HYBRID TERRAIN VISUALIZATION BASED ON LOCAL

TESSELLATIONS

E. G. Paredes

, C. Lema

, M. Amor

and M. B´oo

Dept. Electronic and Computer Eng., Univ. Santiago de Compostela, Santiago de Compostela, Spain

Dept. Electronics and Systems, Univ. Coru˜na, A Coru˜na, Spain

Dept. Electronic and Computer Eng., Univ. Santiago de Compostela, Santiago de Compostela, Spain

Keywords:

Hybrid terrain representation, Interactive visualization, Tessellation, Convexiﬁcation.

Abstract:

Hybrid terrain models represent an effective approach to combine geographic data with different acquisition

properties. Terrain models constituted by regular grid elevation data may locally integrate detailed TIN meshes

to represent morphologically complex terrain features and artiﬁcial objects. However, direct rendering of

hybrid terrain models poses additional difﬁculties: holes and geometric discontinuities between the borders of

the different parts would appear in the images. In this paper we present two new software based proposals for

efﬁcient hybrid terrain visualization. Both proposals generate high-quality geometrically continuous models

and support multiresolution methods over regular grids.

1 INTRODUCTION

Interactive visualization of large Digital Terrain Mod-

els (DTM) is an important challenge in the ﬁeld of

computer graphics. Due to the increasing utilization

of applications that use 3D geographic models on a

large scale –such as Geographic Information Systems

(GIS), cartography, urban planning, virtual reality and

computer games– in recent years, differentmethods to

optimize the process of visualization have been suc-

cessfully developed (VTerrain, 2008). Most of the op-

timization techniques are based on employing several

representations of the original model with different

Level Of Detail (LOD) (Luebke et al., 2002).

An interesting situation arises when one base rep-

resentation of the terrain exists together with another,

in a different type of representation, for areas requir-

ing a ﬁner sampling, such as topographicallycomplex

terrain features and artiﬁcial man-made microstruc-

tures. This permits the enhancement of existing reg-

ular terrains by adding details to speciﬁc regions of

interest without having to increase the overall resolu-

tion or having to convert the whole terrain model into

a ﬁner and irregular representation. Microstructures

integrated in grid-based terrain models also improve

the graphical and perceptual quality of visualized ter-

rain models, since they provide a more precise and

adequate geometry, shading, and illumination of mor-

phologically important terrain features (typically af-

fecting less than 20% of the complete terrain surface).

Proposals analyzing the problem of directly rep-

resenting hybrid terrain models have recently ap-

peared. An adaptive tessellation procedure to con-

nect both meshes is suggested in (Dykes et al., 2005)

to avoid discontinuities in the junction between rep-

resentations. However, no speciﬁc tessellation algo-

rithms were proposed in these works. Based on this

idea, a technique for interactive visualization of hy-

brid meshes was presented in (B´oo et al., 2007; Amor

and B´oo, 2008). The main characteristic of this Hy-

brid Meshing (HM) algorithm is that an efﬁcient LOD

level independent scheme is used for representing the

local adaptive triangulation between mesh borders.

In this paper we present two software oriented al-

gorithms for the visualization of hybrid terrains. Our

proposals, inspired in the hardware oriented algorithm

developed in (B´oo et al., 2007; Amor and B´oo, 2008),

are based on the generation of the additional required

triangles following a cell-based strategy. Speciﬁcally,

we have employed two algorithms to generate those

triangles. The ﬁrst one computes local tessellations

using the incremental randomized triangulation algo-

rithm for triangulating polygons (Seidel, 1991). The

second one adapts the HM algorithm to a software im-

Paredes E., Lema C., Amor M. and Bóo M. (2009).

HYBRID TERRAIN VISUALIZATION BASED ON LOCAL TESSELLATIONS.

In Proceedings of the Four th International Conference on Computer Graphics Theory and Applications, pages 64-69

DOI: 10.5220/0001768200640069

 SciTePress

(a) (b)

Figure 1: Hybrid terrain model. (a) Grid (b) Grid with tex-

ture (c) Hybrid model (d) Hybrid model with texture.

plementation. A performanceevaluation of our exper-

imental implementation of both methods and a com-

parison between them is presented here.

