Using AutoCAD for descriptive geometry exercisesin undergraduate structural geology

p

Carl E. Jacobson*

Department of Geological and Atmospheric Sciences, 253 Science I, Iowa State University, Ames, IA 50011-3212, USA

Received 1 January 1999; accepted 14 February 2000

Abstract

The exercises in descriptive geometry typically utilized in undergraduate structural geology courses are quicklyand easily solved using the computer drafting program AutoCAD. The key to e�cient use of AutoCAD for

descriptive geometry involves taking advantage of User Coordinate Systems, alternative angle conventions, relativecoordinates, and other aspects of AutoCAD that may not be familiar to the beginning user. A summary of thesefeatures and an illustration of their application to the creation of structure contours for a planar dipping bed

provides the background necessary to solve other problems in descriptive geometry with the computer. The ease ofthe computer constructions reduces frustration for the student and provides more time to think about the principlesof the problems. 7 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Geoscience education; Computer-assisted learning; Computer-aided drafting; Structure contours

1. Introduction

Undergraduate courses in structural geology typi-

cally include a series of lab exercises that use descrip-

tive geometry to analyze apparent-dip, three-point,

contour-contact, fault-o�set, and related problems

(Ragan, 1985; Marshak and Mitra, 1988). Tradition-

ally, these problems have been solved by hand draft-

ing. The advent of personal computers, however,

allows the necessary drawings to be created more

quickly and accurately using computer-aided drafting

and design (CAD) software. At Iowa State University,

we use the commercially available drafting program

AutoCAD in the structure lab, and ®nd that most stu-

dents prefer this approach to hand drafting. In thispaper, a simple example (Fig. 1) is used to outline theapproach needed to solve problems of descriptive geo-

metry with AutoCAD. A longer version of this manu-script, providing more detail about individualAutoCAD commands and additional geological

examples, can be downloaded from the IAMG server(www.iamg.org/CGEditor/index.htm). The methodspresented here were tested using AutoCAD Map 3.0,which is a variant of AutoCAD Release 14. They are,

however, applicable to a broad range of AutoCADversions.

2. AutoCAD commands used in the constructions

This paper assumes familiarity with certain basicAutoCAD capabilities. These include the creation of

Computers & Geosciences 27 (2001) 9±15

0098-3004/01/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.

PII: S0098-3004(00 )00060-1

pCode available at http://www.iamg.org/CGEditor/

index.htm

* Tel.: +1-515-294-4480; fax: +1-515-294-6049.

E-mail address: cejac@iastate.edu (C.E. Jacobson).

simple objects such as lines and text, as well as the ma-nipulation of such objects using the ERASE, COPY,

ARRAY, MOVE, OFFSET, TRIM, and EXTENDcommands (speci®c AutoCAD command names areindicated by italicized capital letters). It is also import-

ant to be able to create layers, control layer color andline type, and move objects from one layer to another.Furthermore, the user should know how to control the

screen display using the LIMITS, ZOOM, PAN,GRID, and SNAP commands. Instruction on basicAutoCAD functions is available from the online man-

uals supplied with AutoCAD and from numerousthird-party tutorials and manuals (e.g., Beall et al.,1997). In addition, an AutoCAD tutorial geared to ge-ologists is publicly available from the aforementioned

IAMG server.Besides the basic functions, there are several features

of AutoCAD (e.g., User Coordinate Systems, alterna-

tive angle conventions) that greatly expedite the geo-metric constructions, but which may not be familiar tothe beginning user. These are summarized next and

described in more detail in the extended version of themanuscript.

2.1. Coordinate systems

AutoCAD stores the coordinates of all objects in adrawing in a ®xed reference frame known as the

`World Coordinate System' (WCS). In the WCS, the X

axis is east±west, the Y axis is north±south, and the Zaxis, which we will not utilize, is perpendicular to the

screen. In addition to the WCS, it is possible to createone or more User Coordinate Systems (UCSs), whichinvolve a temporary shift of the origin point and/or

orientations of the X, Y, and Z axes. For example, inthe various descriptive geometry problems, construc-tion is often simpli®ed by rotating the X axis parallel

to some line with arbitrary orientation. Control of thecoordinate system is provided by the UCS command.The current status of the coordinate system is indi-

cated by an icon, called the `UCS icon', that normallyappears in the lower-left corner of the AutoCADgraphics window (`graphics window' is AutoCAD'sterm for that part of the screen in which the drawing

is displayed). Fig. 2 illustrates the appearance of theUCS icon when the WCS is in e�ect. This can be con-trasted to the orientation of the icon in Fig. 3, where

the X axis of the UCS is parallel to the line labeled`Folding Line'.

2.2. Angles

By default, AutoCAD uses the standard mathemat-ical convention for angles, with 08 along the positive Xaxis (east) and positive angles measured counterclock-

wise. However, the SURVEYOR option of the DDU-NITS command can be used to replace this systemwith standard geological quadrant notation. Quadrantnotation is the convention adopted by Ragan (1985)

and Marshak and Mitra (1988), and the one used here.Directions for enacting 3608 geological notation (azi-muths) are provided in the extended manuscript.

