remote sensing
Article
Integration of Constructive Solid Geometry and
Boundary Representation (CSG-BRep) for 3D
Modeling of Underground Cable Wells from
Point Clouds
Ming Huang, Xueyu Wu, Xianglei Liu *, Tianhang Meng and Peiyuan Zhu
Engineering Research Center of Representative Building and Architectural Heritage Database, The Ministry of
Education, Key Laboratory for Urban Geomatics of National Administration of Surveying, Mapping and
Geoinformation, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
huangming@bucea.edu.cn (M.H.); 2108521518037@stu.bucea.edu.cn (X.W.);
2108521518012@stu.bucea.edu.cn (T.M.); 2108521516023@stu.bucea.edu.cn (P.Z.)
* Correspondence: liuxianglei@bucea.edu.cn; Tel.: +86-10-6120-9335
Received: 26 March 2020; Accepted: 29 April 2020; Published: 4 May 2020
Abstract: The preference of three-dimensional representation of underground cable wells from
two-dimensional symbols is a developing trend, and three-dimensional (3D) point cloud data
is widely used due to its high precision. In this study, we utilize the characteristics of 3D
terrestrial lidar point cloud data to build a CSG-BRep 3D model of underground cable wells,
whose spatial topological relationship is fully considered. In order to simplify the modeling process,
first, point cloud simplification is performed; then, the point cloud main axis is extracted by OBB
bounding box, and lastly the point cloud orientation correction is realized by quaternion rotation.
Furthermore, employing the adaptive method, the top point cloud is extracted, and it is projected for
boundary extraction. Thereupon, utilizing the boundary information, we design the 3D cable well
model. Finally, the cable well component model is generated by scanning the original point cloud.
The experiments demonstrate that, along with the algorithm being fast, the proposed model is effective
at displaying the 3D information of the actual cable wells and meets the current production demands.
Keywords: point cloud data; CSG-BRep model; spatial topology relationship; cable well; underground
cable; self-adaptive boundary extraction
1. Introduction
Underground cable wells, which are an essential component of urban infrastructure and the
bedrock of urban functions, constitute the “lifeline” to ensure the smooth operation of cities [1,2].
Therefore, underground cable wells information has evolved into an indispensable component
for present-day urban construction and a fundamental resource for urban decision-making [3].
Underground cable wells information management systems that have been established in major
cities around the world will ensure effective management and comprehensive utilization of existing
underground cable wells. However, due to the wide variety of available underground cable wells,
the diverse cable wells are widely distributed and intertwined with complex topological relations
within the urban underground space. The two-dimensional management method is inadequate at
accurately reflecting the spatial positional relationship between the cable wells. The representation
scheme of underground cable wells has been gradually upgraded from traditional two-dimensional
symbols to the three-dimensional [4,5]. Therefore, universally establishing a three-dimensional (3D)
model of underground cable wells and developing a 3D cable wells information system has evolved
Remote Sens. 2020, 12, 1452; doi:10.3390/rs12091452
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into a crucial element of cable wells survey [6]. Research into 3D modeling of underground cable wells
is imperative, as it is an essential component of any underground cable wells information system.
According to the different data source, it can be divided into two categories for 3D modeling.
One is based on traditional two-dimensional data, with the help of existing tools or commercial
software, to realize the human interactive 3D modeling and visualization, the other is surface modeling
based on the 3D terrestrial lidar point cloud. Transcoding is a procedure to make use of large productive
geospatial databases: a process of turning raw geospatial data, which are mostly two-dimensional,
into 3D models suitable for standard rendering engines. Therefore, transcoding is the most common
method to establish a 3D pipeline segment model, per the existing pipeline geospatial database [7].
Schall et al. [7,8] developed the Vidente system, using transcoding and augmented reality technology,
which superimposed the underground water supply cable wells model into practical usage for field
construction and detection. In cases of incomplete cable wells 3D spatial data, a ground-penetrating
radar is often used to detect the underground cable wells, determine its position, orientation, and
depth, in order to build the 3D modeling of the cable wells segment. Talmaki et al. [9], Tabarro et al. [10]
and Dutta et al. [11] researched and developed applications for the use of ground-penetrating radar
in underground cable wells. The modeling method based on human interaction mainly using FME,
AutoCAD, ArcGIS and other mature data conversion tools or commercial software to complete manual
modeling. Jun et al. [12] proposed a modeling method of underground cable wells network using
BIM technology to generate Brep [13] models of underground cable wells, adopting Revit software
for cable wells modeling and visualization, with the belief that mature software usage contributes to
enhanced results. Guoqiang et al. [14] proposed a rapid modeling method of the cable wells database
using Autodesk Map, in order to quickly generate and peruse a model of the underground cable
wells. Lingyan et al. [2] used the 3D module of AutoCAD to simplify the model of pipe points and
cable wells segments, and performed 3D rapid modeling of underground cable wells. Based on the
spatial database engine and ArcGIS Engine components, Wang Shu et al. [3] built a constructive solid
geometry (CSG) [15] 3D model of cable wells and actualized 3D visualization. The abovementioned
modeling methods predominantly use existing software for manual modeling. Although these 3D
models of underground cable wells are accurate, due to the inefficient consumption of manpower and
material resources, it is prohibitive to build models of large-scale underground cable wells.
For underground facility modeling based on lidar point cloud, Vanneschi et al. [16] used 3D
laser scanning technology to collect the data and generated the ordinary triangular mesh model of
a quarry in Italy. Zlot et al. [17] used 3D laser scanning technology for mobile scanning and built
the models of two caves in Australia. Russell [18] conducted photogrammetry using an UAV to
collect the data from inaccessible stopes in underground mines, and successfully constructed the
stope model from the captured images. Grehl et al. [19] successfully developed a 3D texture model
of the interior of a mine by collecting data of underground mines using a stereo camera mounted on
a mobile robot. Estellers et al. [20], Fridovich-Keil et al. [21] and Odille et al. [22] used point cloud
data for 3D refinement modeling. Rico and Jürgen [23] presented a concept of the implementation of
a system infrastructure that was capable of integrating, analyzing, and visualizing 3D point clouds.
An important approach that attributed 3D point clouds with semantic information (e.g., object class
category information) was presented, which enables more effective data processing, analysis, and
visualization. Stephan et al. [24] introduced a new city modeling approach based on rich point
clouds, and presented a new paradigm included four key elements in 3D city modeling. Although the
abovementioned modeling methods are able to model the underground facilities automatically, they are
frequently affected by data quality. Moreover, the models constructed by the abovementioned methods
are one of the CSG model, the ordinary triangular mesh model and the BRep model, which have
certain limitations and are inadequate in meeting the actual production requirements. The CSG model
can express the basic geometric elements that constitute the entity [15], but it cannot effectively record
the boundaries and vertices information of model. The ordinary triangular mesh model is simple to
model, but is contains a large amount of data. It is not only difficult to split, but also lacks topological
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simple to model, but is contains a large amount of data. It is not only difficult to split, but also lacks
relationship relationship
information. The
BRep model
good for
calculating
the for
geometric
characteristics
of the
topological
information.
Theis BRep
model
is good
calculating
the geometric
model [13], andofisthe
easy
to connect
withisthe
surface
modeling
butmodeling
its largest software,
modeling but
unitits
is
characteristics
model
[13], and
easy
to connect
withsoftware,
the surface
surface modeling
instead of unit
object.
It lacks instead
the expression
of the
basicthe
components
model
is incapable
largest
is surface
of object.
It lacks
expressionofofthe
the
basicand
components
of
of taking
topological
relationshipthe
between
various
components.
Constructive
the
modelinto
andconsideration
is incapable ofthe
taking
into consideration
topological
relationship
between
various
solid geometryConstructive
and boundary
representation
(CSG-BRep)
model
can record topological
relationship
of
components.
solid
geometry and
boundary
representation
(CSG-BRep)
model can
3D model
in detail relationship
[25].
record
topological
of 3D model in detail [25].
proposes
a 3Damodeling
algorithm
for underground
cable wellscable
considering
Therefore, this
thisstudy
study
proposes
3D modeling
algorithm
for underground
wells
considering
spatialThe
topology.
The algorithm
fully capitalizes
on the advantages
point
cloud
data
spatial topology.
algorithm
fully capitalizes
on the advantages
of point of
cloud
data
[26–29],
[26–29],
and the
generates
the model expeditiously
through
cloud data
preprocessing
and
and generates
model expeditiously
through point cloud
datapoint
preprocessing
and boundary
extraction.
boundary
extraction.
Additionally,
study
cablethrough
well component
model through
Additionally,
this study
constructs thethis
cable
wellconstructs
componentthe
model
real-time scanning
of point
real-time
scanning
of point
cloud data,
while fullyrelationship
consideringbetween
the topological
relationship
between
cloud data,
while fully
considering
the topological
the models
and displaying
the
the
models andof
displaying
the 3D
information
the actual
cableproduction
wells in order
to meet
the real-life
3D information
the actual cable
wells
in order toofmeet
the real-life
needs.
The contributions
production
contributions
of this paper
arepoint
as follows:
(1) for large-scale
discrete
point
of this paperneeds.
are asThe
follows:
(1) for large-scale
discrete
cloud geometric
modeling,
an adaptive
cloud
geometric
modeling,
an geometric
adaptive parameters
extraction of
boundarytocontour
geometric
parameters
is
extraction
of boundary
contour
is proposed
construct
3D models
of wells and
proposed
construct3D
3Dtopological
models of wells
cables.
(2)topological
CSG-Brep 3D
topological
model
with spatial
cables. (2)to
CSG-Brep
modeland
with
spatial
relation
expression
between
wells
topological
expression between wells and cable is established.
and cable isrelation
established.
2. Methods
Methods
2.
In view
view of
of the
the lack
lack of
of spatial
relationship in
in the
the existing
existing 3D
3D point
automatic
In
spatial topological
topological relationship
point cloud
cloud automatic
modeling, this
a modeling
method
of underground
cablecable
wells wells
considering
the spatial
modeling,
thispaper
paperproposed
proposed
a modeling
method
of underground
considering
the
topological
relationship.
(1)
After
the
point
cloud
denoising
and
simplification,
the
main
axis
of
the
spatial topological relationship. (1) After the point cloud denoising and simplification, the main axis
point
cloud
is
determined
by
calculating
the
Oriented
Bounding
Box
(OBB)
of
the
well.
