© 2017 Copyright held by the owner/author(s). In this work we present separate procedural methods to generate features that are found in natural terrains which are difficult to reproduce with heightmap-based methods. We approximate overhangs, arches and caves using procedural functions and a reduced set of parameters. This produces visually plausible terrain feature topologies as well as a high degree of artistic control. Our approach is more intuitive and art-directable than other existing volumetric methods that are more complex to integrate into existing voxel engines, due to the framework changes necessary, or rely on automatic procedural generation, thus reducing the ability to provide creative input

Dey, R.

Doig, J.G.

Gatzidis, Christos

Rahul Dey

Jason G. Doig

Christos Gatzidis

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Procedural feature generation for volumetric terrains

Bournemouth University Research Online

Procedural Feature Generation for Volumetric TerrainsRahul DeyBournemouth University & SonyInteractive Entertainment Euro R&D13 Great Marlborough StreetLondon, UK W1F 7HPi7697909@bournemouth.ac.ukJason G. DoigSony Interactive Entertainment EuroR&D13 Great Marlborough StreetLondon, UK W1F 7HPJason.Doig@sony.comChristos GatzidisBournemouth University, Faculty ofScience and Technology, CreativeTechnology DepartmentPoole House, Talbot CampusPoole, Dorset, UK BH12 5BBcgatzidis@bournemouth.ac.ukFigure 1: Procedurally generated features with our method: arches (left), an overhang (middle) and a cave (right).ABSTRACTIn this work we present separate procedural methods to generatefeatures that are found in natural terrains which are difficult toreproduce with heightmap-based methods. We approximate over-hangs, arches and caves using procedural functions and a reducedset of parameters. This produces visually plausible terrain featuretopologies as well as a high degree of artistic control. Our approachis more intuitive and art-directable than other existing volumetricmethods that are more complex to integrate into existing voxelengines, due to the framework changes necessary, or rely on auto-matic procedural generation, thus reducing the ability to providecreative input.CCS CONCEPTS•Theory of computation→Computational geometry; •Com-puting methodologies→ Real-time simulation; Volumetricmodels; Shape modeling;KEYWORDSProcedural generation, Terrain, VolumetricACM Reference format:Rahul Dey, Jason G. Doig, and Christos Gatzidis. 2017. Procedural FeatureGeneration for Volumetric Terrains. In Proceedings of SIGGRAPH ’17 Posters,Los Angeles, CA, USA, July 30 - August 03, 2017, 2 pages.DOI: 10.1145/3102163.3102216Permission to make digital or hard copies of part or all of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for third-party components of this work must be honored.For all other uses, contact the owner/author(s).SIGGRAPH ’17 Posters, Los Angeles, CA, USA© 2017 Copyright held by the owner/author(s). 978-1-4503-5015-0/17/07.DOI: 10.1145/3102163.31022161 INTRODUCTIONTerrains are a key feature for portraying realistic virtual outdoorenvironments. Current methods often use heightmap-based terrainrepresentations, where a 2D displacement map perturbs verticeson a polygonal grid. However, heightmaps do not allow for specificfeatures of terrains such as cliffs, naturally-formed arches and caves.In contrast, volumetric representations of terrains are not limited inany such way and are gaining traction in practical applications suchas procedurally generated computer games. This work presentsprocedural methods for generating features that are found in real-world terrains and can be complex to represent using heightmap-based methods.Existing methods for creating overhangs have applied vector dis-placement to output vertices of heightmap-based terrains [Gamitoand Musgrave 2001], though this work relies on unintuitive manip-ulation of the vector field data to achieve desired results. A hybridapproach introduced by [Peytavie et al. 2009] uses a signed-distancefield to construct the terrain mesh. While implicit surfaces allow formany operations to be performed on the mesh, generating implicitfunctions can be computationally expensive. Recently, [Becher et al.2017] presented the concept of voxelizing input feature curves toform the terrain mesh, allowing the formation of features suchas overhangs and arches. However, our method generates a set oflocal delta values that can be applied directly to the volumetric data,which eliminates the need for a voxelization step.2 OUR APPROACHThis work has been produced for integration into Sony InteractiveEntertainment’s proprietary game engine PhyreEngineTM and pro-poses a procedural method for each of the three main features foundin terrains by directly acting on the underlying volume represen-tation. It extends prior work with voxel grammars where terrainsSIGGRAPH ’17 Posters, July 30 - August 03, 2017, Los Angeles, CA, USA R. Dey et. al.are generated using a set of transforms [Dey et al. nd]. These trans-forms are a set of voxel replacements and the features described inthis work here have been developed as more intuitive extensions.Overhangs and arches are functions that generate a set of local vox-els that can be additively blended