2 HYBRID REPRESENTATION

OF TERRAIN MESHES

Digital Terrain Models are represented in different

ways depending on several factors such as the nature

of the capturing technology, input data, or applica-

tion domain. Digital Elevation Model (DEM) (Lue-

bke et al., 2002) is a simple and widely employed

representation method that stores a collection of regu-

larly spaced elevation samples of the terrain surface in

a gridded 3D mesh. An alternative data model for ter-

rain representation is the Triangulated Irregular Net-

works (TIN) (Luebke et al., 2002). TIN meshes ap-

proximate the terrain by a set of non-overlappingcon-

tiguous triangles, generated by connecting a ﬁnite set

of irregularly spaced sampled data points.

Hybrid representation of terrain meshes integrates

information from different data models, usually from

DEM and TIN. These hybrid models act as a memory-

efﬁcient approach for detailing terrains with complex

topographic structures. But, as data points are usually

provided from different measuring systems, a method

to connect the data is required to avoid discontinuities

in the junction of the meshes.

When real-time visualization is needed, multires-

olution techniques are often used. However, includ-

ing multiresolution in hybrid terrains implies that the

connections between DEM and TIN models would

depend on the LOD. Due to this dependence, pre-

computingand transmitting LOD-dependent informa-

tion would not be optimal. The solution presented

in (Yang et al., 2005) is based on the generation of

a preprocessed mesh combining both representations.

Speciﬁcally, the Delanuay triangulation of square tiles

of the grid is performed according to the TIN infor-

mation. The main disadvantage of this method is the

implied modiﬁcation of the original data.

We present in this paper a software oriented solu-

tion based on the local tessellation of the grid cells.

Our proposal consists in generating additional trian-

gles to join the models, following the strategy devel-

oped on (B´oo et al., 2007; Amor and B´oo, 2008). This

strategy leads to the generation of high quality mod-

els, as it avoids any modiﬁcation of the original data.

Figure 1 shows an example of application. The ﬁrst

two subﬁgures present a grid and the enriched ver-

sion with a texture. The last subﬁgures are based on

the hybrid model representation. Note that the higher

quality of the image is associated with the utilization

of a detailed TIN model of the crater.

The ﬁnal hybrid model is formed by the union of

the grid and TIN in a single, coherent mesh. The gen-

eration is performed as follows: ﬁrst, the entire TIN

and non covered cells of the grid (NC cells) are di-

rectly rendered; next, completely covered grid cells

(CC cells) are eliminated, as they will be replaced by

the more detailed TIN data; ﬁnally, those grid cells

partially covered (PC cells) by the TIN have to be

adaptive tessellated. This local tessellation strategy

was selected due to its simplicity and the relatively

easy adaptation for use in conjunction with LOD sys-

tems. An interesting consequence of joining models

through a local, cell-based strategy is that high quality

triangulations are generated.

In this paper we work with two tessellation algo-

rithms, based on the incremental randomized triangu-

lation algorithm (Seidel, 1991) and a software imple-

mentation of the HM strategy suggested in (B´oo et al.,

2007; Amor and B´oo, 2008).

3 PROPOSAL BASED ON THE

INCREMENTAL RANDOMIZED

TRIANGULATION METHOD

Our ﬁrst proposal is based on the identiﬁcation of the

non covered part of each PC cell and the utilization

of a standard polygon triangulation algorithm to con-

nect the TIN and grid models. The ﬁrst step is the

HYBRID TERRAIN VISUALIZATION BASED ON LOCAL TESSELLATIONS

TIN

Figure 2: Corner tessellation example.

identiﬁcation of the polygon made by the non-covered

grid cell corners and the vertices of the TIN bound-

ary falling into this cell. As shown in the example

of Figure 2, the identiﬁcation is performed on the XY

projection of the meshes. In this example the polygon

to be tessellated is made by the cell corners c

, c

and the TIN boundary vertices v

− v

. Note that to

assure a cell-based tessellation the intersection ver-

tices between TIN boundary and cell edges have to

be included. In the example represented in Figure 2,

vertices v

and v

were included for that purpose.

In the second step of the algorithm, the objective

is to perform a fast triangulation locally for each PC

cell. As the vertices of the grid in the cell may be

different in each LOD, the tessellation is performed

after extracting the level of detail selected by the mul-

tiresolution model. Consequently, the triangulations

are LOD dependent and have to be completely recal-

culated every frame.