Combined
with
of the point cloud is determined by calculating the Oriented Bounding Box (OBB) of the well.
quaternion transformation,
3D model of wells
constructed
adaptively
extractingby
theadaptively
geometric
Combined
with quaternionthetransformation,
theis3D
model ofbywells
is constructed
parameters
of
the
boundary
contour.
(2)
Using
the
L1
median
method
and
hermit
interpolation
extracting the geometric parameters of the boundary contour. (2) Using the L1 median method and
to obtain
the cable passing
points,
thenpassing
Sweep points,
methodthen
is used
to realize
3D modeling
cable.
hermit
interpolation
to obtain
the cable
Sweep
methodthe
is used
to realizeofthe
3D
(3) According
to the(3)spatial
relationship
between
cable and between
wells, thecable
CSG-BRep
topological
model
modeling
of cable.
According
to the spatial
relationship
and wells,
the CSG-BRep
is established.
topological
model is established.
2.1. Introduction
Introduction and
and Classification
Classification of
of Underground
Underground Cable
Cable Wells
Wells
2.1.
Underground cable
are an
part of underground
cable wells.cable
Globally,
underground
Underground
cablewells
wells
areimportant
an important
part of underground
wells.
Globally,
cable
wells
are
generally
constructed
with
prefabricated
large
concrete
boxes
or
on-site
poured
underground cable wells are generally constructed with prefabricated large concrete boxes orconcrete,
on-site
as
illustrated
in
Figure
1.
Typically,
underground
power
cable
wells
are
divided
into
four
types
[30]:
poured concrete, as illustrated in Figure 1. Typically, underground power cable wells are divided
straight-through
type,
three-way
type,
four-way
type
and
corner
type.
Based
on
real-life
engineering
into four types [30]: straight-through type, three-way type, four-way type and corner type. Based on
needs, power
cable wells
further
divided
into
different
models
meet varied
needs.
Figure
real-life
engineering
needs,are
power
cable
wells are
further
divided
into to
different
models
to meet
varied2
illustrates
several
representative
well
types.
While
different
cable
wells
have
disparate
design
standards,
needs. Figure 2 illustrates several representative well types. While different cable wells have
they can all
be classified
by the
type
tensile
body. Therefore,
by extracting
cableTherefore,
well contour
disparate
design
standards,
they
canofall
be classified
by the type
of tensilethe
body.
by
from
the
point
cloud,
an
overall
model
can
be
constructed.
extracting the cable well contour from the point cloud, an overall model can be constructed.
Figure 1.
1. Underground
Underground cable
cable wells.
wells.
Figure
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(a)
(b)
(c)
(d)
Figure 2. Types of underground cable wells. (a) Straight-through, (b) Three-way, (c) Four-way,
Figure 2. Types of underground cable wells. (a) Straight-through, (b) Three-way, (c) Four-way, and
and (d) Corner.
(d) Corner.
2.2. Modeling Method of Underground Cable Wells
2.2. Modeling Method of Underground Cable Wells
The 3D modeling of underground cable wells is divided into cable well model construction and
The 3D modeling
of model
underground
cable wells
is divided into
cable
model
construction
and
well chamber
component
construction.
The construction
process
of well
the cable
well
model includes
well
chamber component
model
construction.
The
process ofthe
theplanar
cable point
well model
preprocessing
the point cloud
data,
determining
theconstruction
main axis, extracting
cloud,
includes
preprocessing
the
point
cloud
data,
determining
the
main
axis,
extracting
the
planar
point
extracting the boundary, and constructing triangular patches. Based on the spatial characteristics of
the
cloud,
extracting
the
boundary,
and
constructing
triangular
patches.
Based
on
the
spatial
underground cable wells and the element characteristics of the cable wells body, the abovementioned
characteristics
of theaunderground
cable
wells
andwell.
the element
characteristics
of the
cable
method establishes
true 3D model
of the
cable
Considering
the quality
of the
3Dwells
laserbody,
scan
the
abovementioned
method
establishes
a
true
3D
model
of
the
cable
well.
Considering
the
quality
data, firstly, it is necessary to implement adaptive de-noising on large-scale point cloud data
and
of
the
3D
laser
scan
data,
firstly,
it
is
necessary
to
implement
adaptive
de-noising
on
large-scale
point
administer simplifications, while retaining the morphological features of the point cloud model.
cloud
data and administer
simplifications,
while enable
retaining
morphological
features
of the
point
The characteristics
of various
3D entity objects
thethe
quick
extraction of
boundary
contour
cloud
model.
The
characteristics
of
various
3D
entity
objects
enable
the
quick
extraction
of
boundary
information and geometric parameter information from the point cloud data, to construct a 3D model
contour
information
and
geometric
parameter
information
frompipe
the point
cloud data,
to cable
construct
a
of the cable
well. Well
chamber
component
modeling
includes
hole modeling
and
wells
3D
model
of
the
cable
well.
Well
chamber
component
modeling
includes
pipe
hole
modeling
and
modeling. In the pipe hole modeling process, first, the circular hole center of the surface point cloud is
cable
wellsand
modeling.
the pipe hole
modelingbetween
process,the
first,
the circular
hole
centeris of
the surface
extracted,
then theIntopological
intersection
cylinder
and the
surface
performed
to
point
is extracted,
andInthen
topological
intersection
between
the cylinder
and the is
surface
is
obtaincloud
the pipe
hole model.
the the
cable
wells modeling
process,
firstly Hermit
interpolation
directly
performed
to
obtain
the
pipe
hole
model.
In
the
cable
wells
modeling
process,
firstly
Hermit
used to obtain the cable wells path points for cable wells that are difficult to be segmented, while L1
interpolation
tothe
obtain
cablefor
wells
wells
that are difficult
to
median valueisisdirectly
used to used
obtain
paththe
points
the path
pointpoints
cloud for
thatcable
can be
segmented.
And then,
be
segmented,
while
L1
median
value
is
used
to
obtain
the
path
points
for
the
point
cloud
that
can
the cable wells radius is identified to generate the cross-section circle at the starting point of the cable
be
segmented.
And
then, method
the cableofwells
radius is identified
to generate
the cross-section
circle at the
wells.
Finally, the
Sweep
the interpolation
points and
the cross-section
circle generates
the
starting
point
of
the
cable
wells.
Finally,
the
Sweep
method
of
the
interpolation
points
and
the
crosssmooth cable wells. The specific process is illustrated in Figure 3:
section circle generates the smooth cable wells. The specific process is illustrated in Figure 3:
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Original Point Cloud
Percentage
Determine Three Axial
Directions by PCA
Quaternion
Rotation
Moving Mesh Dividing
Determine Main Axis
Self-adapt
Self-adaptation
Re-determine Main Axis
Extract Top & Bottom
Point Cloud
No
Construct Triangular
Patches
No
Find the Edge with Only
One Adjacent Triangle
Parameterize
Complete Plane Point
Cloud
Construct the
Triangulation Net
Incomplete Plane Point
Cloud
Main Body Model
Rotate the Point Cloud to
xoy plane
Separate Top & Bottom
Boundary Points
Construct Model
Yes
Extract Boundary Points
Model Is Consistent with
the Actual Point Cloud
Plane Fitting of
Point Cloud
There Is a
Wellbore Boundary
Project the Top
Point Cloud
Yes
Component Model
The Pipe Hole Model
The Cable Model
Final Model
Flowchart of
of the
the underground cable well modeling algorithm.
Figure 3. Flowchart
2.3. Construction of the Underground Cable Well Model
2.3.
Construction of the Underground Cable Well Model
2.3.1. Simplification of the Point Cloud
2.3.1. Simplification of the Point Cloud
As the point cloud data obtained by scanning contains considerable redundancy, using the original
As the point cloud data obtained by scanning contains considerable redundancy, using the
point cloud for modeling will consume a significant amount of time and resources. Therefore, the point
original point cloud for modeling will consume a significant amount of time and resources. Therefore,
cloud data must be simplified and filtered before it is utilized in modeling. The original methods of
the point cloud data must be simplified and filtered before it is utilized in modeling. The original
point cloud data simplification and filter are primarily based on the principles of distance, curvature and
methods of point cloud data simplification and filter are primarily based on the principles of distance,
normal direction, etc. However, current point cloud simplification methods principally focus on
curvature and normal direction, etc. However, current point cloud simplification methods principally
the following methods: bounding box method, geometric image simplification method, curvature
focus on the following methods: bounding box method, geometric image simplification method,
simplification method, and normal precision simplification method. The bounding box method refers
curvature simplification method, and normal precision simplification method. The bounding box
to grouping the point cloud into the small cubes divided by the smallest bounding box, and only the
method refers to grouping the point cloud into the small cubes divided by the smallest bounding box,
points close to the center of each small cube are retained [31]. For the geometric image simplification
and only the points close to the center of each small cube are retained [31]. For the geometric image
method, point cloud is converted into raster image, and point cloud reduction is realized by the graphic
simplification method, point cloud is converted into raster image, and point cloud reduction is
processing method [32]. For the curvature simplification method, it obtains reference data of local
realized by the graphic processing method [32]. For the curvature simplification method, it obtains
profile of point cloud by establishing a spatial index. The free-form surface is used to approximate to
reference data of local profile of point cloud by establishing a spatial index. The free-form surface is
the data and estimate the curvature of the data, and the point cloud data is simplified according to the
used to approximate to the data and estimate the curvature of the data, and the point cloud data is
curvature distribution [33–36]. Normal precision simplification method is an improvement method of
simplified according to the curvature distribution [33–36]. Normal precision simplification method
curvature simplification method, which refers to the point product of two normal vectors of adjacent
is an improvement method of curvature simplification method, which refers to the point product of
local surfaces to replace the curvature of local surfaces [37].
two normal vectors of adjacent local surfaces to replace the curvature of local surfaces [37].
In view of the aforementioned analysis and summary of the existing algorithms, this study
In view of the aforementioned analysis and summary of the existing algorithms, this study
adopts a point cloud simplification filtering algorithm using movable mesh generation. The algorithm
adopts a point cloud simplification filtering algorithm using movable mesh generation. The
primarily simplifies the point cloud through a spatial mesh, which has an obvious advantage of speed in
algorithm primarily simplifies the point cloud through a spatial mesh, which has an obvious
advantage of speed in processing, and is able to achieve the required effect. Additionally, the
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processing, and is able to achieve the required effect. Additionally, the simplification criterion of twice
moving mesh divisions is capable of incorporating the criterions of the abovementioned algorithms.