with the existing data to createthe desired topologies. The cave generation method is a subtractivefunction utilising a particle-based approach that produces a setof negative density values removing voxels in the terrain (whenblended). The user begins with either an empty or initialised voxeldataset. They can then add either overhangs, arches or caves whichare layered on top of the existing data to ensure the editing is non-destructive. The parameters for the features are set, an optionaltransformation matrix (translation and rotation) is applied to thefeature and the resulting voxel values are submitted to the GPUfor surface extraction and rendering. Each feature has user-defineddimensions in voxels (Fdim ) and the index of each voxel (I ) beingprocessed is calculated as the unit cube coordinates of the currentvoxel (Vindex ) within the feature’s bounding box (I =VindexFdim).2.1 Overhang GenerationCliffs and overhangs are constructed by approximating their topol-ogy as a bicubic Bézier surface. A Bézier surface (S(u,v)) uses a 4x4geometry matrix (G) of vectors containing the control points of thesurface. The second and third rows of control points act as erosionparameters to the resulting overhang. The final surface functionis combined with a parabolic function (P(u)) using a user-definedexponent (k) to emulate realistic plateaus and is shown in Equation1, where u = Iz and v = 1 − Iy .U =[1 u u2 u3]V =[1 v v2 v3]B =1 0 0 0−3 3 0 03 −6 3 0−1 3 −3 1S(u,v) = U · B ·G · BT ·VTP(u) = (4u · (1 − u))kDClif f (u,v) ={1, if Ix < min(S(u,v), P(u))0, otherwise(1)2.2 Arch GenerationArches are created by sweeping a sphere along a cubic Bézier spline,with the four control points governing the resultant shape. Each endof the arch has optional tapering parameters (radius multipliers (Mi )and exponents (Ei )), as well as interpolants (Ii ) to define where thetapering occurs. This results in feasible natural arches simulatinggreater erosion towards the middle of the arch. At each step of thesweep (t ), the radius (r ) is updated using the tapering parameters(Ti ). This uses the function in Equation 2 whereV is the voxel beingprocessed and P is the position of a voxel after the radius has beenapplied at the current step.Ti = r ·Mi · (1 − IEii )radius = r +T0 +T1DArch (V , P) ={1, if ∥P −V ∥ < radius0, otherwise(2)2.3 Cave GenerationIn order to generate cave-like structures, we adopt a particle-basedapproach where a sphere is traced in a user-specified direction for aset number of iterations. A decay parameter (λ) reduces the radiusof the sphere for each iteration. At each step (t ), the direction (D) isfurther affected by gravity (G) and a velocity vector (U ) generatedby curl noise [Bridson et al. 2007]. This efficiently computes aviable estimation of speleological erosion, reducing the need for acomplex fluid dynamics system sculpting the internal structure ofthe cave. The position (P ) and radius (r ) of the particle are used tocheck whether a voxel is within the sphere, and therefore subjectto removal, using Equation 3.P(t) = P + t · (D +G +U )r (t) = r − tλDCave (V , P , r ) ={0, if ∥P −V ∥ < r1, otherwise(3)3 EXPERIMENTAL RESULTSWe have implemented these methods using a sparse voxel buffer.However, any underlying volumetric representation can be used asour methods are independent of any data structure, meaning thatintegration into existing procedural volumetric engines is trivialassuming the voxel data can be read from and written to. The meshis extracted from the volumetric data using surface nets [Gibson1998]. Initial results can be seen in Figure 1 and show features inte-grated with a terrain generated using Perlin noise. For future work,we are developing GPU accelerated feature generators to createmore detailed, large scale features at higher voxel resolutions andmaintain interactive rates in order to maximise design efficiency.4 ACKNOWLEDGEMENTSWe thank the EPSRC-funded Centre of Digital Entertainment project(EP/G037736/1) and Sony Interactive Entertainment Euro R&D fortheir support plus NVIDIA Corporation for hardware donations.REFERENCESMichael Becher, Michael Krone, Guido Reina, and Thomas Ertl. 2017. Feature-basedVolumetric Terrain Generation. Proceedings of the 21st ACM SIGGRAPH Symposiumon Interactive 3D Graphics and Games, Article 10, 10:1–10:9 pages. DOI:https://doi.org/10.1145/3023368.3023383Robert Bridson, JimHourihan, andMarcus Nordenstam. 2007. Curl-noise for proceduralfluid flow. ACM Transactions on Graphics (TOG) 26, 3, 46.Rahul Dey, Jason G. Doig, and Christos Gatzidis. n.d.. Procedural Terrain Generationwith Voxel Grammars. Submitted to Computer Animation and Virtual Worlds (n.d.).Manuel N Gamito and F KentonMusgrave. 2001. Procedural landscapes with overhangs.10th Portuguese Computer Graphics Meeting 2, 3.Sarah Gibson. 1998. Constrained elastic surface nets: Generating smooth surfacesfrom binary segmented data. Medical Image Computing and Computer-AssistedIntervention MICCAI98 (1998), 888–898.Adrien Peytavie, Eric Galin, Jérôme Grosjean, and Stéphane Mérillou. 2009. Arches: aFramework for Modeling Complex Terrains. Computer Graphics Forum 28, 2 (Apr2009), 457–467. DOI:https://doi.org/10.1111/j.1467-8659.2009.01385.x

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