We have selected for our implementation, among

all polygon tessellation methods, the Incremental

Randomized Triangulation algorithm (Seidel, 1991).

This algorithm has been widely implemented due to

its simplicity and efﬁciency. Good results in terms of

quality are obtained following this cell-based strategy

as will be shown in Section 5.

4 PROPOSAL BASED ON THE

HYBRID MESHING METHOD

The HM algorithm was presented in (B´oo et al., 2007;

Amor and B´oo, 2008) as a hardware oriented method

to achievehigh performanceand good quality in inter-

active visualization of hybrid terrains. The algorithm

generates an efﬁcient LOD level independent repre-

sentation which is used for the adaptive triangulation

of every PC cell of the model.

The HM algorithm has two main cores: the local

convexiﬁcation of the TIN and the adaptive tessella-

tion of the resulting convex structure. The convexiﬁ-

cation of the TIN can be performed as a preprocessing

step and the corresponding information efﬁciently en-

coded. As this information can be precomputed and

encoded, the triangles associated with this step can be

generated in run-time by simple decoding operations.

On the other hand, the ﬁnal tessellation to be executed

in run-time is very simple, due to the convex structure

of the TIN. This will achieve good results in terms of

execution time for this algorithm.

4.1 Triangulation between Tin and Grid

using Convex Tin Structures

During the rendering process, the grid cells partially

covered by a TIN mesh are connected with TIN

boundary vertices. Assuming that the TIN boundary

has been previously convexiﬁed, the method works

generating triangles that connect uncovered cell cor-

ners of the grid with consecutive TIN vertices while

the introduced triangle does not overlap with the TIN.

The shift in the grid corner employed is easily de-

tected by evaluating the angles between the corner

and consecutive vertices of the TIN, which is efﬁ-

ciently implemented by testing the sign of the cross

product of consecutive edges in the TIN boundary.

Consider the example shown in Figure 2 where

a partially covered (PC) cell and the corresponding

convex TIN silhouette are depicted. TIN boundary

vertices (v

, v

) and the cell corners uncov-

ered by the TIN (c

, c

) are assumed to be pro-

cessed in a clockwise order. The HM algorithm acts

by connecting the list of corners with the list of ver-

tices following a sequential order. This way, c

cor-

ner is consecutively connected with the vertices of the

boundary where possible. In this example corner c

connected with vertices v

, v

and v

, but not with

because the new triangle (c

, v

) would overlap

with the TIN. Therefore, corner c

is then selected and

connected with v

and with v

4.2 Incremental Convexiﬁcation

As the triangulation process requires a properly con-

vexiﬁed TIN boundary to work without ﬂaws, a con-

vexiﬁcation process for the TIN boundary is locally

performed in each cell. The resulting convexiﬁed

boundary is efﬁciently stored, for all different con-

vexiﬁcation levels, in a simple and lightweight data

structure.

The convexiﬁcation inside each cell has three

steps: compute the convex hull of the TIN boundary

GRAPP 2009 - International Conference on Computer Graphics Theory and Applications

(a) (b) (c)

Figure 3: Four cells of a grid with the TIN silhouette. (a) Before convexiﬁcation (b) Finest LOD level convexiﬁcation (c)

Coarser level convexiﬁcation.

in the cell, identify concave cavities on the boundary

and, ﬁnally, triangulate those cavities. Following this

cell-based strategy and to assure a local tessellation, it

is assumed that there is a vertex in every intersection

point between the TIN boundary and the cell borders.

In the ﬁrst step the convexiﬁcation is performed

for the ﬁnest grid resolution level. Figure 3(a) shows

four cells corresponding to the ﬁnest resolution level

of the grid and the corresponding TIN silhouette cov-

ering this area. The TIN is depicted in grey, the TIN

boundary is explicitly marked and vertices on it are

indicated with circles. The local convexiﬁcation re-

sults are indicated in Figure 3(b). Local convex hulls

are delimited by vertices {0, 1, 3, 4} (up-right cell),

{4, 12} (up-left cell) and {12, 13, 15, 16} (down-left

cell). Once the convex hull for each cell is deter-

mined, the triangles inside the caves are generated us-

ing any standard tessellation algorithm.