2.3.2. Determination of the Main Axis by Calculating the OBB Bounding Box
Three directions can be obtained by using the OBB bounding box [38]. Based on the length of
the side, the initial main axis direction of the geometric solid can be selected. This study uses the
OBB bounding box method to obtain axial directions and takes the direction of the longest side as
the initial main axis direction. The method is also referred to as principal component analysis (PCA).
The reference [39] enhances the above method by assigning different Gaussian weights to each point.
Thus, the influence of various distance points on the normal are varied, and the points closer to the
point have greater influence, generating a more realistic estimation result. In this study, the direction
with the wellbore is defined as the main axis direction of the cable well. In case the initial direction is
inconsistent with the main axis direction, either due to a subsequent wellbore boundary or in instances
when the model is consistent with the actual point cloud, the direction correction is conducted to
determine the final main axis direction.
Rotation by Quaternion
According to the obtained axial direction, it may be set to n = (a, b, c), unitize n, and calculate the
angle between n and the coordinate axis z by Formula (1).
cosθ = n · n1
(1)
where n1 = (0, 0, 1), and the symbol · represents the dot product of two vectors.
Based on the quaternion rotation method, only one rotation axis and one rotation angle are needed
to complete the arbitrary rotation in space (around any axis, rotating at any angle). Among them,
the rotation angle is θ, obtained from Formula (1), and the rotation axis can be solved by Formula (2).
dir = n × n1
(2)
where n and n1 are the same as Formula (1), and the symbol × represents the cross product of two
vectors. The result is a vector and will unitize dir as well. The rotation process is completed according
to the quaternion rotation Formula (3) [40].
P1 = uPu−1
(3)
θ
θ
+ dirsin
(4)
2
2
θ
θ
µ−1 = cos − dirsin
(5)
2
2
where P represents any point in the original point cloud to be rotated, and P1 represents the
corresponding point after rotation according to the quaternion This formula can complete the conversion
process from P to P1 , so that the original point cloud stands in the Z-axis direction.
Using the quaternion rotation method above, the rotation axis of the rotating body is rotated to
the Z-axis direction, and the corresponding rotation matrix is calculated. Then, the point cloud data is
multiplied by the rotation matrix, respectively, so the rotating body stands upright in 3D space along
the rotation axis direction.
µ = cos
Extraction of the Cable Well Top Point Cloud
In this study, the top point cloud extraction is performed by the adaptive method. The highest
point, zmax , and the lowest point, zmin , are obtained by calculating the maximum and minimum values
on the Z-axis of the rotated point cloud. Define the layering distance to 0.1 m, the point cloud was
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extracted
from
top to
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25
bottom, and the normal direction of the extracted plane
calculated in real-time until it is parallel to the main axis (it can be considered parallel if the angle
calculatedininreal-time
real-timeuntil
untilit itisisparallel
paralleltotothe
themain
mainaxis
axis(it(itcan
can beconsidered
consideredparallel
parallelif ifthe
theangle
angle
calculated
between them is less than
a certain degree).
As shown
in Figure be
4.
between
them
is
less
than
a
certain
degree).
As
shown
in
Figure
4.
between them is less than a certain degree). As shown in Figure 4.
Layering
Layering
Layering
Layering
(a)(a)
(b)
(b)
Figure
4.
Point
cloud
layering.
(a)
Perspective
view,
and
(b)
Front
view.
Figure
Point
cloud
layering.
Perspective
view,
and
(b)
Front
view.
Figure
4.4.
Point
cloud
layering.
(a)(a)
Perspective
view,
and
(b)
Front
view.
Asthe
thetop
topand
and
bottom
faces
of the
cable
well
are inclined,
or
not completely
flat 5a,
Figure
5a,
As
bottom
faces
the
cable
wellare
areinclined,
inclined,
notcompletely
completely
flatFigure
Figure
during
As
the top
and bottom
faces
ofofthe
cable
well
orornot
flat
5a, during
during
the
actual
production
process,
it
results
in
an
incomplete
separation
of
the
scanned
point
cloud
theactual
actualproduction
productionprocess,
process,it itresults
resultsininananincomplete
incompleteseparation
separationofofthe
thescanned
scannedpoint
pointcloud
cloudFigure
Figure
the
Figure
5b. Intoorder
tothe
satisfy
the set threshold,
the separated
pointiscloud
is shown
in 5c.
Figure
5c. study,
In this
5b.
In
order
satisfy
set
threshold,
the
separated
point
cloud
shown
in
Figure
In
this
5b. In order to satisfy the set threshold, the separated point cloud is shown in Figure 5c. In this study,
study,
the
top
point
cloud
is
extracted
by
plane
fitting
multiple
times.
thetop
toppoint
pointcloud
cloudisisextracted
extractedbybyplane
planefitting
fittingmultiple
multipletimes.
times.
the
(b)
(b)
(c)(c)
(a)(a)
Figure
Separation
the
top
point
cloud.
(a)Front
Front
view,
(b)Complete
Complete
top
point
cloud,
and(c)(c)
Figure
5.Separation
Separationof
ofofthe
top
point
cloud.
(a)(a)
Front
view,
(b) Complete
top point
cloud,
and
(c) Incomplete
Figure
5.5.
top
point
cloud.
view,
(b)
top
point
cloud,
and
Incomplete
top
point
cloud.
top point cloud.
Incomplete
top
point
cloud.
Thisstudy
study
performs
fitting
by by
RANSAC
algorithm
[41–44].
WhenWhen
parameters
are extracted,
This
studyperforms
performsplane
plane
fitting
byRANSAC
RANSAC
algorithm
[41–44].
Whenparameters
parameters
are
This
plane
fitting
algorithm
[41–44].
are
the
barycentric
coordinates
of
the
point
cloud
are
used
to
realize
the
plane
fitting
optimization.
As
extracted,
the
barycentric
coordinates
of
the
point
cloud
are
used
to
realize
the
plane
fitting
extracted, the barycentric coordinates of the point cloud are used to realize the plane fittingthe
separated top
point
cloud
maytop
have
a missing
part,
tohave
accomplish
plane
fitting,
the point
cloud
within
optimization.
As
theseparated
separated
toppoint
point
cloudmay
mayhave
missing
part,to
toaccomplish
accomplish
plane
fitting,
optimization.
As
the
cloud
a amissing
part,
plane
fitting,
a
certain
distance
threshold
from
the
plane
is
extracted
from
the
overall
point
cloud
based
on
the
fitting
the
point
cloud
within
a
certain
distance
threshold
from
the
plane
is
extracted
from
the
overall
point
the point cloud within a certain distance threshold from the plane is extracted from the overall point
parameters.
With
the
gradually
reduced
threshold,
multiple
iterations
are
performed
to
obtain
the
top
cloudbased
basedononthe
thefitting
fittingparameters.
parameters.With
Withthe
thegradually
graduallyreduced
reducedthreshold,
threshold,multiple
multipleiterations
iterationsare
are
cloud
point cloud
data
without
any
missing
parts,
and
the point
cloud
is projected
onto
fitting
plane.
performed
obtain
thetop
toppoint
pointcloud
cloud
data
without
any
missing
parts,and
andthe
thepoint
pointcloud
cloud
performed
toto
obtain
the
data
without
any
missing
parts,
isis
projected
onto
the
fitting
plane.
projected onto the fitting plane.
Extraction of the Boundary by Constructing the Triangulation Network
Extraction
theBoundary
Boundary
byConstructing
Constructing
theTriangulation
Triangulation
Network
Before
extracting
the by
boundary,
it is necessary
to establish
the topological relationship between
Extraction
ofofthe
the
Network
triangles,
edges,
and the
vertices.
Then,
thenecessary
recursivetomethod
isthe
conducted
to extract
the boundary.
Beforeextracting
extracting
boundary,
establishthe
topological
relationship
between
Before
the boundary,
it itisisnecessary
to establish
topological
relationship
between
Using
a
loop
process,
first,
identify
an
edge
with
only
one
adjacent
triangle
in
the
edge
set, and
the
triangles,
edges,
and
vertices.
Then,
the
recursive
method
is
conducted
to
extract
the
boundary.
Using
triangles, edges, and vertices. Then, the recursive method is conducted to extract the boundary. Using
two
endpoints
of
it
are
used
as
the
previous
and
current
point
of
the
polygon
boundary,
respectively.
loopprocess,
process,first,
first,identify
identifyananedge
edgewith
withonly
onlyone
oneadjacent
adjacenttriangle
triangleininthe
theedge
edgeset,
set,and
andthe
thetwo
two
a aloop
Then,
in
the
adjacent
triangles
of
the
current
point,
find
the
edge
with
just
one
adjacent
triangle
endpointsofofit itare
areused
usedasasthe
theprevious
previousand
andcurrent
currentpoint
pointofofthe
thepolygon
polygonboundary,
boundary,respectively.
respectively.
endpoints
Then,
in
the
adjacent
triangles
of
the
current
point,
find
the
edge
with
just
one
adjacent
triangleand
and
Then, in the adjacent triangles of the current point, find the edge with just one adjacent triangle
with
the
two
endpoints
that
have
one
and
only
one
point
that
coincides
with
the
current
point
or
the
with the two endpoints that have one and only one point that coincides with the current point or the
previouspoint.
point.The
Thenon-coincident
non-coincidentendpoint
endpointofofthe
theedge
edgeserves
servesasasthe
thenext
nextpoint
pointofofthe
thepolygon
polygon
previous
Remote Sens. 2020, 12, 1452
8 of 23
and with the two endpoints that have one and only one point that coincides with the current point
or the previous point. The non-coincident endpoint of the edge serves as the next point of the
polygon boundary, and consecutive points of the boundary are successively identified by the recursive
method. The boundary extraction is complete when the next point coincides with the first point of the
boundary [45]. Consequently, enter the next loop to extract the next boundary until all boundaries
have been extracted.
After extracting the boundary, this study uses the RANSAC algorithm for spatial circle fitting [46]
and extracts the wellhead parameters by setting the radius threshold. For peripheral boundary
points, this study adopts the straight-line fitting method to extract key points. As the extracted
boundary in this study is ordered, taking the starting point as the benchmark, in order to determine
key points, the straight-line parameters are obtained by performing straight-line fitting on adjacent
points respectively. Then, two key points are respectively fitted to determine if a curve or a straight
line is formed. Finally, the curve points are extracted while the straight-line points are deleted, in order
to establish the subsequent triangular patches.
