ISPRS, Vol.34, Part 2W2, "Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
Starting from the primal invalid TIN, all the invalid TIN can be
traced by the following procedures:
Stepl: Initial set {InvalidTIN} with the primal invalid TIN as its
only member.
Step2: Initial set {InvalidTINEdge} with the edges of primal
invalid TIN.
Step3: Delete one edge E from the set {InvalidTINEdge}.
Step4: Find the triangle T baS e that is non-planer and shares E,
if exists, take the vertex V base that has different
elevation value as the base point for regeneration of
TIN.
Step5: Find the triangle T that is planer, shares E and doest
not belong to the set {InvalidTIN}
Step6: It 7 exists, add it to the set {InvalidTIN}
Step7: Repeat step 3 until {InvalidTINEdge} becomes empty.
2.3 Generation of new break-lines
This phase generate new break-lines to disable formation of
most of flat TINs. According to the shapes of the boundaries
formed by flat TINs, we prepare two approaches for generation
new break-lines. The two approaches correspond to simple
shape and complex shape respectively. When all the edges on
the boundary are visible from the centroid of the shape, it is
called a simple shape. Shapes that do not satisfy the above
conditions are called complex shape. The procedures for
generating new break-lines are as follows:
(1) Boundary generation
Sort the vertices of the flat TINs in their connection order to
obtain the boundary of the flat TIN area. The vertex V baS e
belonging to the non-flat TIN obtained in 2.2 is included as the
starting point of the boundary.
(2) New break-line for simple shapes
A new break-line for a simple shape is generated in the following
procedures:
Stepl: find the furthest point Vf Ur1h estfrom centroid C
Step2: calculate the horizontal distant D1 (from C to V (urt h e st)
and D2 (from C to V base ) respectively
Step3: let Z=Z base +(Z-Z)*D2/(D1+D2) be the height value of
centroid C
Step4: Add the line segment Uase-centrow as new break-line
Fig.2 shows an example of simple shape and the derived new
break-line.
Fig.2 Asimple shape and the new break line
A new break-line for a complex shape is generated in the
following procedures:
Stepl Starting from T base , trace the connection tree of the flat
TINs, which will have only two branches wherever
exist
Step2. Starting from V base , connect the middle point of shared
edges to form a path tree, which will have only two
branches wherever exist. The terminal point will be the
common vertex shared by the two line segments
belonging to the same contour line.
Step3. Calculate the height value of each branch node
recursively. The height value of the first branch node is
calculated by the same method as 2.2, with D2 being
the distance from the node to the furthest terminal
point in the tree. The rest will be calculated with the
first node as starting point.
Step 4: Calculate the height values of each intermediate
vertex of a branch. The height value a vertex is
determine by the proportion of it length to starting
vertex against the total length.
Step 5: Add each branch as new break-lines.
Fig.3 shows an example of complex shape and the derived
new break-lines.
Fig.3 complex shape and the new break lines
2.4 Partial reconstruction of TIN
After generating new break-lines, we will generate the TIN once
more with the new break-lines as added constrains. The new TIN
set will not have any flat TIN area of complex shape, but there
might still be flat triangles of simple shape.
If there is any flat TIN area, we will then trace them by the same
method stated in 2.2 to form flat TIN area. Then reconstruct the
flat TIN area in the following procedures:
Stepl: Delete all the invalid triangles from the TIN result
Step2: Sort all vertexes {V} of the invalid triangles by the
connection order on the contour line.
Step3: Form new triangles of V base and Vi,V K i of {V}
(1=1....N-1; where N is the number of elements in {V})
Fig.4 shows an example of reconstructed TIN.
(3) New break-line for complex shapes