After computing the convex hull for all cells in

the ﬁnest level of detail, the following coarser level is

processed following an incremental strategy and the

triangles generated in previous convexiﬁcations are

preserved. Following the previous example of Fig-

ure 3(a), the next coarser level of detail is analyzed

in Figure 3(c). In this ﬁgure, the new convexiﬁcation

triangles are shown and, with a different colour, the

ones generated in previous steps. The new local con-

vex hull is determined by vertices {0, 1, 15, 16}. The

procedure continues for each cell and each level of the

grid until the coarsest level is processed.

4.3 Hybrid Model Representation

As has been shown previously, the key point of the

HM algorithm for achievinggood performanceresults

is the compact and efﬁcient representation of the con-

vexiﬁed boundary information of the TIN. The sim-

plicity of the tessellation procedure is directly related

to this representation as well. As a result, and given

a LOD, the corresponding triangles can be extracted

from this representation in run-time by means of very

simple decoding operations.

Together with this information, two additional

lists are used to directly identify the cells and the ver-

tices implied in the tessellation: the Grid Classiﬁca-

tion list and the Vertex Classiﬁcation list. The ﬁrst

one permits the identiﬁcation of the cells to be di-

rectly rendered and the cells to be tessellated. The

second one indicates the TIN Boundary (TB) vertices

to be employed in the local tessellation for each cell.

In the following we summarize only the representa-

tion to encode the convexiﬁcation triangles. A com-

plete description of the representation can be found in

(B´oo et al., 2007; Amor and B´oo, 2008).

To encode the convexiﬁcation triangles the list of

TB vertices together with some additional connectiv-

ity information is employed. Assuming that the TB is

stored following a clockwise ring structure, the con-

nectivity associated to each vertex indicates the dis-

tance (number of vertices) between that vertex and the

most distant one in the ring connected to it. This way,

if connectivity of vertex v

is j, it means that the far-

thest vertex connected to it is v

+ j. Let us consider

the example described in Figure 3(c) to illustrate this

storing strategy. In that example the TB array is:

TB = {0(1), 1(14), 2(1), 3(10), 4(9), 5(6), 6(1),

7(2), 8(1), 9(1), 10(1), 11(1), 12(1), 13(2),

14(1), 15(1), 16(1)}

where the connectivity value of each vertex is indi-

cated within brackets. For example, vertex 4, with a

connectivity value of 9, is connected with vertex 13

and all the vertices between them that are not inside a

nested cavity. In this case, connectivity values show

two nested cavities: between 5 and 11 and between 7

and 9. The algorithm assumes a sequential connection

of the starting vertex of a cavity to all the vertices in-

side it, but this connecting structure is broken if nested

HYBRID TERRAIN VISUALIZATION BASED ON LOCAL TESSELLATIONS

Table 1: Size and complexity of the test scenes.

Grid cells TIN triangles

Scene 1 400 3144

Scene 2 400 1563

Scene 3 1089 9872

Scene 4 5445 49360

Table 2: Performance results obtained with both proposals.

Triangles Inc. triang. HM based

generated based proposal proposal

Scene 1 186 442 fps 1356 fps

Scene 2 158 523 fps 1776 fps

Scene 3 444 308 fps 753 fps

Scene 4 2220 46 fps 132 fps

caves exist. For this example, vertex 4 is connected to

all vertices between 5 and 13, but not inside a nested

cavity, that is: {6, 7, 9, 10, 11}, and so on.

As explained in (B´oo et al., 2007; Amor and B´oo,

2008) the connectivity values generated for the coars-

est LOD can be employed for any other LOD, and

this uniﬁed representation may be employed for the

reconstruction of the convexiﬁcation triangles associ-

ated with different levels of detail.

5 EXPERIMENTAL RESULTS

We have tested our two strategies employing a hy-

brid terrain visualization software that includes the

two tessellation algorithms.

Test computer hardware is a Intel Core 2 Duo

E6600 with 2 GB of RAM and a GeForce 8800GT

512 MB. We have used four different scenes in our

testing. The ﬁrst three of them are formed by a regu-

lar grid partially covered by a TIN patch. The last one

is a synthetic model consisting of ﬁve copies of the

meshes present in scene 3. The number of grid cells

and TIN triangles of each scene is shown in Table 1.