Refining the Cable Well Model by Constructing Triangular Patches
Using the abovementioned method, the bottom face of the point cloud data is extracted, and the
plane fitting is performed on it. The parameters are used to calculate the distances between the two
planes. Based on the top face boundary line, the projection of the top face boundary points to the bottom
face is identified. Triangular patches are constructed, depending upon the boundary information and
the height of the model, to conduct refined modeling to fit the point cloud data. To identify boundary
points of the top wellhead, this study uses the spatial circle fitting method based on RANSAC to extract
the center and radius of the well borehole. Consequently, along with the overall boundary points,
the triangular patches are generated to complete the construction of the cable well model.
2.4. Construction of the Underground Cable Wells Component Model
2.4.1. Construction of the Cable Well Pipe Hole Model
The pipe hole of the cable well is the foundation of the cable connection. In this study, the plane
separation of the point cloud and the model is carried out based on the original point cloud data and
the generated model parameters. The boundary line to fit the pipe hole center is extracted for the
separated point cloud plane, after its rotation and projection.
As the separated plane by the actual point cloud is an arbitrary plane in space, it is rotated to the
xoy plane by the Rodrigues’ rotation matrix. Let the initial normal of the space plane be n = (nx , n y , nz ),
and after rotation the normal is n0 = (0, 0, 1), so the rotation angle θ is
n · n0
θ = arccos
|n||n0 |
!
(6)
Then, the rotation axis ω(ωx , ω y , ωz ) is
ω = n × n0
The rotation matrix is

cos θ + ωx 2 (1 − cosθ)


Rω (θ) =  ωz sinθ + ωx ω y (1 − cosθ)

−ω y sinθ + ωx ωz (1 − cosθ)
ωx ω y (1 − cosθ) − ωz sinθ
cosθ + ω y 2 (1 − cosθ)
ωx sinθ + ω y ωz (1 − cosθ)
(7)
ω y sinθ + ωx ωz (1 − cosθ)
−ωx sinθ + ω y ωz (1 − cosθ)
cosθ + ωz 2 (1 − cosθ)



 (8)


After the point cloud rotation, the projection of the point cloud to the xoy plane is conducted,
and then the boundary line extraction is carried out. The RANSAC method is also applied to perform
Remote Sens. 2020, 12, 1452
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the spatial circle fitting of all extracted boundary lines. By setting the circle radius threshold, the pipe
Remote
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PEERflow
REVIEW
9 of 25
hole
center
is extracted.
is shown in Figure 6.
(a)
(b)
(d)
(c)
Figure 6. Pipe hole model generation. (a) Projected point cloud, (b) extracted boundary lines and pipe
Figure 6. Pipe hole model generation. (a) Projected point cloud, (b) extracted boundary lines and pipe
hole centers, (c) constructed triangular patches, and (d) generated pipe hole model.
hole centers, (c) constructed triangular patches, and (d) generated pipe hole model.
Distinct errors remain between the actual obtained center point and the actual model surface.
Distinct errors remain between the actual obtained center point and the actual model surface.
The ray projection method is used to obtain the projection point of the center of the circle on the wall
The ray projection method is used to obtain the projection point of the center of the circle on the wall
triangulation network. Taking the projection point as the reference, the 3D model cutting algorithm
triangulation network. Taking the projection point as the reference, the 3D model cutting algorithm is
is used to perform topological shearing on the wall triangulation network of the cable well to
used to perform topological shearing on the wall triangulation network of the cable well to complete
complete the secondary cutting of the model. Currently, there are certain inconsistencies in the
the secondary cutting of the model. Currently, there are certain inconsistencies in the existing 3D
existing 3D model cutting methods. In instances of complex target entities, such as curved surface
model cutting methods. In instances of complex target entities, such as curved surface walls which are
walls which are cut to obtain doors, windows or pipe holes, cutting errors occur. The algorithm is
cut to obtain doors, windows or pipe holes, cutting errors occur. The algorithm is modified to achieve
modified to achieve a stable topological shearing suitable for architectural expression by the
a stable topological shearing suitable for architectural expression by the application of a combination
application of a combination of OpenCASCADE and Cork in model cutting. Try to merge the top
of OpenCASCADE and Cork in model cutting. Try to merge the top triangulation network cutting
triangulation network cutting method [47] to solve the cutting problems of the complex triangulation
method [47] to solve the cutting problems of the complex triangulation network of the unclosed surface,
network of the unclosed surface, the non-manifold edge and the self-intersecting. Finally, the pipe
the non-manifold edge and the self-intersecting. Finally, the pipe hole model is generated.
hole model is generated.
2.4.2. Construction of the Cable
2.4.2. Construction of the Cable
While the cable is an essential component of the underground cable well, a direct cable connection
While
cable
is an
essential component
of inevitably
the underground
cable
a directof cable
between
pipethe
holes
is not
aesthetically
pleasing and
results in
the well,
intersection
the
connection
between
pipe
holes
is
not
aesthetically
pleasing
and
inevitably
results
in
the
intersection
cable models. Therefore, in this study, in order to optimize the cable model, the cubic Hermite
of the cable models.
Therefore,
this to
study,
in order
to optimize the
cablepath
model,
the cubic Hermite
interpolation
[48] of two
nodes isinused
achieve
the interpolation
of cable
points.
interpolation
of model
two nodes
is used to achieve
the interpolation
of cable
points.
Before the[48]
cable
is constructed,
the starting
and ending point
of path
the cable
are chosen by
Before
the
cable
model
is
constructed,
the
starting
and
ending
point
of
the
cable are
chosen
by
3D interaction. As the starting and ending position of the cable are located on the planes
of the
cable
3D
interaction.
As
the
starting
and
ending
position
of
the
cable
are
located
on
the
planes
of
the
cable
model, the normals, na = (nx , n y , nz ) and nb = (nx , n y , nz ), of the planes, where the cable starting point
𝑛𝑎 = (𝑛
𝑛𝑧 ) and
, 𝑛 ), of the planes, where the cable starting
𝑥 , 𝑛𝑦 , point
pamodel,
= (xa , the
ya , znormals,
ending
pb =𝑛𝑏(x=b , (𝑛
yb𝑥, z, 𝑛
a ) and the cable
b )𝑦are𝑧 located, can be obtained. Let dir = na × nb ,
point
𝑝
=
(𝑥
,
𝑦
,
𝑧
)
and
the
cable
ending
point
𝑝
=
(𝑥𝑏 , 𝑦𝑏The
, 𝑧𝑏 )resultant
are located,
can beisobtained.
Let
𝑎 ×
𝑎 represents
𝑎
where the𝑎 symbol
the cross product of two𝑏 vectors.
dir, which
the normal
𝑛𝑎 ×where
𝑛𝑏 , where
the symbol
represents
cross product
of The
twoGaussian
vectors. plane
The resultant
𝑑𝑖𝑟,
of𝑑𝑖𝑟
the=plane
the curve
lies, is a vector
and canthe
be unitized
as well.
rectangular
which
is
the
normal
of
the
plane
where
the
curve
lies,
is
a
vector
and
can
be
unitized
as
well.
The
coordinate system x0 0 y0 is constructed based on the plane, whose coordinate origin is the midpoint of
Gaussian
plane rectangular coordinate system 𝑥00 𝑦0 is constructed based on the plane, whose
the
pa , pb connection.
coordinate origin is the midpoint of the 𝑝𝑎 , 𝑝𝑏 connection.
Let dis represent the distance between pa and pb . After the conversion, the coordinates of
𝑝𝑎 and 𝑝𝑏 are 𝑝′ 𝑎 = (−𝑑𝑖𝑠/2,0,0) and 𝑝′ 𝑏 = (𝑑𝑖𝑠/2,0,0) . Set the rotation matrix to
translation vector to t (t x , t y ,t z ) , then
𝑝′ 𝑎 = 𝑅 ⋅ 𝑝𝑎 + 𝑡
R
and the
(9)
Remote Sens. 2020, 12, 1452
10 of 23
Let dis represent the distance between pa and pb . After the conversion, the coordinates of pa and
pb are p0 a = (−dis/2, 0, 0) and p0 b = (dis/2, 0, 0). Set the rotation matrix to R and the translation vector
to t(tx , t y , tz ), then
p0 a = R · pa + t
(9)
p0 b = R · pb + t
pc =
pa + pb
+ dir
2
p0 c = (0, 0, 1)
(10)
(11)
(12)
The rotation matrix R can be solved inversely according to the relationship between the three
corresponding points [49].
Let the center of the point set p be C and the center of the point set p0 be C0 . Get barycentric
coordinates of the point cloud by
pci = pi − C
(13)
p0 ci = p0 i − C0
(14)
and calculate the matrix H by
H=
n
X
pci p0 ci
(15)
i=0
Finally, perform the singular value decomposition (SVD) on the matrix H, that is,
H=U
X
VT
(16)
where the 3×3 rotation matrix R is
R = VUT
(17)
t = C − RC0
(18)
and the translation vector t(tx , t y , tz ) is
Let dirx = (1, 0, 0), dir y = (0, 1, 0), n0 a = (nx , n y , nz ) and n0 b = (nx , n y , nz ). Then the slope of point
a in the Gaussian plane rectangular coordinate system is
ka =
and for point b, the slope is
kb =
R · n0 a · dir y
R · n0 a · dirx
R · n0 b · dir y
R · n0 b · dirx
(19)
(20)
The interpolation function is not only required to have the same value as the function at the node,
but also required to have the same first-order, second-order and even higher-order derivative values
as the function at the node, which is the Hermite interpolation problem. In this study, the Hermite
interpolation with equal function values and first-order derivative values to the interpolation function
at the node is used, in order to optimize the cable curve by achieving the interpolation of the curved
cable path points. The interpolation process is shown in Figure 7.
In the instances of the cable well with spare parts, the L1 median skeleton line extraction method is
used to extract the cable well central axis and the cable well point cloud is segmented by preprocessing.
The local L1 median can be expressed by the below optimized formula [50]:
arg m minx
XX
i∈I j∈J
kxi − q j kθ(kxi − q j k) + R(X)
(21)
Remote Sens. 2020, 12, 1452
n o
where Q = q j
j∈J
11 of 23
∈ R3 is the input point cloud data, X = {xi }i∈I ∈ R3 is the point set randomly sampled
from Q, and the points number I<<J. R(X) is a regular term. In order to avoid the local gathering
center phenomenon caused by the use of local L1 median, the constraint is added to deter the shrinking
Remote
Sens.gathering
2019, 11, x FOR PEER
REVIEW
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sample points
from
in the
center.
