BLOCK AND QUADTREE BASED SIMPLIFICATION IN TILED

BLOCKS TERRAIN ALGORITHMS

Ivo Leitão and Beatriz Carmo

Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Lisboa, Portugal

Keywords: Terrain Rendering Algorithms, Level-of-Detail, Spatial and Temporal Coherence.

Abstract: With the advent of modern graphic processors, rendering a complex terrain in real time was suddenly

possible. However the constant struggle between rendering quality and real time performance is still

demanding more that we can actually get. Terrains are a prime example of that, the sheer amount of

geometry and the constant need to achieve higher standards in image quality are always taking the graphical

processors to their limits. Level of detail techniques, are therefore very important in this area and were used

in multiple algorithms through the years. Tiled blocks are a category of terrain algorithms where the terrain

is partitioned into square patches that are tessellated at different resolutions. This paper describes and

compares two of the most common approaches used in the simplification process: block based

simplification, where the simplification is local to the block, and quadtree based simplification, which uses

the spatial partitioning principle of the quadtree to perform the simplification.

1 INTRODUCTION

Rendering terrain areas is an integral part of many

applications, ranging from the entertainment

industry to architectural visualizations, cartography

applications and military simulations. Unfortunately

it is still a difficult challenge, despite the ever

growing power of the graphical processors available

today. To cope with that, level of detail techniques

appeared as an essential tool in this area especially

for large terrains. Most of them were used in the

course of years in a number of algorithms that were

specially designed for the rendering of large terrains

at interactive frame rates. Two of the most

commonly used, especially by the game industry, are

the Geomipmapping (Boer, 2000) and the Chunked

LOD (Ulrich, 2002) algorithms. They belong to a

class of terrain algorithms commonly described as

Tiled Blocks, following the classification proposed

in (Lossaso, 2004). In these algorithms, the terrain is

partitioned into square patches that are tessellated at

different resolutions. In the Geomipmapping

algorithm the level of detail decreases by the

individual simplification of each block. In the

Chunked LOD algorithm the level of detail

decreases by the substitution of four blocks by one

that represents the same area. Our objective was to

analyze these two approaches, not by the specific

features of each individual algorithm but in more

general terms as two different simplification

techniques shared by other algorithms in the same

category. We called this two approaches block based

and quadtree based simplification and they will be

the focus of this paper.

This paper is organized as follows. In Section 2

we talk briefly about the evolution of terrain

rendering algorithms giving special emphasis to tiled

block approaches. In Section 3 the main concepts

beyond the two types of simplification are

explained. In Section 4 the common points in the

two simplification methods are highlighted and how

we unified them under a unique framework. In

Section 5 the role of the error metric in the

simplification process is described. In Section 6 are

discussed methods to correct cracks between

adjacent blocks with different levels of detail. In

Section 7 geomorphing is described as the method

used to correct the “popping” effect resulting from a

change of detail. In Section 8 the testing

environment and the particular features implemented

for each simplification algorithm are described. In

Section 9 results of the performed tests are presented

and in Section 10 we summarize the conclusions and

point out future work.

205

LeitÃ

co I. and Carmo B.

BLOCK AND QUADTREE BASED SIMPLIFICATION IN TILED BLOCKS TERRAIN ALGORITHMS.

DOI: 10.5220/0001797502050210

In Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2009), page

ISBN: 978-989-8111-67-8

2 RELATED WORK

Terrain rendering algorithms have a long history,

and a comprehensive overview of this subject is

beyond the scope of this paper. For a more detailed

presentation, we refer the reader to (Pajarola, 2007).

In the following we will briefly trace a temporal line

covering the most important algorithms and trends

with special emphasis on the tiled block techniques.

