The advantage of this method is that most 
interpolation algorithms still can be used for each 
triangle locally. Only difference is that two normal 
direction has to be found and assigned to those 
points on the break lines. For example, the Akima 
and Bezier interpolations can be used with the 
above modifications. 
Find TWO normal directions 
at a point on break line 
There are many ways to find a normal direc- 
tion at a point on the common edge. A simple 
method used is to find an 'average' normal direc- 
tion from given points around. Some methods 
concerning distance weight from these given point 
may be better. If the point is on a break line, the 
surface space is assumed to be cut by the break 
line. A normal direction at a point on the break 
line will be calculated for each side from those 
given points on the side of the break line. Another 
normal direction is calculated from those given 
points on another side of the break line. In this 
Way, a point on the break line edge can have more 
than one normal directions. Each of them behaves 
corespondently to the surface at one side. The 
point and one normal direction can be seen as an 
extension property from one side of the surface. 
Conclusions 
The method presented in this paper has been 
successfully implemented in Arc/Info 6.0 above 
release version. It provides the capability of surface 
model integrated with break lines. The quality and 
reality of surface model are enhanced. The perfor- 
mance of the modified interpolation is very good, 
actually has not been effected obviously, after 
modified. 
References 
Akima, H., "A Method of Bivariate Interpolation 
and Smooth Surface Fitting for Irregular Dis- 
tributed Data Points." ACM Transactions on 
Mathemetical Software 4 (June 1978): pp. 
148-159. 
Robert E. Barnhill and Wolfgong Boehm, ed., 
1983, "Surface in Computer Aided 
Geometric Design, North-Holland Publis. 
Comp., Amsterdam. 
Zi-Tan Chen, "Break lines on Terrain Surface", 
Proceedings of GIS/LIS'88 conference, San 
Antonio, Dec. 1988, pp. 781-790. 
Zi-Tan Chen, "A Spatial Low-Pass filter working 
for Triangular Irregular Network (TIN) and 
Restricted by Break Lines", Proceedings of 
AUTO-CARTO 9, Baltimore Maryland, 
April 1989, pp. 138-145. 
ESRI Inc., ARC/INFO User's Guide 6.0: Surface 
Modeling with TIN, 1992. 
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