2.3. Relative coordinates

Many AutoCAD commands prompt the user toenter coordinates, such as for the beginning or ending

point of a line, the center of a circle, or the insertionpoint of text. Coordinates can be entered in either ab-solute or relative form. Absolute coordinates are inter-

preted with respect to the origin of either the WCS ora UCS, whichever is currently active. Relative coordi-nates are interpreted with respect to the last pointentered. Absolute coordinates are indicated by entering

the values of X and Y separated by a comma. Relativecoordinates are denoted by preceding the coordinateswith the `@' sign. Both absolute and relative coordi-

nates can be entered in polar form. This involves pro-viding a distance followed by an angle in degrees, withthe `< ' character as the separator.

2.4. Cursor coordinates

The coordinates of AutoCAD's drawing cursor areindicated along the left side of the status line locatedFig. 1. Solution to structure contour problem.

C.E. Jacobson / Computers & Geosciences 27 (2001) 9±1510

at the bottom of the AutoCAD window (e.g., Fig. 2).The coordinate display has three modes: (1) the coordi-

nates update continuously as the cursor is movedabout the screen; (2) they update only when the leftmouse button is clicked; or (3) they update continu-

ously, with the values in polar coordinates. To cyclebetween the three modes, use the F6 function key ordouble-click the left mouse button while the cursor is

positioned in the coordinate display area. The polarcoordinate mode is available only when AutoCAD isdisplaying a rubber-band line from within a drawing

command.

2.5. Object snaps

Object snaps provide a simple way to locate pointsprecisely. For example, object snaps can be used toforce a line to meet exactly with the endpoint or mid-

point of another line, the center of a circle, or a pointof intersection between two other objects. Object snapscan be utilized in most situations in which AutoCAD

prompts the user to select a point. They are enacted byentering the name or abbreviation of a speci®c snap

type at the command line.

3. Structure contours

Many problems in descriptive geometry require con-struction of one or more lines of equal elevation (struc-

ture contours) on a planar dipping bed. Here a simpleexample is considered in which a bed with strike anddip N258E 358NW crops out on a level plain with el-

evation of 1500 m above sea level. The goal will be todraw structure contours at 100 m intervals, down toan elevation of 1100 m (Fig. 1). The solution involves

the `folding-line' method, which is described by bothRagan (1985) and Marshak and Mitra (1988). In sum-mary, a line is drawn in map view to represent the

strike of a bed. A cross-section view is joined to themap along a `folding line' perpendicular to strike ofthe bed, and the true dip of the bed is drawn in the

Fig. 2. Creating a folding line by using object snap to drop perpendicular to outcrop trace of bed (step 4 in text).

C.E. Jacobson / Computers & Geosciences 27 (2001) 9±15 11

cross section. A depth scale perpendicular to the fold-ing line allows determination of the spacing of the

structure contours.Before proceeding to a solution in AutoCAD, it is a

good idea to make a rough sketch of the problem with

pencil and straightedge. The sketch should not requireuse of a ruler or protractor Ð estimates of distancesand angles will generally be su�cient. The sketch will

help with conceptualization of the problem and willallow a preliminary estimate of the AutoCAD limits,an important step in creation of any new drawing. In

this example, we can use the ®nal solution (Fig. 1) as aproxy for the sketch. The size of the drawing is con-strained by the number and spacing of contours. Noreal-world coordinates are speci®ed, so the position in

space is arbitrary.

3.1. Solution

1. Run the LIMITS command. A value of (0,0) wasused for the lower-left limit and (1500,1200) for the

upper right, assuming the AutoCAD units to rep-

resent meters. After the LIMITS command, run

ZOOM ALL to reset the graphics window to ®t the

new limits.

2. Run DDUNITS to set the angle mode to SUR-

VEYOR.

3. Use the LINE command to draw the strike of the

bed. Because we are assuming a level ground sur-

face, the strike line will be equivalent to the outcrop

trace of the bed. For the starting point, use an arbi-

trary location near the bottom of the screen and

somewhat to the right of center (Fig. 2). Make sure

the coordinate counter is set for polar display.

Move the rubber-band line toward the top of the

screen along a trend of approximately N258E. Read

the coordinate counter to determine approximately

how long the line needs to be in order to nearly

reach the top of the screen. The exact value does

not matter. A length of 1000 was used, which,

together with the angle, was entered at the com-

mand prompt as the relative coordinate @1000 <

Fig. 3. Construction of trace of dipping bed in cross section (step 5 in text).

C.E. Jacobson / Computers & Geosciences 27 (2001) 9±1512

n25e.

4. Create the folding line, which is perpendicular tothe outcrop trace of the bed. Start the LINE com-mand and select a point in the upper left part of the

screen (Fig. 2). The exact starting location is arbi-trary, but some judgement is needed to produce thedesired relative size of the map view and cross sec-

tion. Once the ®rst point is entered, type `perp' atthe command line to activate the perpendicularobject snap (Fig. 2). Click anywhere on the outcrop

trace to ®nish the folding line.5. Draw the trace of the bed in the cross-section view

(Fig. 3). Since the dip angle (358) is measured rela-

tive to the folding line, the easiest way to enter itsvalue is to align the UCS parallel to the foldingline. Run the UCS command, choose the OBJECT

option, and select the folding line anywhere alongits right half. The Y direction on the UCS iconshould end up pointing to the lower left (Fig. 3).

