ul 2004 
ner can 
n those 
ress the 
en be + 
>ctional 
ipping" 
thening 
n of the 
lomena. 
“all the 
meshes 
er have 
1 angle- 
itioning 
apping” 
n taken 
it is not 
V. 
used to 
vays, in 
lete the 
ve been 
e values 
rom the 
lirection 
s along 
ts along 
ir valid 
of each 
us, it is 
rm both 
  
les 
uire that 
: kind of 
n in the 
is in one 
ent next 
ampling 
  
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
| t3 | 
| ®---9 1 
-- 
i 
* 
A TA 
i 4-9 14 | 
2U 
A 
à 
$--- 
= 
4---w#72 | 
[Ltée d 
Fig.8 right corresponding 
LA 
ba € 
  
t^t 
« 
Fig.9 wrong corresponding 
fig.9 shows us when a uniform relationship between the 
sampling direction and the flow direction could not be 
guaranteed all the way, “wresting” of the output meshes will be 
sure to come into being as displayed in fig.10 and fig.11. 
MERE EO 
A 
PU CDL i 
Hn 
FE 3 
   
ve ie i-] 
1 tte td \ 
,* 
phenomenon 
Fig.10 “wrest 
  
  
Fig.11 “wrest” phenomenon, magnified 
Another prescription has been made that the sampling direction 
along each section should obey the “right-hand” rule with the 
flow direction there to avoid this “wresting” phenomenon 
(thumb of the right hand points to the sampling direction), and a 
corresponding method has been worked out to tell the starting 
from the ending of each two ends, that is, to confirm the 
sampling direction in this section. 
First, following two coordinate systems have been set up to help 
us analyze this uniform relationship between the flow direction 
and the sampling direction. 
f HD m 
| b ; 
j F p ; 
L Ci E RES s CEA “<= --- E m ze, 
pp rf X 
| pi A 
f + ; 
iba i agp / 
ES A, 
Fig.12 coordinate systems for vertical sections 
  
quU Ny A 
D 4 ^. 
E p 2x 
% : d ET 
Y WA nr. A, d 
E bon , ad 
l * ~ 5 i 
| x \ 
| 3 A 
em" 
  
Fig.13 coordinate systems for horizontal sections 
According to “numerical expression of the flow direction” 
described in §3.2, flow direction can be represented by one 
Sect-Point (P) pointing to another one next to it (£1 or PI’), 
here; EE represents the section in above coordinate systems, a 
non-negative slope value has been adopted as the threshold to 
classify all the sections into two classes, those sections whose 
absolute slope value is below the threshold are ascribed into one 
class, they are horizontal sections, others are ascribed into the 
second class, they are vertical sections. Choice of the threshold 
doesn't need to take much severe attention, e.g., 0.5 in the 
implementation of this algorithm as presented in this paper, 
“capable of differentiating those relatively horizontal sections 
from vertical ones" is the only principle to be observed here. 
Then, judgements upon which ends (Z, or £;) of the section is 
the starting could be made according to the above coordinate 
systems, 
l. As for vertical sections, we shall choose the coordinate 
system in fig.12 to make judgements like this: sign of the 
coordinate increments along axis X ascertain the sampling 
direction, if positive, indicating that the Sect-Point next to 
P is P] but not Pl', the end with smaller coordinate value 
in axis Y (£5) is the starting point and the other (E) is the 
ending; contrarily if negative, the end with larger 
coordinate value in axis Y (Ej) is the starting. 
2. As for the horizontal sections, we shall use the coordinate 
system in fig.13 to do like this: sign of the coordinate 
increments along axis Y ascertain the sampling direction, 
if positive, indicating that the Sect-Point next to P is PI' 
but not P1, the end with larger coordinate value in axis X 
(E,) is the starting point and the other (£3) is the ending; 
contrarily if negative, the end with smaller coordinate 
value in axis X (£5) is the starting. 
At last, coordinates of certain number of sampling points in 
each section have been calculated by sequence under uniform 
relationship (e.g. right-hand rule) between sampling direction 
and flow direction, all the preparations for elevation 
computation have been accomplished, now. 
Many interpolation methods have been widely applied in 
elevation computations in GIS, such as Weighted Average 
method, Multidimensional Function method, Finite-Element 
method, Least Square method and other improved methods 
(Andres Almansa, 2002; Prades-Nebot, 1998), however, “As 
proved by experiments, due to the instability of the terrain in 
reality, resolution and precision of the interpolation would 
mainly lie on the density and distribution of source sample 
points and whether we have taken the characteristics of the 
terrain into account, the interpolation methods adopted will not 
have dominant influences as for the same source data " (Wang 
Jiayao, 2001), at last, a Bi-Linear Multinomial Interpolation 
method, which has the advantages of simplicity, efficiency and 
convenience of solving the problems relating to the river 
boundary, has been picked out to do successive elevation 
computations for each sample points in the riverway, here is a 
brief introduction of its principle, as shown in fig.14. 
  
  
  
  
  
y^ 
rl... 4 
dr Plz yx 
df= d 
dr 
J |... ' 
cns s 
T THI vr 
  
- ; Pr 
Fig.14 bi-linear multinomial interpolation method 
Cn