The plane
where the curve lies
(a)
The plane where the curve lies
(b)
(c)
Figure 7. Hermite curve interpolation. (a) The plane defined by the cable starting point a, ending point
Hermite
curve
interpolation.
(a) they
Theare
plane
defined
by the cable
starting point
a, ending point
b and the
normals
of the planes where
located,
(b) the Gaussian
plane rectangular
coordinate
system of
based
the plane
in thethey
global
dimensional
space
coordinateplane
system,
and (c) the coordinate
normals
theon
planes
where
arethree
located,
(b) the
Gaussian
rectangular
constructed Gaussian plane rectangular coordinate system.
Figure 7.
b and the
system based on the plane in the global three dimensional space coordinate system, and (c) the
constructed Gaussian
plane
coordinate
system.
In the instances
of rectangular
the cable well with
spare parts,
the L1 median skeleton line extraction method
is used to extract the cable well central axis and the cable well point cloud is segmented by
preprocessing.
The local L1
median
can be expressed
by the sample
below optimized
formula
[50]:
The steps
of the algorithm
are
as follows:
randomly
a group
of sample
points from the
original point cloud data as the initial
center
points;
compare
the
distance
of
the
point
in
the point cloud
𝑎𝑟𝑔 𝑚 𝑚𝑖𝑛𝑥 ∑ ∑‖𝑥𝑖 − 𝑞𝑗 ‖ 𝜃(‖𝑥𝑖 − 𝑞𝑗 ‖) + 𝑅(𝑋)
(21)
𝑖∈𝐼 𝑗∈𝐽
to each center point, and divide all the points
into the nearest category to form the initial classification;
3
whereis𝑄calculated
= {𝑞𝑗 }𝑗∈𝐽 ∈ 𝑅by
isL1,
the and
inputthe
point
cloud data, 𝑋
= {𝑥𝑖median
}𝑖∈𝐼 ∈ 𝑅3 ispoint
the point
set randomly
the local median
established
local
is taken
as the new central
sampled from 𝑄, and the points number I<<J. 𝑅(𝑋) is a regular term. In order to avoid the local
point; after iterative reclassification, each point is allocated to the neighborhood of the nearest central
gathering center phenomenon caused by the use of local L1 median, the constraint is added to deter
point, and asthe
a consequence
the from
steadily
expanding
neighborhood, some details are repeated.
shrinking sampleof
points
gathering
in the center.
stepsand
of thegenerate
algorithmthe
are as
follows:
randomly sample
a group
sample
points from
the The smooth
Set the cableThe
radius
cable
cross-section
circle
at theofcable
starting
point.
original point cloud data as the initial center points; compare the distance of the point in the point
cable is generated
through the Sweep method [51] of the interpolation points and the cross-section
cloud to each center point, and divide all the points into the nearest category to form the initial
circle. The Sweep
method
has
beenis widely
design
and
generation
of as
graphics as a
classification;
the local
median
calculatedapplied
by L1, andin
thethe
established
local
median
point is taken
the new central
after iterative
reclassification,
each point
is allocated to the neighborhood
method of generating
3Dpoint;
graphics
by combining
simple
two-dimensional
graphics, of
especially for
the nearest central point, and as a consequence of the steadily expanding neighborhood, some details
cable modeling,
as it is more convenient and flexible than other methods. The method is a powerful
are repeated.
means of constructing
3D shapes.
The
principle
ofcross-section
geometriccircle
modeling
with
the method
Set the cable
radius and
generate
the cable
at the cable
starting
point. Theis as follows:
smooth
is generated
the cross-section
Sweep method [51]
interpolation
the crossfirst, determine
thecable
trajectory
linethrough
and the
ofofa the
graphic,
and points
then and
move
the cross-section
section circle. The Sweep method has been widely applied in the design and generation of graphics
along the determined trajectory line to form a geometric model. As only one trajectory line and one
as a method of generating 3D graphics by combining simple two-dimensional graphics, especially
cross-sectionfor
arecable
needed,
theasmethod
isconvenient
very simple
and efficient.
demonstrated
modeling,
it is more
and flexible
than otherAs
methods.
The method[52],
is a the surface
means
of constructing
3D shapes.
Thebe
principle
of geometric
generated bypowerful
sweeping
along
a path can
usually
expressed
as modeling with the method is
as follows: first, determine the trajectory line and the cross-section of a graphic, and then move the
cross-section along the determined trajectory line to form a geometric model. As only one trajectory
S(u,v) =the
C(method
+ c2(and
B
v) + c1is
(u,v
) Nsimple
u,v)efficient.
line and one cross-section are needed,
very
As demonstrated [52],
the surface generated by sweeping along a path can usually be expressed as
(22)
where C(v) represents the trajectory line,
c1=(u,v
c2(u,v
the plane cross-section,
and N or
) or
) represent
𝑆(𝑢,𝑣)
𝐶(𝑣)
+ 𝑐1(𝑢,𝑣)
𝑁+
𝑐2(𝑢,𝑣) 𝐵
(22)
B represent the unit vector in the moving frame moving along the trajectory line. As illustrated in
where 𝐶(𝑣) represents the trajectory line, 𝑐1(𝑢,𝑣) or 𝑐2(𝑢,𝑣) represent the plane cross-section, and N
Figure 8, the or
moving
frame can be used for positioning and posture adjustment of the moving object.
B represent the unit vector in the moving frame moving along the trajectory line. As illustrated
in Figure
8, the moving
frame the
can be
usedisfor
positioning
and posture
adjustment
of the moving
The method
of sweeping
along
path
used
to indicate
the tubular
object.
During the sweep,
object. shape is fixed and only its size and scale are changed until the entire trajectory line
the cross-sectional
is traversed. Throughout the process, the trajectory line and cross-sectional shape can be specified
by parameters, and the splicing of the surface can be reduced to better indicate the tubular surface.
The generated cables are illustrated in Figure 9.
2.5. The Construction of the Topological Relationship in Cable Wells
The model is composed of basic elements, which are grouped into vertices, edges, wires, faces,
shells, solids, complex solids and compounds, presenting a recursive relationship from simple to
complex. As shown in Figure 10.
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Remote
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2020,
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1452
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Sens.
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Figure 8. Moving frame diagram.
The method of sweeping along the path is used to indicate the tubular object. During the sweep,
the cross-sectional shape is fixed and only its size and scale are changed until the entire trajectory line
is traversed. Throughout the process,
the trajectory
line
and cross-sectional
shape can be specified by
Figure
Moving
frame
diagram.
Figure
8.8.Moving
frame
diagram.
parameters, and the splicing of the surface can be reduced to better indicate the tubular surface. The
generated
cablesofare
illustratedalong
in Figure
9.
The method
sweeping
the path
is used to indicate the tubular object. During the sweep,
the cross-sectional shape is fixed and only its size and scale are changed until the entire trajectory line
is traversed. Throughout the process, the trajectory line and cross-sectional shape can be specified by
parameters, and the splicing of the surface can be reduced to better indicate the tubular surface. The
generated cables are illustrated in Figure 9.
(a)
(b)
(a)
(c)
(b)
(d)
Figure
9. Construction
(a)Cable
Cablepoint
point
cloud,
single
cable
model,
(c) overall
Figure
9. Constructionofofthe
thecable
cable model.
model. (a)
cloud,
(b)(b)
single
cable
model,
(c) overall
model,
point
cloudand
andmodel.
model.
cablecable
model,
andand
(d)(d)
point
cloud
2.5.
The Construction
of the Topological
Relationship
in Cable
Through
the construction
of the topology
model,
theWells
underground cable well model constructed
by the algorithm
can
be decomposed
each unit,
andare
thereby
theinto
componentization
of thefaces,
cable well
The model
is composed
of basicby
elements,
which
grouped
vertices, edges, wires,
model
is achieved.
In underground
cable wells,presenting
there is a aphysical
logical
relationship
between
shells,
solids, complex
solids and
recursiveand
relationship
from
simple
to
(c)compounds,
(d)
complex.
shown
in Figure
the walls
andAs
the
attached
pipe10.
holes of each cable well through cable well connections. In order to
Figure
9. Construction
of the
model. (a)
Cable
pointand
cloud,
(b) single
cable
model,
(c) overall
visualize
the data
organization,
andcable
to perform
spatial
query
spatial
analysis
of the
3D underground
cable model,
andit(d)
cloud to
and
model. a 3D model that can effectively describe the network
cable wells
network,
is point
necessary
establish
system, and provide a complete formal representation of the spatial relationship. Through the spatial
2.5. The Construction
of the Topological
in Cable
Wells
elements
mentioned above,
this studyRelationship
accomplishes
the construction
of a comprehensive topology
modelThe
(CSG-BRep
model
[53]).
Under
the
constraint
of
topological
consistency,
the complex
3D
model is composed of basic elements, which are grouped into
vertices, edges,
wires, faces,
geometric
modelcomplex
is constructed
by basic
geometric
In this
process, the
lower-level
shells, solids,
solidsprogressively
and compounds,
presenting
a voxels.
recursive
relationship
from
simple to
topological
objects
are in
constructed
complex. As
shown
Figure 10.step by step into higher-level topological objects and the construction
across levels cannot happen. The model synthesizes the macroscopic combination of CSG model [54]
and the microcosmic expression of BRep model [55]. By geometric abstraction, the complex objects are
decomposed into CSG basic voxels, and the parameters of the corresponding axis or edge are extracted
Remote Sens. 2020, 12, 1452
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to develop the parameter equation, which is conducive to further calculation. In addition, the model
can comprehensively and meticulously record the topological relationship inside the cable well.
Remote Sens. 2019, 11, x FOR PEER REVIEW
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Compound
COMPLEX
SOLID
VERTEX
Vertex
Solid
Edge
Boundary
Shell
Face
COMPOUND
SOLID
EDGE
Complex Solid
FACE
SHELL
Boundary
Figure 10. Topology model structure diagram.
Figure
10. Topology model structure diagram.
Through the construction of the topology model, the underground cable well model constructed
As shown
in Figurecan11,
overall by
design
of the
cable well ofmodel
is based on
by the algorithm
be the
decomposed
each unit,
and underground
thereby the componentization
the cable
the building
surface,
thatIncontains
pipecable
holes,
channel
andand
other
structures.
wellwall
model
is achieved.
underground
wells,
there is holes
a physical
logical
relationship The cable
the walls
and the attached
pipe holes
through
cable
well connections.