Use the ``int'' object snap to begin a line from theexact intersection of the strike line and folding line.

Stretch the rubber-band line along the approximate

direction of dip (Fig. 3). Read the coordinate coun-ter to determine an appropriate length for the line.The line was ®nished by entering the relative coordi-

nate @900 < 35. (AutoCAD is currently in Sur-veyor mode for angles, but entering a value instandard angle notation overrides this.)

6. Draw the depth lines in the cross-section view(Fig. 4). Make sure the UCS is still in the orien-tation generated in step 5. Start the ARRAY com-

mand, select the folding line, then choose theRECTANGULAR option. Specify 5 rows, 1 column,and a spacing between rows of 100 units. Once the

depth lines are drawn, it may be necessary to zoomthe display to make sure all objects are completelyvisible. Also, check to see if the outcrop trace of the

bed extends to the deepest of the 100 m elevationlines. If not, as is the situation in Fig. 4, use theEXTEND command to force the two to meet.

7. Create the structure contour lines (Fig. 5). Leavethe UCS in the same orientation as in steps 5 and 6.

Fig. 4. Use of ARRAY command to create series of depth lines at 100 m spacing in cross-section view (step 6 in text).

C.E. Jacobson / Computers & Geosciences 27 (2001) 9±15 13

Start the ARRAY command, select the outcrop

trace of the bed, and choose the RECTANGULAR

option. Specify 1 row and 5 columns (the number of

rows and columns is reversed from step 6 because

the outcrop trace of the bed is parallel to the Y axis

of the UCS, whereas the folding line is along the X

axis). When prompted for the distance between col-

umns, type `int' to enact an intersection object snap,

then click on the intersection between the outcrop

trace and the 1400 m elevation line (i.e., the ®rst el-

evation line beneath the folding line). Now enter

`int' again and select the intersection between the

1400 m elevation line and the trace of the bed in

cross section. AutoCAD determines the distance

between the two selected points and uses it to create

the array. If desired, use the TRIM command with

the cross-section trace of the bed as the cutting edge

to eliminate unnecessary parts of line segments(compare Figs. 1 and 5).

4. Discussion

The methods illustrated previously can easily beextended to other types of exercises typical in under-

graduate structural geology. These include three-pointproblems, determining strike and true dip from twoapparent dips, predicting outcrop trace of dippingbeds, determining thickness and depth of beds, and

calculating fault o�sets. Examples of several of theseare provided in the extended version of the manu-script.

Fig. 5. Structure contours created by arraying outcrop trace of bed through intersections between cross-section trace of bed and

100 m elevation lines (step 7 in text).

C.E. Jacobson / Computers & Geosciences 27 (2001) 9±1514

AutoCAD provides quick, accurate, and precise sol-utions to problems of descriptive geometry. The im-

portant question, however, is how it compares to handdrafting in terms of helping students visualize three-dimensional geologic relations. An objective evaluation

of this issue has not been attempted, but, some anec-dotal points are worth considering. Several instructorssuggest that the act of drawing by hand is an import-

ant component of the visualization process and shouldnot be discarded. There is truth to this, which is whystarting each problem with a hand-drawn sketch

should be emphasised. However, my observation afterteaching the traditional drafting method for over 15years, is that students often lose sight of the overallpoint of the exercises because they get bogged down in

the details of correctly measuring angles and lengths.In this sense, the computer frees the student of thetedium of manual drafting, allowing more time to

think about the problem. Furthermore, because editingis easy, the computer method eliminates the frustrationof throwing out a nearly complete exercise after disco-

vering a mistake made early in the drawing. Finally,because computer drafting produces an exact answer,comparison to a posted answer key can allow the stu-

dent to discern immediately if he/she committed an

error. With hand drafting, di�erences in distances andangles between the student's answer and the posted

key may be ambiguous, because they can result eitherfrom acceptable drafting inaccuracies or incorrect ap-plication of the method.

Acknowledgements

The manuscript bene®ted from suggestions by JohnBaldwin and Jim Connelly. The work was supported

by NSF grants EAR-9526589 and DUE-9650264.

References

Beall, M.E., Burchard, B., Guingao, J., Peterson, M.T.,

Pitzer, D.M., Sage, M., et al., 1997. Inside AutoCAD 14.

New Riders Publishing, Indianapolis, Indiana. 1008 pp.

Marshak, S., Mitra, G., 1988. Basic Methods of Structural

Geology. Prentice Hall, Englewood Cli�s, New Jersey. 446

pp.

Ragan, D.M., 1985. Structural Geology: An Introduction to

Geometrical Techniques, 3rd ed. John Wiley & Sons, New

York. 393 pp.

C.E. Jacobson / Computers & Geosciences 27 (2001) 9±15 15