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Journal articles on the topic 'Terrain following'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 January 2023

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1

Huskić, Goran, Sebastian Buck, Matthieu Herrb, Simon Lacroix, and Andreas Zell. "High-speed path following control of skid-steered vehicles." International Journal of Robotics Research 38, no. 9 (July 2019): 1124–48. http://dx.doi.org/10.1177/0278364919859634.

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We present a robust control scheme for skid-steered vehicles that enables high-speed path following on challenging terrains. First, a kinematic model with experimentally identified parameters is constructed to describe the terrain-dependent motion of skid-steered vehicles. Using Lyapunov theory, a nonlinear control law is defined, guaranteeing the convergence of the vehicle to the path. To allow smooth and accurate motion at higher speeds, an additional linear velocity control scheme is proposed, which takes actuator saturation, path following error, and reachable curvatures into account. The combined solution is experimentally evaluated and compared against two state-of-the-art algorithms, by using two different robots on several different terrain types, at different speeds. A Robotnik Summit XL robot is tested on three different terrain types and two different paths at speeds up to [Formula: see text] m/s. A Segway RMP 440 robot is tested on three different terrain types and two different path types at speeds up to [Formula: see text] m/s.

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2

Lee, Hyunju, Sunghyun Hahn, Sangchul Lee, Sangil Lee, and Kwansik Seo. "A Study on Terrain Profile Generation for Terrain Following." Journal of the Korean Society for Aeronautical & Space Sciences 51, no. 1 (January 31, 2023): 49–56. http://dx.doi.org/10.5139/jksas.2023.51.1.49.

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3

Nachbin, André. "A Terrain-Following Boussinesq System." SIAM Journal on Applied Mathematics 63, no. 3 (January 2003): 905–22. http://dx.doi.org/10.1137/s0036139901397583.

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4

Xu, Qin, and Jie Cao. "Semibalance Model in Terrain-Following Coordinates." Journal of the Atmospheric Sciences 69, no. 7 (July 1, 2012): 2201–6. http://dx.doi.org/10.1175/jas-d-12-012.1.

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Abstract By partitioning the hydrostatically balanced flow into a nonlinearly balanced primary-flow part and a remaining secondary-flow part and then truncating the secondary-flow vorticity advection and stretching–tilting terms in the vector vorticity equation, the previous semibalance model (SBM) in pseudoheight coordinates is rederived in terrain-following pressure coordinates, called η coordinates. The involved truncation is topologically the same as that in pseudoheight coordinates but the truncated terms in η coordinates are not equivalent to those in pseudoheight coordinates. Because its potential vorticity (PV) is conserved and invertible, the rederived SBM is suitable for studying balanced dynamics via “PV thinking” in real weather events, such as slowly varying vortices and curved fronts in which the primary-flow velocity and secondary-flow vorticity are nearly parallel in η coordinates.

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5

Humi, M. "Long's equation in terrain following coordinates." Nonlinear Processes in Geophysics 16, no. 4 (August 7, 2009): 533–41. http://dx.doi.org/10.5194/npg-16-533-2009.

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Abstract. Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorporates the terrain as part of the differential equation rather than the geometry of the domain. This new formulation enables us to compute analytically steady state gravity wave patterns over complex topography in some limiting cases of the parameters that appear in this equation.

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6

Decker, Steven G. "Nonlinear Balance in Terrain-Following Coordinates." Monthly Weather Review 138, no. 2 (February 1, 2010): 605–24. http://dx.doi.org/10.1175/2009mwr2971.1.

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Abstract Potential vorticity (PV) is a powerful concept in geophysical fluid dynamics. One property of PV that makes it so powerful is that it may be inverted under certain conditions, one of which is the imposition of a balance constraint. Previous studies have made use of a particular nonlinear balance constraint suited to isobaric coordinates as part of their inversion procedures. The present study constructs and tests a new nonlinear balance constraint that may be applied directly to the output of the Weather Research and Forecasting (WRF) model on its native terrain-following vertical coordinate. Output from the nonlinear balance operator is examined in the context of idealized and real-data WRF forecasts, and the results indicate that the simplifications necessary to derive the nonlinear balance operator are justified on the synoptic and meso-α scales. On the other hand, once the scales resolved by the model are small enough, neglected terms reach magnitudes on the order of the retained terms, even over flat terrain. This suggests that the use of this operator within a PV inversion scheme that also uses the WRF vertical coordinate would not capture a divergent portion of the flow that may be significant.