In surface
well bodybetween
composed
of multiple
surfaces,
suchofaseach
thecable
pipewell
hole
model
attached
to the wall
order to visualize the data organization, and to perform spatial query and spatial analysis of the 3D
and responsible for the cable connection in the well, and body elements such as the cable wellbore
underground cable wells network, it is necessary to establish a 3D model that can effectively describe
superimposed
on thesystem,
main body
of the acable
well,formal
constitute
the underground
well 3D model.
the network
and provide
complete
representation
of the spatial cable
relationship.
For the wall
surface
with
pipe
holes,
this
study
carries
out
the
Boolean
operation
between
thea cable well
Through the spatial elements mentioned above, this study accomplishes the construction of
comprehensive
topology
model
(CSG-BRep
model
[53]).
Under
the
constraint
of
topological
model surface and the cylinder, based on the intersection of the parametric curve and the parametric
consistency, the complex 3D geometric model is constructed progressively by basic geometric voxels.
surface. Under
the constraint of topological consistency and using the progressive construction method,
In this process, the lower-level topological objects are constructed step by step into higher-level
the edge istopological
constructed
wire,
the wire
is constructed
a face,
and the
face is the
constructed
objectsinto
andathe
construction
across
levels cannot into
happen.
The model
synthesizes
into a shellmacroscopic
and a solid,
in orderofto
build
a 3D
of the compound.
underground
combination
CSG
model
[54] model
and the microcosmic
expressionThe
of BRep
model [55]. Bycable well
geometricin
abstraction,
thebuilds
complex
objects
decomposed
intothe
CSG
basicsurface,
voxels, and
the parameters
model developed
this study
the
pipearehole
model on
wall
which
in turn provides a
of the corresponding axis or edge are extracted to develop the parameter equation, which is
comprehensive description of the topological relationships within the cable well model, because cable
conducive to further calculation. In addition, the model can comprehensively and meticulously
well models
notthe
only
possessrelationship
a point–line
and
line–line
record
topological
inside
the acable
well. relationship, but also the point–surface and
line–surface relationship.
As shown in Figure 11, the overall design of the underground cable well model is based on the
Remote Sens. 2019, 11, x FOR PEER REVIEW
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building wall surface, that contains pipe holes, channel holes and other structures. The cable well
body composed of multiple surfaces, such as the pipe hole model attached to the wall surface and
responsible for the cable connection in the well, and body elements such as the cable wellbore
superimposed on the main body of the cable well, constitute the underground cable well 3D model.
Pipe Hole
For the wall surface
with pipe holes, this study carries out the Boolean operation between the cable
Cable
Wellofbody
well model surface and the cylinder, based on the intersection
the parametric curve and the
parametric surface. Under the constraint of topological consistency and using the progressive
Cable well
construction method, the edge
is constructed into a wire, the wire is constructed
into a face, and the
Wellbore
wall
face is constructed into a shell and a solid, in order to build a 3D model of the compound. The
Vertex Edge Wire
underground cable well model developed in this study builds the pipe hole model on the wall
Complex Solid relationships within
surface, which in turn provides a comprehensive description of the topological
the cable well model, because cable well models not only possess a point–line and a line–line
relationship, but also the point–surface and line–surface relationship.
Cable well body
Cable well
Compound
Interwell line
Wellbore
Cable well
Wall 1
Wall 2
Wall...
Multiple
cable holes
Single
cable hole
Fiber hole
Multiple
cable holes
Single
cable hole
Fiber hole
Multiple
cable holes
Single
cable hole
Fiber hole
Connection
In-well cable
Excess cable
Cable pipe
Cable line
CSG-BRep Model Topological Structure
Figure 11. Topological structure of the underground cable well model.
Figure 11. Topological
structure of the underground cable well model.
3. Modeling Experiment and Test Data
3.1. Instrument and Data
The experimental instrument used in this study is the Faro S150 3D laser scanner. The scanning
distance is set to indoor 10 m, the resolution is 28.9 MPTs, the distance error is ±2mm, the measuring
horizontal angle is 0°– 360°, and the measuring vertical angle is −65° to 90°. As illustrated in Figure
12, during the experiment, the scanner is lowered into the cable well by tripod to avert accidental
Remote Sens. 2020, 12, 1452
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3. Modeling Experiment and Test Data
3.1. Instrument and Data
The experimental instrument used in this study is the Faro S150 3D laser scanner. The scanning
distance is set to indoor 10 m, the resolution is 28.9 MPTs, the distance error is ±2mm, the measuring
horizontal angle is 0◦ –360◦ , and the measuring vertical angle is −65◦ to 90◦ . As illustrated in Figure 12,
during the experiment, the scanner is lowered into the cable well by tripod to avert accidental injuries
to the staff, thereby fully capitalizing on the non-contact measurement features of laser scanning.
The original data scanned by the experiment is in FLS data format, and it can be converted to PTX or
Remote Sens. 2019, 11, x FOR PEER REVIEW
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PTS format by Faro’s own software SCENE.
Figure 12. Experimental instruments and data acquisition.
Figure 12. Experimental instruments and data acquisition.
Firstly, as a result of the comparison of several simplification algorithms, it is concluded that the
simplification
twice
moving mesh
divisions
is efficientalgorithms,
and effective.
in that
contrast
Firstly, asalgorithm
a result ofof
the
comparison
of several
simplification
it isTherefore,
concluded
the
to the density-based
adaptive
simplification
and divisions
the percentage
simplification,
this study
uses the
simplification
algorithm
of twice
moving mesh
is efficient
and effective.
Therefore,
in
simplification
twice moving
mesh divisions.
The and
simplification
effects
of the variousthis
methods
contrast
to the of
density-based
adaptive
simplification
the percentage
simplification,
study
are illustrated
in Figureof
13.twice
The simplification
of various
methodseffects
is detailed
Table 1.
uses
the simplification
moving meshcomparison
divisions. The
simplification
of theinvarious
From thisare
table
above, it
be concluded
that the simplification
moving
mesh
methods
illustrated
incan
Figure
13. The simplification
comparisonofoftwice
various
methods
is divisions
detailed inis
quicker
generates
superior
effect.
Table
1. and
From
this table
above, simplified
it can be concluded
that the simplification of twice moving mesh
divisions is quicker and generates superior simplified effect.
Table 1. Comparison of simplification results of multiple algorithms.
Simplification Methods
Data Set
Original Point
Cloud
After
Simplifying
Run Time (s)
Twice moving mesh
divisions simplification
Density-based
adaptive simplification
Point Cloud 1
Point Cloud 2
Point Cloud 1
Point Cloud 2
Point Cloud 1
Point Cloud 2
10,962,732
2,563,302
10,962,732
2,563,302
10,962,732
2,563,302
2,832,227
983,771
3,273,368
1,022,895
5,481,366
1,281,651
3.23
0.75
4.21
0.92
3.40
0.87
Percentage simplification
Quality
Good (Evenly distributed)
General (With
distinct striations)
General (Middle dense,
both sides sparse)
Figure 13. Effects of different simplification methods. (a) Original point clouds (top row represents
Point Cloud 1, bottom row represents Point Cloud 2), (b) twice moving mesh divisions, (c) density-
contrast to the density-based adaptive simplification and the percentage simplification, this study
uses the simplification of twice moving mesh divisions. The simplification effects of the various
methods are illustrated in Figure 13. The simplification comparison of various methods is detailed in
Table 1. From this table above, it can be concluded that the simplification of twice moving mesh
divisions
quicker
Remote
Sens. is
2020,
12, 1452and generates superior simplified effect.
15 of 23
Remote Sens. 2019, 11, x FOR PEER REVIEW
16 of 25
Table 1. Comparison of simplification results of multiple algorithms.
3.2.
Simplification
Original Point
After
Run
Data Set
Quality
Methods
Cloud
Simplifying
Time (s)
Twice moving
Point Cloud 1
10,962,732
2,832,227
3.23
Good (Evenly
mesh divisions
Point Cloud 2
2,563,302
983,771
0.75
distributed)
simplification
Point Cloud
1
10,962,732
3,273,368
4.21
FigureDensity-based
13. Effects of different
simplification
methods. (a)
Original point
clouds (top
row(With
represents
General
adaptive
Figure
13.
Effects
of
different
simplification
methods.
(a)
Original
point
clouds
(top
row
represents
Point Cloud 1, bottom row
represents
Cloud 2), (b) twice
moving mesh
(c) striations)
density-based
Point
Cloud 2 Point
2,563,302
1,022,895
0.92divisions,
distinct
simplification
Point
Cloud
1,
bottom
row
represents
Point
Cloud
2),
(b)
twice
moving
mesh
divisions,
(c)
densityadaptive, and (d) percentage.
Point Cloud 1
10,962,732
5,481,366
3.40
General (Middle
Percentage
based adaptive, and (d) percentage.
dense, both sides
simplification
PointofCloud
2
2,563,302
0.87
The Modeling
Experiment
Underground
Cable Wells 1,281,651
and the Corresponding
Results
sparse)
In order to verify the effect of the generated underground cable wells model, this study uses a
3.2. The Modeling Experiment of Underground Cable Wells and The Corresponding Results
variety of underground cable wells data types for cable well model construction and internal cable
In order to verify the effect of the generated underground cable wells model, this study uses a
well model construction. Four main geometric forms of point cloud are selected as the experimental
variety of underground cable wells data types for cable well model construction and internal cable
data. Point
Cloud
is the Turning
Point Cloud
the cloud
Three-way
type,
Point
Cloud 3 represents
well
model1construction.
Four type,
main geometric
forms 2ofis
point
are selected
as the
experimental
data. Point Cloud
1 isand
the Turning
type, Point
Cloud 2 is the
Three-way
type,
Point As
Cloud
3 represents
the Straight-through
type
Point Cloud
4 represents
the
Four-way
type.
illustrated
in Figure 14,
the
Straight-through
type
and
Point
Cloud
4
represents
the
Four-way
type.
As
illustrated
in
Figure
the applicability of the proposed algorithm is verified by modeling multiple data types.
14, the applicability of the proposed algorithm is verified by modeling multiple data types.
1
2
3
a
4
b
c
14. Construction
of different
cable models.
well models.
