We introduce a new approach to construct smooth piecewise curves representing realistic road paths. Given a GIS database of road networks in which sampled points are organized in 3D polylines, our method creates horizontal, then vertical curves, and finally combines them to produce 3D road paths. We first estimate the possibility of each point of being a junction between two separate primitive curve segments. Next, we design a tree-traversal algorithm to expand sequences of local best fit primitives which are then merged together with respect to the G1 continuity constraint and civil engineering rules. We apply the Levenberg-Marquardt method to minimize the error between the resulting curve and the sampled points while preserving the G1continuity

1. REALISTIC ROAD PATH RECONSTRUCTION
FROM GIS DATA
Hoàng Hà NGUYỄN, Brett DESBENOIT, and Marc DANIEL
LSIS – CNRS – Aix*Marseille university

2. An output
road path

3. Realistic road path reconstruction from GIS data Seoul 10/10/2014 3 of 18
Outline
Problem statement
Proposed method
Results
Conclusion

4. Realistic road path reconstruction from GIS data Seoul 10/10/2014 4 of 18
Realistic and accurate 3D models of road networks
Transportation simulation
Serious games
Virtual traveling
Realistic: must respect civil engineering rules
Accurate: manage inaccuracy of input data
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

5. Realistic road path reconstruction from GIS data Seoul 10/10/2014 5 of 18
Road sample points
 Stored in 3D polylines
 Accuracy: 1m  2.5m
Terrain point cloud
 5mx5m regular grid
 Accuracy: 2.5m
Aerial images
GIS database
How to exploit and combine multimodal data types?
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

6. Realistic road path reconstruction from GIS data Seoul 10/10/2014 6 of 18
 By grammar rules or pattern-based method: [PHM01, SYBG02, CEW*08]
 fictitious roads
 From GIS data [WSL12], do not use clothoid, do not aim at driving
experience
 Use procedural methods [BN08, GPMO10, GPMG11], do not take into
account engineering rules  lack of realism
3D road reconstruction
REFERENCES
 [PHM01] PARISH, H. Y. I., MULLER P.: Procedural modeling of cities. In Proceedings of the 28th annual conference on
Computer graphics and interactive techniques (New York, USA, 2001), SIGGRAPH ’01, pp. 301–308,
 [SYBG02] SUN J., YU X., BACIU G., GREEN M.: Templatebased generation of road networks for virtual city modeling.
Proceedings of the ACM symposium on Virtual reality software and technology (2002), 33–40
 [CEW∗08] CHEN G., ESCH G., WONKA P., MÜLLER P., ZHANG E.: Interactive procedural street modeling. SIGGRAPH ’08,
 [WSL12] WILKIE D., SEWALL J., LIN M. C.: Transforming gis data into functional road models for large-scale traffic simulation.
IEEE Transactions on Visualization and Computer Graphics 18, 6 (2012), 890–901
 [BN08] BRUNETON E., NEYRET F.: Real-time rendering and editing of vector-based terrains. In Eurographics (2008)
 [GPMG10] GALIN E., PEYTAVIE A., MARÉCHAL N., GUÉRIN E.: Procedural generation of roads. Computer Graphics Forum
(Proc. of Eurographics) 29, 2 (2010), 429–438
 [GPGB11] GALIN E., PEYTAVIE A., GUÉRIN E., BENES B.: Authoring hierarchical road networks. Computer Graphics Forum
(Proc. of Pacific Graphics) 30, 7 (2011), 2021–2030
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

7. Realistic road path reconstruction from GIS data Seoul 10/10/2014 7 of 18
 Use input points as control points of clothoid splines [WM05] 
big deviation
 [MS09, BLP10] build clothoid splines from polyline  only 2D,
insufficient road path rules
Piecewise curve reconstruction
REFERENCES
 [WM05] WALTON D. J., MEEK D. S.: Technical section: A controlled clothoid spline. Comput.
Graph. 29, 3 (June 2005), 353–363.
 [MS09] MCCRAE J., SINGH K.: K.: Sketch-based path design. In Proc. Graphics Interface
(2009), pp. 95–02
 [BLP10] BARAN I., LEHTINEN J., POPOVIC J.: Sketching clothoid splines using shortest paths.
Computer Graphics Forum, 29 (2010)
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work
Need a method to create road path with civil engineering
rules

8. PROPOSED METHOD
LSGA + Primitive merging

9. Realistic road path reconstruction from GIS data Seoul 10/10/2014 9 of 18
 Piecewise curves
 Horizontal curve (projection on a plane) = [straight line | arc | clothoid]
 Vertical curve (altitude along horizontal curve) = [straight line | parabola]
 Grammar of primitive sequence
 G1 continuous
 Connected
 Tangents at junction are parallel
 Restriction of primitive length (min, max)
 Guidelines: few primitives, simple primitives in higher priority
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work
Highway horizontalNormal horizontal Vertical
Straight
line
Parabola
*
Circle
Arc
Straight
line
Clothoid
0:2
*
Circle
Arc
Straight
line
Clothoid
1:2

10. Realistic road path reconstruction from GIS data Seoul 10/10/2014 10 of 18
z
Input 3D polyline
y
x x
Horizontal polyline
y
z
Vertical polyline
length
x
Horizontal piecewise
curvey
z
Vertical piecewise
curve
length
Road path
z
y
x
Build horizontal
and vertical
curve separately
Lift horizontal
curve to the
altitude given by
vertical curve
Preprocess 3D
polyline to get
2D polylines
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