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7

SATOH, Yuki, and Masafumi MIWA. "UAV terrain following flight using RTK-GPS." Proceedings of Conference of Chugoku-Shikoku Branch 2021.59 (2021): 10a2. http://dx.doi.org/10.1299/jsmecs.2021.59.10a2.

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8

Restle, M., W. Grimm, and T. Kopfstedt. "Terrain Optimized Nonholonomic Following of Vehicle Tracks." IFAC Proceedings Volumes 43, no. 16 (2010): 264–69. http://dx.doi.org/10.3182/20100906-3-it-2019.00047.

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9

SATOH, Yuki, and Masafumi MIWA. "UAV terrain following flight using RTK-GPS." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2021 (2021): 1P3—B06. http://dx.doi.org/10.1299/jsmermd.2021.1p3-b06.

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10

Menon, P. K. A., E. Kim, and V. H. L. Cheng. "Optimal trajectory synthesis for terrain-following flight." Journal of Guidance, Control, and Dynamics 14, no. 4 (July 1991): 807–13. http://dx.doi.org/10.2514/3.20716.

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11

Samar, Raza, and Abdur Rehman. "Autonomous terrain-following for unmanned air vehicles." Mechatronics 21, no. 5 (August 2011): 844–60. http://dx.doi.org/10.1016/j.mechatronics.2010.09.010.

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12

Yi-Yuan, Li, Wang Bin, and Wang Dong-Hai. "Characteristics of a Terrain-Following Sigma Coordinate." Atmospheric and Oceanic Science Letters 4, no. 3 (January 2011): 157–61. http://dx.doi.org/10.1080/16742834.2011.11446922.

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13

Cao, Jie, and Qin Xu. "Computing Hydrostatic Potential Vorticity in Terrain-Following Coordinates." Monthly Weather Review 139, no. 9 (September 2011): 2955–61. http://dx.doi.org/10.1175/mwr-d-11-00083.1.

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The hydrostatic potential vorticity (HPV) formulated in terrain-following coordinates is reviewed and shown to be equivalent to the widely used HPV formulations in the height, pressure, and isentropic coordinates in the sense that they all represent the same HPV substance and retain the same conservation property. The HPV formulation in terrain-following coordinates can be applied directly to model-simulated velocity and thermodynamic fields on the model’s original terrain-following grid to avoid coordinate transformation and eliminate grid interpolation error. This advantage and its significance are demonstrated by a numerical example.

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14

Klemp, J. B. "A Terrain-Following Coordinate with Smoothed Coordinate Surfaces." Monthly Weather Review 139, no. 7 (July 1, 2011): 2163–69. http://dx.doi.org/10.1175/mwr-d-10-05046.1.

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Abstract An alternative form for a height-based terrain-following coordinate is presented here that progressively smoothes the coordinate surfaces with height to remove smaller scale (steeper) terrain structure from the surfaces. Testing this approach in comparison with traditional and hybrid terrain-following formulations in resting-atmosphere simulations demonstrates that it can significantly reduce artificial circulations caused by inaccuracies in the horizontal pressure gradient term. The simulations also suggest that some further improvement in the accuracy of the horizontal pressure gradient terms can be achieved using a simplified version of Mahrer’s approach, which can be implemented with little increase in computational cost or complexity.

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15

Bagherian, Mehri. "Unmanned Aerial Vehicle Terrain Following/Terrain Avoidance/Threat Avoidance trajectory planning using fuzzy logic." Journal of Intelligent & Fuzzy Systems 34, no. 3 (March 22, 2018): 1791–99. http://dx.doi.org/10.3233/jifs-161977.

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16

Melita, Carmelo Donato, Dario Calogero Guastella, Luciano Cantelli, Giuseppe Di Marco, Irene Minio, and Giovanni Muscato. "Low-Altitude Terrain-Following Flight Planning for Multirotors." Drones 4, no. 2 (June 25, 2020): 26. http://dx.doi.org/10.3390/drones4020026.