(left)
Original
point
clouds,(middle)
(middle) generated
Figure 14.Figure
Construction
of different
cable well
(left)
Original
point
clouds,
generated cable well models, and (right) cable and pipe hole models.
cable well models, and (right) cable and pipe hole models.
Remote Sens. 2020, 12, 1452
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Remote Sens. 2019, 11, x FOR PEER REVIEW
17 of 25
Figure 15
15 illustrates
illustrates the
the overall
overall point
point cloud
cloud of
of the
the underground
underground cable
cable well
well in
in the
the original
original scene
scene
Figure
and
the
image
generated
by
the
single-site
point
cloud.
Figure
15a
shows
the
actual
situation
of
the
and the image generated by the single-site point cloud. Figure 15a shows the actual situation of the
connection between
between underground
underground wells,
wells, Figure
Figure 15b
15b shows
showsthe
thedistribution
distributionof
ofcables
cablesinside
insidethe
thewells,
wells,
connection
Figure
15c
reflects
the
overall
situation
of
the
wells
after
modeling,
and
Figure
15d
shows
the
overall
Figure 15c reflects the overall situation of the wells after modeling, and Figure 15d shows the overall
effect of
of well
well modeling
modeling and
and internal
internal cable
cable modeling.
modeling.
effect
(a)
(c)
(b)
(d)
Figure 15. Overall modeling effect. (a) Overall original point cloud and pipe connections, (b) original
Figure 15. Overall modeling effect. (a) Overall original point cloud and pipe connections, (b) original
point cloud internal image, (c) overall model and connections between models, and (d) internal cable
point cloud internal image, (c) overall model and connections between models, and (d) internal cable
model generation.
model generation.
4. Results and Discussion
4. Results and Discussion
In order to validate the exceptional accuracy and practicability of the proposed algorithm at
In
order
validate thecable
exceptional
accuracy
and with
practicability
the proposed
algorithm
modeling
the to
underground
well point
cloud data
holes, weof
utilize
three different
types at
of
modeling
the
underground
cable
well
point
cloud
data
with
holes,
we
utilize
three
different
types
of
cable well wall data: the curved surface point cloud data Figure 16a, the rectangular planar point cloud
cable
well wall
the irregular
curved surface
rectangular
planar
point
data Figure
16bdata:
and the
planarpoint
pointcloud
cloud data
data Figure
Figure 16a,
16c, the
adopting
multiple
modeling
cloud
data
and the
planar
point cloud
data Figure
16c, adopting multiple
methods
to Figure
generate16b
models
and irregular
comparing
the subsequent
modeling
results.
modeling
methods
to
generate
models
and
comparing
the
subsequent
modeling
results.
The methods used for comparison include the 3D Delaunay triangulation surface
reconstruction
The
methods
used
for
comparison
include
the
3D
Delaunay
triangulation
surface
reconstruction
method based on surface growth in the CGAL V5.0 library [56], the implicit surface modeling
method
method
based
on
surface
growth
in
the
CGAL
V5.0
library
[56],
the
implicit
surface
modeling
method
in the common point cloud modeling software Geomagic [57], and the surface modeling method in
in
point
cloudlibrary
modeling
software Geomagic
surface triangulation
modeling method
in
thethe
3Dcommon
CAD open
source
OpenCASCADE
V4.7.0.[57],
Theand
3Dthe
Delaunay
surface
the
3D
CAD
open
source
library
OpenCASCADE
V4.7.0.
The
3D
Delaunay
triangulation
surface
reconstruction method in CGAL is able to reconstruct the point cloud models of terrain scanning,
reconstruction
method
in CGAL
is able
reconstruct
point cloud algorithm
models ofused
terrain
scanning,
building scanning
and fine
scanning.
ThetoWRAP
surfacethe
reconstruction
by Geomagic
building
scanning
and
fine
scanning.
The
WRAP
surface
reconstruction
algorithm
used
by
Geomagic
Studio V11 is an implicit surface algorithm. OpenCASCADE is a software development platform
Studio
V113D
is surface
an implicit
surface
OpenCASCADE
is a software
developmentwhich
platform
providing
modeling
andalgorithm.
solid modeling,
CAD data exchange,
and visualization,
can
providing
3D
surface
modeling
and
solid
modeling,
CAD
data
exchange,
and
visualization,
which
be used to develop CAD, CAM and CAE related software.
can be
used
to develop results,
CAD, CAM
and CAE
related16,
software.
The
experimental
illustrated
in Figure
are qualitatively analyzed. For the same data,
using Geomagic Studio V11 or Delaunay surface reconstruction, the generated model is incomplete,
as the missing point cloud part of the cable well wall surface will result in defective modeling, making it
impossible to restore the overall wall model. Additionally, as the pipe holes are unrecognizable and,
due to the existence of other distortions, the pipe holes in the wall cannot be separately modeled,
the pipe holes in the modeled wall lack the physical definition of the “pipe hole” in the 3D space,
Remote Sens. 2020, 12, 1452
17 of 23
and the topological relationship between them and the wall surface is also ambiguous, resulting in
creating inaccurate cable connections in the well. While modeling with the 3D modeling algorithm
of OpenCASCADE V4.7.0 is accurate for the rectangular plane wall surface and polygonal plane
wall surface, curved wall surface distortions occur when performing the topological operation on the
curved wall surface. However, with the proposed algorithm in this study, there are no disruptions in
the overall modeling of the wall surface, and the pipe hole model of the wall surface can be completely
constructed
to provide
topological
cable
Remote Sens. 2019,
11, x FORaPEER
REVIEW structure that can accurately accomplish the subsequent 18
of 25
connections in the well.
(a)
(b)
(c)
Figure16.16.Comparison
Comparisonofofvarious
variousmodeling
modelingeffects
effectsofofdifferent
differentcable
cablewell
well
wall
data.(a)(a)The
Thecurved
curved
Figure
wall
data.
surfacepoint
point
cloud,
rectangular
point and
cloud
and
(c) the planar
irregular
planar
point
surface
cloud,
(b)(b)
thethe
rectangular
planarplanar
point cloud,
(c) ,the
irregular
point
cloud.
cloud.
From the analysis of the experimental results illustrated in Figure 17 and described in Table 2, it is
observed
the use of results,
refined surface
reconstruction
the modeling
of theFor
cable
Thethat
experimental
illustrated
in Figure 16,prolongs
are qualitatively
analyzed.
thewell
samebody
data,
and
causes
some surface
Moreover,
in the
refined surface
theistopological
using
Geomagic
Studio vacancies.
V11 or Delaunay
surface
reconstruction,
thereconstruction,
generated model
incomplete,
relationships
between
all faces
of of
thethe
cable
well
and
between
the
face
and in
thedefective
internal cable
well are
not
as the missing
point cloud
part
cable
well
wall
surface
will
result
modeling,
making
considered.
However,
the proposed
comprehensively
the topological
relationships
it impossible
to restore
the overallalgorithm
wall model.
Additionally,considers
as the pipe
holes are unrecognizable
ofand,
the due
model,
and
has wide-ranging
practicability
based
on the
rapid
of the cable
well
to the
existence
of other distortions,
the pipe
holes
in the
wallconstruction
cannot be separately
modeled,
body
model.
Moreover,
as shown
inlack
Figure
there are
some vacancies
regions
point
the pipe
holes
in the modeled
wall
the17,
physical
definition
of the “pipe
hole”ininthe
theoriginal
3D space,
and
clouds
due to partial
occlusionbetween
of duringthem
scanning.
In this
theisvacancies
regions can
be filledin
the topological
relationship
and the
wallpaper,
surface
also ambiguous,
resulting
automatically
using the
fitting
method forinthe
boundary,with
and the
as the
of the vacancies
creating inaccurate
cable
connections
thefound
well. contour
While modeling
3Darea
modeling
algorithm
regions
is relatively small,
not affect
each
method. plane wall surface and polygonal plane wall
of OpenCASCADE
V4.7.0itiswill
accurate
for the
rectangular
To evaluate
performance
the proposed
algorithm,
model
and source
surface,
curved the
wallactual
surface
distortions of
occur
when performing
thereference
topological
operation
on the
model
arewall
built
according
to the four
of well algorithm
point cloud.
The study,
sourcethere
model
S is
curved
surface.
However,
withgroups
the proposed
in this
are
noautomatically
disruptions in
constructed
the proposed
algorithm,
and the reference
R is manually
using Maya
the overallbymodeling
of the
wall surface,
and the model
pipe hole
model ofcompleted
the wall by
surface
can be
2019.
Subsequently,
we reference
the modeling
evaluation
method proposed
Khoshelham
et al. [58,59]
completely
constructed
to provide
a topological
structure
that can by
accurately
accomplish
the
and
calculatedcable
the Completeness
,
Correctness
M
and
Accuracy
M
,
as
follows:
subsequent
connections inM
the
well.
Comp
Corr
Acc
From the analysis of the experimental results
illustrated
in
Figure
17
and
described in Table 2, it
Pn Pm
i ∩ b(R j )
S
is observed that the use of refined surface reconstruction
prolongs the modeling of the cable well
i=1
j=1
Pm inj the refined surface reconstruction,(23)
Comp (b) = Moreover,
body and causes some surfaceMvacancies.
the
j=1 R
topological relationships between all faces of the cable well and between the face and the internal
Pn proposed
Pm
cable well are not considered. However, the
comprehensively considers the
i algorithm
j
i=1
j=1 S ∩ b (R )
topological relationships of theMmodel,
and
has
wide-ranging
practicability
based on the rapid
(
b
)
=
(24)
Pm
Corr
i
S
j
=
1
construction of the cable well body model. Moreover, as shown in Figure 17, there are some vacancies
regions in the original point clouds due to partial occlusion of during scanning. In this paper, the
vacancies regions can be filled automatically using the fitting method for the found contour
boundary, and as the area of the vacancies regions is relatively small, it will not affect each method.
Remote Sens. 2020, 12, 1452
18 of 23
MAcc (r) = MedkπTj pi k, i f kπTj pi k ≤ r
(25)
where m and n denote the number of surfaces in reference model R and source model S. kπTj pi k is the
perpendicular
distance
a vertex point pi in the source and the corresponding surface
plane π j
Remote Sens. 2019,
11, x FORbetween
PEER REVIEW
19 of 25
in the reference, and r is the cut-off value, distances beyond which are excluded from the median.
(a)
(c)
(b)
Figure
Construction of
of different
different cable
(a) (a)
Original
pointpoint
clouds,
(b) fine
Figure
17.17.