The main results obtained with the two proposals

are summarized in Table 2. The number of triangles

generated to connect the differentrepresentation mod-

els (second column) is the same for the two methods.

This is coherent with the fact that the polygons to be

triangulated are the same for any method.

As is shown in the table, the HM based proposal

(fourth column) clearly outperforms the one based on

incremental randomized triangulation (third column).

HM method is, in the worst scenery, 2.44 times faster,

and it reaches the maximum difference in Scene 1,

where it is 3.40 times faster. This is a direct conse-

quence of using the preprocessed connectivity infor-

mation of the TIN boundary in the HM algorithm, to

generate the adaptive tessellation during run-time. As

the method based on the incremental randomized tri-

angulation does not perform any preprocessing of the

meshes, the tessellation is computed directly from the

selected vertices of the boundaries for each grid cell.

Table 3: Average compactness value of the triangles ob-

tained with both proposals.

Inc. triang. HM based

based proposal proposal

Scene 1 0,53 0,49

Scene 2 0,53 0,47

Scene 3 0,49 0,49

With respect to the quality of the triangulation,

high quality models can be generated with both meth-

ods. An example of application is shown in Figure 4.

These are the resulting models when a detailed TIN

is applied to the scenes 1, 2 and 3. For both algo-

rithms the meshes are softly joined and the connec-

tions are performed locally to each cell. The triangles

generated are small and all the holes and cracks in the

borders are eliminated. Despite the fact that the tri-

angles generated with both methods are different, in

terms of visual quality they are in fact quite similar.

This fact is also shown in Table 3, where the average

compactness values obtained for the two methods are

presented. The compactness value (Gueziec, 1995) is

an indication of the triangles shape, usually employed

as a measure of quality, being zero for a degenerated

triangle and one for an equilateral triangle. As shown

in the table, triangulations obtained with both algo-

rithms are very similar. However, the high quality

results obtained in terms of speed with the HM al-

gorithm make it a better solution for hybrid terrain

rendering.

6 CONCLUSIONS

In this paper we have presented two different solu-

tions to the interactive visualization of hybrid terrain

meshes. Both methods are based on a process of

adaptive local tessellation between the boundaries of

a multiresolution grid model and a detailed TIN mesh.

Our ﬁrst proposal is based on a standard polygon tri-

angulation algorithm (Seidel, 1991) and represents a

simple and direct approach to the problem: it con-

nects the models by performing a triangulation be-

tween the grid cell corners and the TIN boundary ver-

tices. The second proposal is based on the hardware

oriented HM algorithm (B´oo et al., 2007; Amor and

GRAPP 2009 - International Conference on Computer Graphics Theory and Applications

(a) (b) (c)

(d) (e) (f)

Figure 4: Adaptive tessellations generated by both proposals. Subﬁgures (a), (b) and (c) are generated by the proposal based

on the incremental randomized triangulation. Subﬁgures (c), (d) and (e) are generated by HM based proposal.

B´oo, 2008), adapted to a software implementation.

The results of our tests indicate that both methods

can obtain high quality meshes, without holes or any

other triangulation artifact, in real-time. In terms of

performance, however, HM based method runs sev-

eral times better than standard polygon triangulation

strategy. This important difference is caused by the

efﬁciently encoded, uniﬁed representation of the con-

vexiﬁcation information in the TIN boundary for the

HM algorithm. This means that part of the triangles

are precomputed and decoded in run-time with simple

operations. Additionally, the remaining triangles are

generated through a straightforward procedure.

ACKNOWLEDGEMENTS

This work was partially supported by the Ministry

of Science and Technology of Spain under contract

TIN 2007-67537-C03, the Ministry of Education and

Science of Spain under the contract MEC TIN2004-

07797-C02, Xunta de Galicia under the contracts

08TIC0011206PR and Programa de consolidaci

on y

estructuraci

on de unidades de investigaci

on compe-

titivas, and also supported by the High Performance

Computing Galician Thematic Network (G-HPC).

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HYBRID TERRAIN VISUALIZATION BASED ON LOCAL TESSELLATIONS