From a historical perspective the first algorithms

specially designed for the rendering of terrains

appeared in the late seventies, for example (Fowler,

1979). However it was only in the middle nineties,

when consumer hardware was already capable of

representing terrains in real time, that some of the

most important algorithms appeared. Approaches

like (Lindstrom, 96), (Duchaineau, 97) and (Rottger,

98) became very popular. For most of them the main

objective was to reach the perfect triangulation

reducing the number of triangles processed by the

graphic card but increasing the work on the CPU

side. However, with the appearance of powerful

graphical processors, reaching the perfect

triangulation stopped being the main objective. On

the contrary, sending big blocks of geometric data to

the GPU is now the dominating trend. This means

that the focus switched from the triangle to blocks of

geometry which became in this process the new

target of level of detail techniques. To deal with this

new reality new types of algorithms started to appear

mainly tiled block approaches that applied level of

detail techniques to blocks of geometry. Algorithms

like (Boer, 2000), (Ulrich, 2002), (Laurisen, 2005)

and (Vistnes, 2006) are only examples of approaches

that followed this new trend. The most recent

algorithms are taking this trend even further

offloading most of the work to the graphical

processor. They use concentric rings of detail that

work on a focal area using a windowed view of the

terrain. One of the main characteristics of this new

approach is the usage of vertex textures, a new

functionality of shader model 3.0. This functionality

enables the sampling of a texture in the vertex

shader. This is particularly useful for terrain

rendering, since it enables the storage of the

elevation values in a texture which can be used in

the vertex shader to displace the vertices.

Algorithms like (Asirvatham, 2005) (Clasen, 2006)

and (Pangerl, 2008) are good examples of this.

3 SIMPLIFICATION METHODS

To comprehend the differences between block based

simplification and quadtree based simplification we

have to understand precisely what happens in each

one of the methods. For that, we will use a top view

representation of a recursive walk on a quadtree in a

33x33 terrain with a 5x5 block, like the ones

depicted in Figure 1. In this figure the triangle

represents the frustum and the tessellated squares

correspond to the blocks that are contained or

intersected by the frustum. In Figure 1 a) all the

blocks are at maximum resolution (5x5), so it

represents the typical brute force approach to terrain

rendering. Decreasing the resolution, i.e., level of

detail of the blocks, is the purpose of block and

quadtree based simplification. Block size is critical

in these methods because the number of levels

needed to represent the terrain in the quadtree is

based on it.

Figure 1: Simplification methods.

Let us start with block based simplification. This

kind of simplification is depicted in Figure 1 b). In

this method an error metric is used to determine the

most appropriate level of detail for each block, so

the simplification is completely independent from

the one applied to the other blocks. Therefore it is

common to have neighbouring blocks with different

levels of detail. Moreover, the number of vertices

changes according to the detail level but the size of

the block is constant, so the number of draw calls

issued in this method only depends on the number of

blocks that intersect or are contained in the frustum.

With quadtree based simplification like the one

depicted in Figure 1 c), the size of the block can

change but the number of vertices in each block is

constant. This kind of simplification uses the spatial

partitioning principle of the quadtree to determine

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206

the most appropriate block size. More precisely an

error metric is used on the recursive walk made on

the quadtree to decide the most appropriate block

size for each region of the terrain. Higher levels of

the quadtree represent larger areas of the terrain with

lower detail. Lower levels of the quadtree represent

smaller areas of the terrain with greater detail. This

works recursively from the root node of the quadtree

to the leaf nodes where the underlying resolution of

the terrain is matched. In this method the number of

draw calls depends not only on the point of view but

also on the error metric. Also, a block can have

neighbours with different sizes, making any possible

correlation between blocks difficult to achieve.

4 UNIFYING THE APPROACHES

Making a comparison between these two approaches

will be surely flawed if they are seen as completely

different. The common point here is the underlying

spatial partitioning structure, the quadtree. With that

in mind we can differentiate the two methods by

assuming that each one represents a different way of

making the recursive walk on the quadtree. With a

block based simplification scheme the quadtree is

used only to identify the visible blocks, i.e. blocks

that are intersected or are contained in the frustum.