11. Realistic road path reconstruction from GIS data Seoul 10/10/2014 11 of 18
 LSGA (Least-error Sequence Growing Algorithm): given a polyline,
find an appropriate sequence of primitives
 Primitive merging: from disconnected primitives, build a G1 curve
with acceptable total square deviations
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

12. Realistic road path reconstruction from GIS data Seoul 10/10/2014 12 of 18
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8Try longer
primitives
Reset with the least
error sequence
 Finish:
 Reach the last point
 Max and Mean deviation ≤ thresholds
Grow the current
sequence by
adding a primitive
Preprocess: estimate testing order
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work
LSGA works by trying to grow a primitive
sequence
LSGA
Split at point having the least
testing order,
Try to fit the simple primitive first
1
2
6 3
5
4
P0 P1 P2 P3 P4
P5
P6
P7
P8
Invoke “primitive merging”
to obtain a G1 curve

13. Realistic road path reconstruction from GIS data Seoul 10/10/2014 13 of 18
 Based on the Levenberg-Marquardt algorithm
 Initial guess:
 Keep 1st primitive
 Translate and rotate the others to obtain G1 curve
 Minimize by optimizing primitives’ parameters
Primitive merging
P5
P 5
+
P5
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

14. RESULTS
10/10/2014 14

15. Realistic road path reconstruction from GIS data Seoul 10/10/2014 15 of 18
Horizontal curve Vertical curve
Input
Polyline length (m) 962
Number of points 46
Horizontal accuracy (m) 1.5
Vertical accuracy (m) 1
Output
Mean horizontal error (m) 0.45
Max horizontal error (m) 1.19
Mean vertical error (m) 0.32
Max vertical error (m) 0.94
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

16. Realistic road path reconstruction from GIS data Seoul 10/10/2014 16 of 18
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

17. Realistic road path reconstruction from GIS data Seoul 10/10/2014 17 of 18
Construction of complex and realistic road networks
 Roundabouts must be added
Forthcoming work:
 Road surface construction
 Based on civil engineering rules
 Mimic operations of civil engineering to modify the terrain
according to the road paths:
 Excavation
 Embankment
 Proposed method
 Required rules
 Method overview
 Algorithms
 Results
 Conclusion
 Problem statement
 Motivations
 Input data
 Related work

18. THANK YOU FOR YOUR ATTENTION

19. Realistic road path reconstruction from GIS data Seoul 10/10/2014 19 of 18
Testing order computation
 𝑆𝑖 = 𝑆 𝑃 𝑖−1 𝑃 𝑖 𝑃 𝑖+1
 𝐽𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑃𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑖 =
𝑚𝑖𝑛 𝑆𝑖 − 𝑆𝑖−1 , 𝑆𝑖+1 − 𝑆𝑖
 From junction priority, set the
testing order for each point
P0 P1 P2 P3 P4
P5
P6
P7
P8
16 3
5
4
2
S4
P0 P1 P2 P3 P4
P5
P6
P7
P8
P0 P1 P2 P3 P4
P5
P6
P7
P8
0.920.36
0.62
0.43
0.61
0.68
JunctionPriority4 = min(|S4-S3|, |S5-S4|)

20. Realistic road path reconstruction from GIS data Seoul 10/10/2014 20 of 18
 Common parameters:
 Starting point (x,y)
 Tangent at starting point
 Specific parameters for each type:
 Line: length
 Circular arc: tangent at ending, radius
 Clothoid: starting curvature, ending curvature, length
 Parabola: tangent at ending, co-efficient A (of y = Ax2 + Bx +C)
Primitives’ parameters

21. Realistic road path reconstruction from GIS data Seoul 10/10/2014 21 of 18
Given input accuracy: δ
To ensure quality of fitting, impose the
criteria:
Max error ≤ δ
Mean error ≤ δ/2
Error criteria

22. Realistic road path reconstruction from GIS data Seoul 10/10/2014 22 of 18
Results: mountain road
Horizontal curve Vertical curve
Input
Polyline length (m) 874.8
Number of points 50
Horizontal accuracy (m) 2.5
Vertical accuracy (m) 2.5
Output
Mean horizontal error (m) 1.05
Max horizontal error (m) 2.45
Mean vertical error (m) 0.57
Max vertical error (m) 0.94

23. Realistic road path reconstruction from GIS data Seoul 10/10/2014 23 of 18
Execution time
Function name Times Total duration (s) %
Road ID TRONROUT0000000040764920 (suburban) 272.27 100
Try to add primitive to current sequence 269.13 98.8
Compute the best fit clothoid 4 2.28 0.8
Primitive merging 53 267.15 98.1
Jacobian 636 236.8 86.9
Matrix operations 979 0.03 0
Compute Deviations, D_mean,D_max 243643 4.66 1.7
Others (reset, maintain memory…) 3.27 1.2
Road ID TRONROUT0000000040981188 (mountain) 19692.13 100
Try to add primitive to current sequence 12420 19668.08 99.9
Compute the best fit clothoid 70 18.15 0.1
Primitive merging 12190 15849.87 80.4
Jacobian 62421 12134.77 61.6
Matrix operations 335515 22.53 0.1
Compute Deviations, D_mean,D_max 9423406 887.26 4.5
Others (reset, maintain memory…) 24.05 0.1