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Surveying with unmanned aerial vehicles flying close to the terrain is crucial for the collection of details that are not visible when flying at higher altitudes. This type of missions can be applied in several scenarios such as search and rescue, precision agriculture, and environmental monitoring, to name a few. We present a strategy for the generation of low-altitude trajectories for terrain following. The trajectory is generated taking into account the morphology of the area of interest, represented as a georeferenced Digital Surface Model (DSM), while ensuring a safe separation from any obstacle. The surface model of the scenario is created by using a UAV-based photogrammetry software, which processes the images acquired during a preliminary mission at high altitude. The solution was developed, tested, and verified both in simulation and in real scenarios with a multirotor equipped with low-cost sensing. The experimental results proved the validity of the generation of trajectories at altitudes lower than most of the works available in the literature. The images acquired during the low-altitude mission were processed to obtain a high-resolution reconstruction of the area as a representative application result.

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17

Zacharias, Greg L., Alper K. Caglayan, and John B. Sinacori. "A visual cueing model for terrain-following applications." Journal of Guidance, Control, and Dynamics 8, no. 2 (March 1985): 201–7. http://dx.doi.org/10.2514/3.19960.

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18

Wei, Yang, Chun-Lin Shen, and Peter Dorato. "U-parameter design for terrain-following flight control." Journal of Guidance, Control, and Dynamics 16, no. 2 (March 1993): 387–89. http://dx.doi.org/10.2514/3.21015.

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19

Lu, Ping, and Bion L. Pierson. "Optimal aircraft terrain-following analysis and trajectory generation." Journal of Guidance, Control, and Dynamics 18, no. 3 (May 1995): 555–60. http://dx.doi.org/10.2514/3.21422.

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20

Rahim, Mohammad, and Seyed Móhammad‐Bagher Malaek. "Aircraft terrain following flights based on fuzzy logic." Aircraft Engineering and Aerospace Technology 83, no. 2 (March 21, 2011): 94–104. http://dx.doi.org/10.1108/00022661111120980.

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21

Yu, Jie. "A terrain-following model of wave boundary layers." Ocean Modelling 108 (December 2016): 20–29. http://dx.doi.org/10.1016/j.ocemod.2016.11.001.

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22

Williams, Paul. "Optimal terrain-following for towed-aerial-cable sensors." Multibody System Dynamics 16, no. 4 (December 5, 2006): 351–74. http://dx.doi.org/10.1007/s11044-006-9030-6.

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23

Garratt, Matthew A., and Javaan S. Chahl. "Vision-based terrain following for an unmanned rotorcraft." Journal of Field Robotics 25, no. 4-5 (2008): 284–301. http://dx.doi.org/10.1002/rob.20239.

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24

Zou, Xun, Yiyuan Li, Jinxi Li, and Bin Wang. "Advection errors in an orthogonal terrain-following coordinate: idealized 2-D experiments using steep terrains." Atmospheric Science Letters 17, no. 3 (February 24, 2016): 243–50. http://dx.doi.org/10.1002/asl.650.

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25

Rédl, Jozef, Veronika Váliková, and Ján Antl. "Modelling of Terrain Surface." Acta Technologica Agriculturae 17, no. 1 (March 1, 2014): 17–20. http://dx.doi.org/10.2478/ata-2014-0004.

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Abstract In this contribution, we deal with the methodology of visualisation of terrain surface, on which experimental measurements of driving manoeuvres of an agricultural technological vehicle MT8-222 were performed. The introduced methodology uses a defined approach when determining the dynamic stability of agricultural vehicles following the standard STN 47 017. Records of the centre of gravity accelerations were obtained from driving manoeuvres at every instance of time during the drive. From records of accelerations and by using Euler‘s parameters with respect to the inertial system, there were evaluated contact points of the wheel with the terrain. Performed driving manoeuvres consisted of movement in the direction of down grade slope as well as in the direction of tractive movement on the slope. We created a model of terrain surface in the Surfer® program from obtained experimental data. Next, by using supporting commands in Matlab®, we created an algorithm for visualisation of terrain surface. Following this algorithm, there was created another model of terrain surface. Both visualisations of terrain surface are depicted in Figs 4 and 5.

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26

Barfield, A. F., J. Probert, and D. Browning. "All terrain ground collision avoidance and maneuvering terrain following for automated low level night attack." IEEE Aerospace and Electronic Systems Magazine 8, no. 3 (March 1993): 40–47. http://dx.doi.org/10.1109/62.199820.

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27

Bao, Jingyi, Fotini Katopodes Chow, and Katherine A. Lundquist. "Large-Eddy Simulation over Complex Terrain Using an Improved Immersed Boundary Method in the Weather Research and Forecasting Model." Monthly Weather Review 146, no. 9 (August 10, 2018): 2781–97. http://dx.doi.org/10.1175/mwr-d-18-0067.1.