No level of detail is calculated at this stage and all

these blocks are at the same level in the quadtree as

they have the same block size. Therefore one

possible optimization is to stop the recursion sooner,

when we reach a node that is completely contained

in the frustum even if the resolution of that node

does not match the desired block size. For example,

if the first quadrant of the first level of the quadtree

is completely contained in the frustum, we can stop

the recursion for that branch adding all the blocks of

the desired block size that are contained in this

larger block. Finally for each one of these blocks we

have to choose the most appropriate level of detail

basing our decision on the error metric. With

quadtree based simplification the main difference

lies on the recursion which can stop sooner because

the level of detail evaluation is done for each node

of the quadtree so it is possible to choose larger

blocks and render them. These larger blocks have

the same number of vertices but the space between

those vertices is greater.

To unify this approaches even further we take

advantage of a very useful property in a regular grid

triangulation: every block can be described by a

scale and a translation factor. To make this property

useful we have to separate the elevation values from

the geometric description of the block. This is

achieved with two vertex streams. A vertex stream is

essentially an array of vertex component data. For

instance it is possible to assemble vertices from

several vertex streams, where each stream consists

of a component of the vertex (e.g., one stream

contains position info, another contains colour info,

another texture coordinate info, etc.). In our

approach the first stream contains the position of the

vertices and the second stream contains the elevation

values. Since we use canonical values for the

position of the vertices this vertex data is valid for

all the blocks of the terrain. Later when rendering,

we transform the canonical values in the vertex

shader to obtain the correct position of the block.

For that we only need a couple of uniform shader

parameters, in this case, the scale and the translation

associated with each block.

The main advantage of a multi-stream approach

is that it enables us to use vertex textures in

machines that support shader model 3.0. In this case,

the memory requirements are reduced since we only

need one stream with the geometric description of

the block because the elevation data is stored on a

texture. Without vertex textures we need to send the

elevation values in a second stream.

To connect the vertices in a block we need a list

of indices, however this list is different in each

method. With quadtree based simplification we only

need to describe a block since in this method the

geometrical structure of the block does not change,

only the area that it occupies. With block based

simplification we need to represent all the possible

levels of detail of a block. For example if we have a

5x5 block, like the one used in the previous figures,

we need to represent a 5x5, a 3x3 and 2x2 block.

This is done with different sequences of indices each

one representing one of the aforementioned levels of

detail.

5 ERROR METRIC

The error metric has a very important role to fulfil in

tiled block algorithms as it is used to decide when

the transition to lower/higher detail levels happens.

With block based simplification it is used to control

the level of detail of the block, i.e., when a

higher/lower detailed version of the block should be

used to represent the associated region on the terrain.

With quadtree based simplification it is used to

decide the number of blocks that should represent a

region of the terrain, more precisely when a block

can be substituted by its four more detailed children

BLOCK AND QUADTREE BASED SIMPLIFICATION IN TILED BLOCKS TERRAIN ALGORITHMS

207

or the other way around, to decide when four blocks

can be substituted by its less detailed parent.

The error metric used in the two algorithms is the

one presented in the Geomipmapping algorithm

(Boer, 2000), which uses block based simplification.

This error metric can be easily adapted, as described

in (Laurisen, 2005), to a quadtree based

simplification. It involves the calculation of a

constant C in a pre-processing stage and of a

minimum distance D, for each level of detail n.

The constant C is calculated with Equation 1,

where n is the near clipping plane, t the top

coordinate of the near clipping plane, τ the error

threshold in pixels and Vres the vertical resolution in

pixels

The D for each level of detail n is calculated

with Equation 2, where δ is the geometric error and

C the constant calculated with Equation 1.

(1)

(2)

6 SPATIAL COHERENCE

The appearance of cracks between neighbouring

blocks with different levels of detail is a common

problem in tiled block approaches like the ones

described in this paper. There are several ways to

correct this problem but most of them are far from

ideal as they have a very noticeable impact in

performance. The fastest methods are the ones that

do not imply changes to the list of vertices or to the

list of indices committed to the graphical processor.

Adding vertical skirts around each block is a

solution that meets this objective. This method was

first introduced in (Ulrich, 2002) and is represented

in Figure 2 a). However, we should select carefully

the skirt size since it can have big impact in the fill

rate. It should be big enough to cover any possible

cracks that can appear between the tile and the

neighbouring tiles but not greater than that.