Construction
cablewell
wellmodels.
models.
Original
clouds,
(b)modeling,
fine modeling,
and
(c)
this
paper’s
modeling
method.
and (c) this paper’s modeling method.
Table2.2. Generation
Generation time
modeling
effect
of different
models.
Table
timeand
and
modeling
effect
of different
models.
Four Types of
Four Types of
Cable Well
Cable Well
Point
Point Clouds
Clouds
Point Cloud 1
Points of the
Points of the
Original
Data
Original
Data
5,203,987
5,203,987
Points after
Points after
Preprocessing
Preprocessing
1,893,678
1,893,678
Point Cloud 2
Point Cloud 2
9,683,276
9,683,276
2,132,587
2,132,587
Point Cloud 3
Point Cloud 3
2,563,302
2,563,302
983,771
983,771
Point
Point Cloud
Cloud 44
10,962,732
10,962,732
2,832,227
2,832,227
Modeling
Modeling
Methods
Methods
Proposed
Proposed
algorithm
algorithm
Geomagic
Geomagic
modeling
modeling
Proposed
Proposed
algorithm
algorithm
Geomagic
Geomagic
modeling
modeling
Proposed
algorithm
Proposed
algorithm
Geomagic
modeling
Geomagic
Proposed
modeling
algorithm
Proposed
algorithm
Geomagic
modeling
Geomagic
modeling
Run
Run
Time
Time
(s)(s)
3.147
3.147
39.271
39.271
3.695
3.695
43.879
43.879
2.598
2.598
30.259
30.259
4.513
4.513
51.286
51.286
Modeling Effect
Modeling Effect
Fully considered topological
Fully considered
relationships
Largetopological
vacancies atrelationships
the top and
Large
vacancies
at the top and
bottom,
without
considering
bottom,
without considering
topological
relationships
relationships
Fully topological
considered topological
Fully considered
relationships
topological
relationships
Top vacancy,
without
considering
Top vacancy,
without considering
topological
relationships
relationships
Fully topological
considered topological
relationships
Fully considered
topological
relationships
Top vacancy,
without
considering
topological
relationships
Top vacancy,
without considering
Fully topological
considered topological
relationships
relationships
Fully considered
Corner
vacancy, without
topological
relationships
considering
Cornertopological
vacancy, without
relationships
considering topological
relationships
To evaluate the actual performance of the proposed algorithm, reference model and source
model are built according to the four groups of well point cloud. The source model S is
𝑀𝐴𝑐𝑐 (𝑟) = 𝑀𝑒𝑑‖𝜋𝑗𝑇 𝑝𝑖 ‖, 𝑖𝑓‖𝜋𝑗𝑇 𝑝𝑖 ‖ ≤ 𝑟
(25)
where m and n denote the number of surfaces in reference model 𝑅 and source model 𝑆. ‖𝜋𝑗𝑇 𝑝𝑖 ‖ is
the perpendicular distance between a vertex point 𝑝𝑖 in the source and the corresponding surface
Remote Sens. 2020, 12, 1452
19 of 23
plane 𝜋𝑗 in the reference, and 𝑟 is the cut-off value, distances beyond which are excluded from the
median.
As
shown in
inFigure
Figure18,
18,the
the
buffer
value
is to
set10tocm,
10 and
cm, the
andthree
the three
quantitative
evaluation
As shown
buffer
value
is set
quantitative
evaluation
values
values
are shown
in3.
Table
3. Among
Completeness
and Correctness
can reach
toand
0.9, it
and
it
are shown
in Table
Among
them, them,
Completeness
and Correctness
can reach
up toup
0.9,
also
also
indicates
that
the
accuracy
of
3D
modeling
is
related
to
the
complexity
of
the
model
itself;
the
indicates that the accuracy of 3D modeling is related to the complexity of the model itself; the simpler
simpler
thethe
model,
thethe
higher
the precision
the model,
higher
precision
value. value.
(a)
(b)
(c)
(d)
Figure 18. Reference cable well models. (a) Point Cloud 1 reference models, (b) Point Cloud 2 reference
Figure 18. Reference cable well models. (a) Point Cloud 1 reference models, (b) Point Cloud 2
models, (c) Point Cloud 3 reference models, and (d) Point Cloud 4 reference models.
reference models, (c) Point Cloud 3 reference models, and (d) Point Cloud 4 reference models.
Table 3. The quantitative evaluation of Completeness, Correctness and Accuracy.
Dataset
Intersection
Area (I)
Reference
Model Surface
Area (R) m2
Source Model
Surface Area
(S) m2
Completeness (I/R)
Correctness (I/S)
Accuracy (mm)
Point Cloud 1
Point Cloud 2
Point Cloud 3
Point Cloud 4
63.48
61.63
34.97
84.03
66.82
65.56
36.05
91.34
65.97
66.84
35.65
92.04
0.95
0.94
0.97
0.92
0.96
0.92
0.98
0.91
0.63
1.06
0.55
1.19
In addition, the quantitative evaluation is performed for the integrity of the internal model of
the underground cable well from an object-oriented perspective, which includes tube hole integrity,
cable integrity, cable connector integrity, and the correctness of tube hole connections, as shown in
Figure 19 and Table 4. The results indicate that the accuracy of 3D modeling is improved 90% by the
proposed method.
As described through the above experiment of the cable well model generation, the proposed
algorithm can be effectively applied to different types of point cloud data and has wide applicability.
The time consumption to generate each model is negligible and the spatial topological relationship is
fully considered. From the modeling effect of the actual point cloud, it can be seen that the algorithm
in this study can effectively meet real-time production needs. In addition to cable wells, the proposed
algorithm has strong applicability to the regular point cloud data, such as a house or building with the
regular flat roof.
Point Cloud 4
84.03
91.34
92.04
0.92
0.91
1.19
In addition, the quantitative evaluation is performed for the integrity of the internal model of
the underground cable well from an object-oriented perspective, which includes tube hole integrity,
cable integrity, cable connector integrity, and the correctness of tube hole connections, as shown in
Remote Sens. 2020, 12, 1452
20 of 23
Figure 19 and Table 4. The results indicate that the accuracy of 3D modeling is improved 90% by the
proposed method.
(a)
(b)b
d
(c)
(d)
Figure 19. Internal cable model generation. (a) Point Cloud 1 internal models, (b) Point Cloud 2
Figure 19. Internal cable model generation. (a) Point Cloud 1 internal models, (b) Point Cloud 2
internal models, (c) Point Cloud 3 internal models, and (d) Point Cloud 4 internal models.
internal models, (c) Point Cloud 3 internal models, and (d) Point Cloud 4 internal models.
Table 4. The quantitative evaluation of internal model Completeness.
Table 4. The quantitative evaluation of internal model Completeness.
Tube Hole
Data Set
Data Set
Point Cloud 1
Point Cloud 2
Point
Cloud
1 3
Point
Cloud
Point
Cloud
Point
Cloud
2 4
Point Cloud 3
Cloud 4
5. Point
Conclusions
Cable
Cable Connector
TubeCompleteness
hole
CableCompleteness
Completeness
Cable
Connector
Completeness
(Modeled/Actual) Completeness
(Modeled/Actual)
(Modeled/Actual)
Completeness
(Modeled/Actua (Modeled/Actua
(Modeled/Actual)
22/24 ≈ 91.67%
7/7 = 100%
7/7 = 100%
l)
l)
62/65 ≈ 95.38%
20/22 ≈ 90.90%
6/6 = 100%
22/24 24/24
≈ 91.67%
7/7 = 100%
= 100% 7/7 = 100%
6/6 = 100%
0/0 100%
≈ 91.89% 20/2219/21
≈ 90.48% 6/6 = 100%
7/8 ≈ 87.5%
62/6568/74
≈ 95.38%
≈ 90.90%
24/24 = 100%
6/6 = 100%
0/0 (100%)
68/74 ≈ 91.89%
19/21 ≈ 90.48%
7/8 ≈ 87.5%
Correctness of
Pipe Holeof
Correctness
Connection
Pipe Hole
(Modeled/Actual)
Connection
14/14 = 100%
(Modeled/Actual)
40/44 ≈ 90.90%
14/14
= 100%
12/12
= 100%
38/42
≈ 90.48%
40/44
≈ 90.90%
12/12 = 100%
38/42 ≈ 90.48%
Based on the 3D terrestrial lidar point cloud, the proposed algorithm in this study reduces the
overall time consumption by preprocessing the original point cloud, extracting the main axis of the
point cloud by the OBB method, and achieving the orientation correction of the point cloud by the
quaternion rotation. Subsequently, this study uses the adaptive method to extract the top point cloud,
conducts the projection of the top point cloud, and then extracts the boundary of the projected top
point cloud. Finally, based on the boundary information, the triangular patches are built to accomplish
the construction of the 3D cable well model. Employing the constructed model, the pipe holes of the
cable well are generated by the triangulation network cutting method. Moreover, the underground
cable wells model is constructed by the Sweep method. The following conclusions can be made based
on experimental testing:
(1) The proposed algorithm can adapt to different underground cable well types, while fully
considering the topological relationship of the cable well model. Moreover, the proposed algorithm is
faster in modeling and has exceptional adaptability when compared to the predominantly used surface
reconstruction algorithms.
Remote Sens. 2020, 12, 1452
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(2) In comparison with the traditional cable well modeling, this study achieves the essential
unification of internal cable wells and external point clouds, which can adequately meet the reappearance
of the original scene.
However, the algorithm in this study still has significant room for improvement, such as fully
integrating GIS and BIM technology for the construction and display of cable wells, and other data
sources integrating modeling and application. Therefore, further research is needed to improve the
related algorithms.
Author Contributions: M.H., X.W. and X.L. conducted the algorithm design, and M.H. wrote the paper and X.L.
revised the paper. T.M. and P.Z. contributed to data acquisition and algorithm programming implementation.
All authors have contributed significantly and have participated sufficiently to take the responsibility for this
research. All authors have read and agreed to the published version of the manuscript.
Funding: This study is funded by the Ministry of Science and Technology of the People’s Republic of China
(2018YFE0206100), the National Natural Science Foundation of China (41971350, 41501494, 41601409, 41871367),
the Beijing Natural Science Foundation (8172016), and Basic scientific research operating expenses of Beijing
municipal universities (X18050).
Conflicts of Interest: The authors declare no conflict of interest.
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