement 6~(wf, wt), which is a function of the face width wI and the desired lumber width wt. Trimming is likewise performed by resetting the face ends by a prescribed displacement trt(lf, lt), which is a function of the face length If and the desired lumber length It. Specifying a piece for resawing allows later processing on that piece. This option is a provision for sawing patterns that are executed by first sectioning the log into quarters, then treating each quarter separately. An example of this is quarter-sawing, which produces edgegrained lumber. When a sawing instruction is unsuccessful, as indicated by program diagnostics, the user has the option to abort the instruction. This action restores the state before the unsuccessful sawing instruction, and discards the data associated with that instruction. Diagnostics are generated by the solid modeUer whenever violations
LUIS G. OCCEf~Aand JOSE M. A. TANCHOCO
576
to the polygon file standard, solid modelling conventions, or the current version of the modeller are detected. An example of the latter is a solid completely enveloped by another solid, a case which defies traditional manufacturing practices with respect to tool approach.
Postprocessing The postprocessing submenu provides the options for evaluating the outcome of the simulated sawing. The sawed-up log can be put together to show the breakdown pattern, saved log quarters can be retrieved for further sawing, or the resulting lumber can be graded. Reconstruct reads the stack in recbrds and renders the stack graphically. The image is a concatenation of the flitches and slabs, and serves as a quick check of the breakdown pattern. Figure 15 shows a sample reconstruction. Resaw retrieves stored log pieces for further sawing. Once chosen, it puts the user in an environment similar to the original sawing environment. Each log piece retrieved for resawing is treated as a completely new log. Upon completion of the sawing, the user is returned to the original sawing environment. The sawed pieces are added to the rest of the stack. Grading submits the extracted lumber face pairs for evaluation. The grading program requires a specific input format. Thus the face data has to be searched for the end vertices of the lumber diagonal, the end vertices of the "boxed" defects, and the defect types. The end vertices of the lumber are easily obtained as the minimum and maximum coordinate points of the data set. The end vertices of the defects are deter-
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mined by bounding each defect orthogonally, to form a "box". Obtaining the end vertices then becomes a similar task to that of lumber. The defect types are identified by associating their end vertices with the bounding planes of the original solid defects. If the end vertices are within a particular set of bounding planes, the defect type is identified. Note that the end vertices still correspond to data from extracted faces. SIMULATED SAWING METHODOLOGY
Simulated sawing sequence The GSS was used to examine a variety of log breakdown patterns. The simulated sawing proceeded in the following sequence:
1. Bring up log representation on the screen. The startup procedure required that the log data be assigned to the input file origsld. Once the program vwply.x was called, the log representation was automatically booted up as the initial display. The image was of the log alone, without defects yet.
2. Superimpose defect representations on log representation. The defects were then rendered on the screen to provide a reference for making breakdown decisions (i.e. saw placements). The log was therefore decomposed with reference to defect locations, although the solid defects were not embedded in the log per se. Instead, the defects were embedded in the resulting flitches, and subsequently in the pair of grading faces. This procedure was done to circumvent the modelling limitations of the current version of the solid modeller as described earlier (the section on unsuccessful cutting).
3. Visually evaluate the defect configuration inside the
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Graphic sawing simulator
log, and determine a breakdown pattern. This step constitutes the decision process in hardwood log sawing. Foreknowledge of defect location and distribution inside the log represented new information which the sawyer now has to consider.
577
Table 1. Comparison of actual and simulated sawing of original pattern.
Aggregate Re~ndts for Six Logs Surface Meas~Lre, (Number of Botrds)
4. Position the log representation relative to the saw representation and perform the breakdown. 5. Postprocess the extracted flitches. (5.1) For eachflitch, subtract the corresponding defects using Boolean difference. Actual defect
Grade
embedding occurs here. To save time, selective subtraction was done, i.e. only those defects that lay in the same region as the flitch were considered. (5.2) Extract flitch faces. From this step onwards, the information pertinent to subsequent operations were limited to parameters found in the wide faces. To capitalize on this knowledge, wide faces were extracted and retained. Other information were discarded. (5.3) Edge and trim faces according to preassigned procedure. There are several sawmill practices on edging and trimming. Severe edging and trimming were used in the study.
Sawmill*
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exhibit a similar trend for high and low yields. More on the use of the GSS are reported in [12].
SAWING RESULTS
Several sawing patterns were examined using the GSS, which included the original sawing pattern (from the sawmill), live-sawing, cant-sawing, around-sawing, and pattern-directed sawing. Figure 16 shows some of the sawing patterns, and Table 1 gives a comparison of the simulated sawing results and the actual sawing results from the sawmill. Despite the use of different grading standards (human grader for the actual sawing and a grading program for the simulation), the results
SUMMARY A graphic simulator for modelling hardwood logs and the log breakdown process was described, including a discussion on its development, data structure, configuration, capabilities, and usage. The GSS has the potential for use as a sawyer training tool and more significantly as a verification tool for computer-generated sawing instructions in the presence of internal defect information. REFERENCES 1. E. L. Adams, DESIM: A system for designing and sim-
2. a) Live-Sawing
b) Cant-Sawing
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7. 8. c) Taper-Sawing
d) Around-Sawing
Fig. 16. Typical sawing pattern.
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