Note that, for optimal performance the skirts

have to be drawn in the same call as the block so the

vertices and the indices should be arranged to make

that possible. This technique can be used with block

or quadtree based simplification. However this

method does not correct the geometry, in fact the

difference of height between adjacent tiles is only

hidden by the skirts. Another technique that can be

used to correct the cracks is to change the

connectivity (or indexing) of the vertices at the edge

of the block. This was originally suggested in (Boer,

2000) and is exemplified in Figure 2 b) for block

based simplification where the tile with the higher

level of detail adapts its borders to the level of detail

of its neighbour(s). This technique implies changes

to the list of indices at runtime and therefore it is not

completely static, quite the contrary of skirts.

Figure 2: Crack correction methods.

Unfortunately it cannot be used with quadtree

based simplification, since adjacent blocks can

change in size. This means that a block can have

triangles bigger than its neighbours. For example, it

can happen that a triangle spans two or more

neighbouring blocks. In these cases any change in

the index connectivity of the neighbours will not

correct the problem.

7 TEMPORAL COHERENCE

Another important problem with tiled blocks and

with level of detail algorithms in general is the so

called “popping” effect. This is the result of a

sudden change of detail (to more or less detail)

which can originate a very noticeable effect. This is

caused by the appearing or disappearing of vertices

which cause a sudden “pop” in the geometry that is

very unnatural and contributes negatively to the

level of realism that we are trying to achieve. The

most common way of handling this problem is with

geomorphing (Luebke, 2003). The objective is to

slowly morph the vertices from one level of detail to

another. This can either be done over time or based

on the error. The latter is the best approach since in

this way the morphing only occurs when the

viewpoint is moving which helps hide the swirling

artefacts that it can cause. Concerning the

simplification methods discussed in this paper there

is no noticeable differences between the two

approaches since what we really need to know when

moving between levels of detail is which vertices

disappear and the error that results from that. This is

what is normally needed to perform the

geomorphing. Therefore all we need to do is to store

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208

that information in the list of elevation values since

it changes with each elevation value. This raises a

problem when we use vertex textures to displace the

vertices in the vertex shader since in that situation

we do not have a list elevation values, but only one

texture. The solution is to use another texture to

store for each vertex the level where it disappears

and the resulting error.

The morphing itself is executed on the vertex

shader. Since we receive all the necessary data this

is normally very fast and therefore it should be used

whenever possible as it can help increase the realism

significantly.

8 TESTING FRAMEWORK

We have developed a framework in XNA which

unifies under the same architecture the most relevant

characteristics of tiled blocks algorithms. With this

framework we have implemented the two

simplification methods and a brute force approach

where we did not make any simplification. The

results of brute force algorithm are used as baseline

performance values. We have also implemented

frustum culling which uses the quadtree to test each

block against the frustum as was already mentioned

in Section 4. To reach meaningful results it was

equally important to use the same error metric in the

simplification methods. Geomipmapping (Boer,

2000) error metric was adopted as explained in

section 5. To correct the cracks we have used the

skirt and the index update methods described in

Section 6 and to correct the “popping” effect we

have implemented geomorphing using the

approaches described in (Boer, 2000) and (Laurisen,

2005) for each one of the simplification methods.

Concerning the lightning we used per-pixel

lightning also known as normal mapping (Kilgard,

2000). Finally for the texturing of the terrain we

have used one colour texture.

9 RESULTS

The tests were performed on three computers: a

laptop with a Mobile Intel 945 GM graphical card,

which we called N1, a laptop with a ATI Mobility

Radeon 9700, which we called N2, and a desktop

with a NVIDIA GeForce 7950 GX2 graphical card,

which we called D1. These setups represent two low

end systems with a graphical card that support

shader model 2.0 and a high-end system with a

graphical card that supports shader model 3.0. Two

procedurally generated terrains were used in the

tests: a 1025x1025 terrain, called Terrace, and a

2049x2049 terrain, called Highland.

To gather the performance results we have pre-

recorded a 60 seconds walk on each terrain at

relatively low altitude.

