Geology Reference
In-Depth Information
Fig. 6.30.
Bézier curves.
a
The four control points that define the curve.
b
Two Bézier cubics joined at
point
P
4
. Points
P
3
,
P
4
, and
P
5
are colinear. (After Foley and Van Dam 1983)
Fig. 6.31.
Spline curve and its control
points
Drawing a cross section (or a map) using the smooth curves just described requires
care to maintain the correct geometry. Constant bed thickness, for example, is not likely
to be maintained if the section is drawn from sparse data. The appropriate bed thick-
ness relationships can be obtained by editing the curves after a preliminary section has
been drawn. The cross section of the Sequatchie anticline illustrates the problems. The
original section (Fig. 6.23) was redrawn by changing the lines from polygons to spline
curves in a computer drafting program. The resulting cross section (Fig. 6.32) may be
more pleasing to the eye than the dip-domain cross section, but it is less accurate. The
unedited spline-curve version (Fig. 6.32a) is much too smooth. Each bedding surface
is defined by 4 to 6 points, a data density that might be expected with control based
entirely on wells. Bedding thicknesses are not constant as in the dip-domain version,
and the amplitude of the structure is reduced. These are the typical results of analyti-
cal smoothing procedures, including the smoothing inherent in gridding as used for
map construction. Editing the spline curves produces a better fit to the true dips
(Fig. 6.32b). A more accurate spline section can be produced by introducing many more
control points, which is the appropriate procedure for producing a final drawing of a
known geometry. The addition of control points to improve an interpretation based on
a sparse data set requires additional information, such as the bedding dips, or the re-
quirement of constant bed thickness.