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Abstract The Weather Research and Forecasting (WRF) Model is increasingly being used for higher-resolution atmospheric simulations over complex terrain. With increased resolution, resolved terrain slopes become steeper, and the native terrain-following coordinates used in WRF result in numerical errors and instability. The immersed boundary method (IBM) uses a nonconformal grid with the terrain surface represented through interpolated forcing terms. Lundquist et al.’s WRF-IBM implementation eliminates the limitations of WRF’s terrain-following coordinate and was previously validated with a no-slip boundary condition for urban simulations and idealized terrain. This paper describes the implementation of a log-law boundary condition into WRF-IBM to extend its applicability to general atmospheric complex terrain simulations. The implementation of the improved WRF-IBM boundary condition is validated for neutral flow over flat terrain and the complex terrain cases of Askervein Hill, Scotland, and Bolund Hill, Denmark. First, comparisons are made to similarity theory and standard WRF results for the flat terrain case. Then, simulations of flow over the moderately sloped Askervein Hill are used to demonstrate agreement between the IBM and terrain-following WRF results, as well as agreement with observations. Finally, Bolund Hill simulations show that WRF-IBM can handle steep topography (standard WRF fails) and compares well to observations. Overall, the new WRF-IBM boundary condition shows improved performance, though the leeside representation of the flow can be potentially further improved.

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28

Li, Jinxi, Jie Zheng, Jiang Zhu, Fangxin Fang, Christopher Pain, Jürgen Steppeler, Michael Navon, and Hang Xiao. "Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains." Atmosphere 9, no. 11 (November 13, 2018): 444. http://dx.doi.org/10.3390/atmos9110444.

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Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs.

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29

Sharma, T., P. Williams, C. Bil, and A. Eberhard. "Optimal three dimensional aircraft terrain following and collision avoidance." ANZIAM Journal 48 (June 26, 2007): 695. http://dx.doi.org/10.21914/anziamj.v47i0.1071.

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30

Li, Y., B. Wang, and D. Wang. "An orthogonal curvilinear terrain-following coordinate for atmospheric models." Geoscientific Model Development Discussions 6, no. 4 (November 27, 2013): 5801–62. http://dx.doi.org/10.5194/gmdd-6-5801-2013.

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Abstract. We have designed an orthogonal curvilinear terrain-following coordinate (the orthogonal σ coordinate, or the OS coordinate) to overcome two well-known problems in the classic σ coordinate, namely, pressure gradient force (PGF) errors and advection errors. First, in the design of basis vectors, we rotate the basis vectors of the z coordinate in a particular way in order to reduce the PGF errors and add a special rotation parameter b to each rotation angel in order to reduce the advection errors. Second, the corresponding definition of each OS coordinate is solved through its basis vectors. Third, the scalar equations of the OS coordinate are solved by expanding the vector equation using the basis vectors. Since the computational form of PGF has only one term in each momentum equation of the OS coordinate, the PGF errors will be significantly reduced, according to Li et al. (2012). When a proper b is chosen, the σ levels over a steep terrain can be significantly smoothed, therefore alleviating the advection errors in the OS coordinate. This is demonstrated by a series of 2-D linear advection experiments under a unified framework.

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31

Lu, Ping, and Bion L. Pierson. "Optimal aircraft terrain-following flight with nonlinear engine dynamics." Journal of Guidance, Control, and Dynamics 19, no. 1 (January 1996): 240–42. http://dx.doi.org/10.2514/3.21604.

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32

Williams, Paul. "Aircraft Trajectory Planning for Terrain Following Incorporating Actuator Constraints." Journal of Aircraft 42, no. 5 (September 2005): 1358–61. http://dx.doi.org/10.2514/1.17811.

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33

Li, Dong-Mei, Di Zhou, Zhen-Kun Hu, and Heng-Zhang Hu. "Design of Optimal Preview Controller for Terrain-Following Flight." TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 44, no. 145 (2001): 142–49. http://dx.doi.org/10.2322/tjsass.44.142.

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34

Klemp, Joseph B., William C. Skamarock, and Oliver Fuhrer. "Numerical Consistency of Metric Terms in Terrain-Following Coordinates." Monthly Weather Review 131, no. 7 (July 2003): 1229–39. http://dx.doi.org/10.1175/1520-0493(2003)131<1229:ncomti>2.0.co;2.