The results obtained using two streams, vertices

and elevation values, are summarized in Table 1

where it is possible to compare the average frames

per second obtained in each terrain. For each

machine we have measured the performance of the

brute force approach and of the two simplification

methods discussed in this paper. We have

considered three different block sizes, 17x17, 33x33

and 65x65 and two types of crack correction

methods: index update and skirts. We have used a

maximum error of 8 pixels.

The quadtree simplification method in

conjunction with skirts was the fastest approach in

two of the three machines considered. This was

expected as the number of draw calls is much lower

in this method. The only exception was the N2

machine where block based simplification was

faster. On the N1 machine, the slowest, it makes in

fact the difference between a working real time

representation of the terrain with a frame rate above

the 60 frames per second and a slow representation

almost unusable and is therefore an obvious choice.

The fastest block size was 17x17 with the exception

of machine N2 where the fastest block size was

33x33. However, on that machine the fastest

simplification method was also different and the two

simplification methods analyzed use different ways

of reducing the detail.

Concerning the crack correction methods used in

block based simplification, in almost every situation

the index update method was slower. In fact it had a

tremendous impact in the performance mainly in

machines N2 e D1. As we have already mentioned

in Section 7, index update implies changes in the list

of indices at runtime and this results confirm that it

can cause a significant frame rate drop.

We have also tested the performance with vertex

textures this time only on the D1 machine since it is

the only that supports shader model 3.0. The results

are summarized in Table 2.

If we compare the results in Table 2 with the

results obtained for the same machine in Table 1 we

can see that using vertex textures is slower. This was

expected since this behaviour was already observed

by other authors, for example it is mentioned in

(Asirvatham, 2005), (Clasen, 2006) and on (Pangerl,

2008). However with vertex textures the fastest

method was block based simplification which shows

that sampling a vertex texture with quadtree based

simplification is somewhat slower than with block

based simplification.

BLOCK AND QUADTREE BASED SIMPLIFICATION IN TILED BLOCKS TERRAIN ALGORITHMS

209

Table 1: Average frames per second.

Brute

Force

Block

(Index Update)

Block

(Skirts)

Quadtree

(Skirts)

Terrace

17x17

52 52 49 126

N1 33x33

43 55 55 99

65x65

26 59 65 45

17x17

107 86 223 211

N2 33x33

102 146

229 180

65x65

92 143 176 139

17x17

606 190 532 1336

D1 33x33

567 328 1302 1051

65x65

514 357 1070 791

Highland

17x17

14 14 13 75

N1 33x33

13 17 17 51

65x65

7 22 25 24

17x17

38 23 74 159

N2 33x33

37 51

174 129

65x65

33 72 131 95

17x17

149 44 121 919

D1 33x33

188 101 498 690

65x65

177 127 785 511

Table 2: Average frames per second with vertex textures.

Brute

Force

Block

(Index Update)

Block

(Skirts)

Quadtree

(Skirts)

Terrace

17x17

384 217 602 742

D1 33x33

256 347

834 329

65x65

216 348 436 252

Highland

17x17

105 52 131 464

D1 33x33

75 112

480 217

65x65

66 125 356 136

10 CONCLUSIONS

We analyzed two of the most common simplification

methods used in tiled block approaches to terrain

rendering. We have discussed algorithms and

techniques to keep temporal and spatial coherence,

respectively, geomorphing and skirts or index

update. We have come to the conclusion that

quadtree based approaches are the best option in

most of the situations, mainly when the terrain is

very large and/or the machine is slow. In these cases

the reduction of the draw calls has a very noticeable

impact in terms of performance.

We have also concluded that skirts are the best

approach to handle the cracks. The other method

implies changes to the list of indices at runtime and

affected performance significantly.

In the future we plan to analyze the impact of

occlusion culling techniques on the performance of

each simplification method and also to pursue new

approaches to the correction of cracks mainly the

generation of all the possible combinations between

a level of detail of a tile and its neighbour’s level of

detail in block based simplification. We are also

planning support out-of-core data to cope with

terrains with sizes beyond the available memory.

ACKNOWLEDGEMENTS

This work was partially supported by LabMAg

through FCT Multiannual Funding Programme.

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