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35

Abdel Moniem, Mohammed, Wahid Kassim, and Abdel Moniem Bilal. "AN INTEGFATED FLIGHT CONTROL SYSTEM PERFORMING TERRAIN FOLLOWING MISSIONS." International Conference on Aerospace Sciences and Aviation Technology 1, CONFERENCE (May 1, 1985): 1–17. http://dx.doi.org/10.21608/asat.1985.26566.

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36

Malaek, S., and A. Kosari. "Novel minimum time trajectory planning in terrain following flights." IEEE Transactions on Aerospace and Electronic Systems 43, no. 1 (January 2007): 2–12. http://dx.doi.org/10.1109/taes.2007.357150.

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37

Pielke, R. A., and J. Cram. "A terrain-following coordinate system?Derivation of diagnostic relationships." Meteorology and Atmospheric Physics 40, no. 4 (1989): 189–93. http://dx.doi.org/10.1007/bf01032459.

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38

Kim, Kangsoo, Takumi Sato, and Atsuo Oono. "Depth-based pseudo-terrain-following navigation for cruising AUVs." Control Engineering Practice 131 (February 2023): 105379. http://dx.doi.org/10.1016/j.conengprac.2022.105379.

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39

Lundquist, Katherine A., Fotini Katopodes Chow, and Julie K. Lundquist. "An Immersed Boundary Method for the Weather Research and Forecasting Model." Monthly Weather Review 138, no. 3 (March 1, 2010): 796–817. http://dx.doi.org/10.1175/2009mwr2990.1.

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Abstract This paper describes an immersed boundary method that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Mesoscale models, such as WRF, are increasingly used for high-resolution simulations, particularly in complex terrain, but errors associated with terrain-following coordinates degrade the accuracy of the solution. The use of an alternative-gridding technique, known as an immersed boundary method, alleviates coordinate transformation errors and eliminates restrictions on terrain slope that currently limit mesoscale models to slowly varying terrain. Simulations are presented for canonical cases with shallow terrain slopes, and comparisons between simulations with the native terrain-following coordinates and those using the immersed boundary method show excellent agreement. Validation cases demonstrate the ability of the immersed boundary method to handle both Dirichlet and Neumann boundary conditions. Additionally, realistic surface forcing can be provided at the immersed boundary by atmospheric physics parameterizations, which are modified to include the effects of the immersed terrain. Using the immersed boundary method, the WRF model is capable of simulating highly complex terrain, as demonstrated by a simulation of flow over an urban skyline.

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40

Shaw, James, and Hilary Weller. "Comparison of Terrain-Following and Cut-Cell Grids Using a Nonhydrostatic Model." Monthly Weather Review 144, no. 6 (May 13, 2016): 2085–99. http://dx.doi.org/10.1175/mwr-d-15-0226.1.

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Abstract Terrain-following coordinates are widely used in operational models but the cut-cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite-volume model enables a like-for-like comparison of terrain-following and cut-cell grids. A series of standard two-dimensional tests using idealized terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain-following coordinate surfaces. These new tests present a challenge on cut-cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain-following velocity fields lead to errors on cut-cell grids. Because of semi-implicit time stepping and an upwind-biased, explicit advection scheme, there are no time step restrictions associated with small cut cells. In contradiction to other studies, no significant advantages of cut cells or smoothed coordinates are found.

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41

Kazemifar, Omid, Ali-Reza Babaei, and Mahdi Mortazavi. "Online aircraft velocity and normal acceleration planning for rough terrain following." Aeronautical Journal 121, no. 1244 (June 23, 2017): 1561–77. http://dx.doi.org/10.1017/aer.2017.27.

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ABSTRACTThis paper attempts to develop an efficient online algorithm for terrain following in completely unknown rough terrain environments while incorporating aircraft dynamics in the guidance strategy. Unlike most existing works, the proposed algorithm does not generate the flight path directly. The algorithm employs acquired information from the vehicle onboard sensors and rapidly issues appropriate Guidance Commands (GCs) at every point along the way. A suitable dynamic model is developed which takes the lags in the vehicle dynamics into account. The flight path forms gradually as a result of applying the GCs to the vehicle dynamics. Terrain-conforming capability afforded by this approach allows for autonomous and safe low-level flight in unknown mountainous areas. It considerably enhances the autonomy level of the vehicle and in the case of manned aircraft could significantly lead to pilot workload reduction. The proposed scheme is proven to be promising for online applications.

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42

Ding, Liang, Hai-bo Gao, Zong-quan Deng, Zhijun Li, Ke-rui Xia, and Guang-ren Duan. "Path-Following Control of Wheeled Planetary Exploration Robots Moving on Deformable Rough Terrain." Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/793526.

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The control of planetary rovers, which are high performance mobile robots that move on deformable rough terrain, is a challenging problem. Taking lateral skid into account, this paper presents a rough terrain model and nonholonomic kinematics model for planetary rovers. An approach is proposed in which the reference path is generated according to the planned path by combining look-ahead distance and path updating distance on the basis of the carrot following method. A path-following strategy for wheeled planetary exploration robots incorporating slip compensation is designed. Simulation results of a four-wheeled robot on deformable rough terrain verify that it can be controlled to follow a planned path with good precision, despite the fact that the wheels will obviously skid and slip.

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43

Warszawski, Korneliusz K., Sławomir S. Nikiel, and Marcin Mrugalski. "Procedural Method for Fast Table Mountains Modelling in Virtual Environments." Applied Sciences 9, no. 11 (June 8, 2019): 2352. http://dx.doi.org/10.3390/app9112352.

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Natural terrains created by long-term erosion processes can sometimes have spectacular forms and shapes. The visible form depends often upon internal geological structure and materials. One of the unique terrain artefacts occur in the form of table mountains and can be observed in the Monument Valley (Colorado Plateau, USA). In the following article a procedural method is considered for terrain modelling of structures, geometrically similar to the mesas and buttes hills. This method is not intended to simulate physically inspired erosion processes, but targets directly the generation of eroded forms. The results can be used as assets by artists and designers. The proposed terrain model is based on a height-field representation extended by materials and its hardness information. The starting point of the technique is the Poisson Faulting algorithm that was originally used to obtain fractional Brownian surfaces. In the modification, the step function as the fault line generator was replaced with a circular one. The obtained geometry was used for materials’ classification and the hardness part of the modelled terrain. The final model was achieved by the erosive modification of geometry according to the materials and its hardness data. The results are similar to the structures observed in nature and are achieved within an acceptable time for real-time interactions.

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44

LI, JinXi, YiYuan LI, Bin WANG, and Xun ZOU. "Advection errors in an orthogonal terrain-following coordinate: Idealized experiments." Chinese Science Bulletin 60, no. 32 (November 1, 2015): 3144–52. http://dx.doi.org/10.1360/n972015-00075.

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45

Livshitz, Arseny, and Moshe Idan. "Preview Control Approach for Laser-Range-Finder-Based Terrain Following." IEEE Transactions on Aerospace and Electronic Systems 56, no. 2 (April 2020): 1318–31. http://dx.doi.org/10.1109/taes.2019.2933955.

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46

Paulino, Nuno, Carlos Silvestre, and Rita Cunha. "Affine Parameter-Dependent Preview Control for Rotorcraft Terrain Following Flight." Journal of Guidance, Control, and Dynamics 29, no. 6 (November 2006): 1350–59. http://dx.doi.org/10.2514/1.19341.

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47

Williams, Paul. "Three-Dimensional Aircraft Terrain-Following via Real-Time Optimal Control." Journal of Guidance, Control, and Dynamics 30, no. 4 (July 2007): 1201–6. http://dx.doi.org/10.2514/1.29145.

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Ezer, Tal, Hernan Arango, and Alexander F. Shchepetkin. "Developments in terrain-following ocean models: intercomparisons of numerical aspects." Ocean Modelling 4, no. 3-4 (June 2002): 249–67. http://dx.doi.org/10.1016/s1463-5003(02)00003-3.

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Chu, Peter C., and Chenwu Fan. "A Terrain-Following Crystal Grid Finite Volume Ocean Circulation Model." Journal of Oceanography 60, no. 6 (November 2004): 945–52. http://dx.doi.org/10.1007/s10872-005-0003-9.

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Shah, Chetan C., Raghu H. Ramakrishnaiah, Sadaf T. Bhutta, Donna N. Parnell-Beasley, and Bruce S. Greenberg. "Imaging findings in 512 children following all-terrain vehicle injuries." Pediatric Radiology 39, no. 7 (March 24, 2009): 677–84. http://dx.doi.org/10.1007/s00247-009-1213-x.

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