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Scales and Scale-like Structures Eric Landreneau Scott Schaefer - - PowerPoint PPT Presentation
Scales and Scale-like Structures Eric Landreneau Scott Schaefer - - PowerPoint PPT Presentation
Scales and Scale-like Structures Eric Landreneau Scott Schaefer Texas A&M University Introduction: Natural Phenomena Introduction: Scales Introduction Examples of scales in artwork Usually modeled/painted manually or with ad hoc
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Introduction: Scales
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Examples of scales in artwork
Usually modeled/painted manually or with ad hoc techniques
Introduction
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- Direct modeling of scales – artist creates scales manually
(slow and painstaking)
- Models – places a scale shape at each position, no
connectivity between scales
- Displacement maps – artist paints scales on a model,
displaces height
- Shell maps/mesh quilting – can create 3d geometry, but
problems with borders, seams (based on 2D parameterization)
Previous Work
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Main Objective Given a mesh
Objectives
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Main Objective Grow scales on the surface
Objectives
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Part 1: Scale Placement
Scale Placement
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Scale Placement
- Segment surface into per-scale regions
- Want evenly spaced scales
- Hexagonal arrangement [1]
- Scales need orientation
[1] Kenneth V. Kardong, Vertebrates: Comparative Anatomy, Function, Evolution, McGraw-Hill, 1998.
Scale Placement
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[2] Liu, Y., Wang, W., Lévy, B., Sun, F., Yan, D., Lu, L., and Yang, C. 2009. On centroidal voronoi tessellation—energy smoothness and fast computation. ACM Trans. Graph. 28, 4 (Aug. 2009)
Solution? CVTs (Centroidal Voronoi Tessellations[2])
Scale Placement
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Even distribution of sites
[2] Liu, Y., Wang, W., Lévy, B., Sun, F., Yan, D., Lu, L., and Yang, C. 2009. On centroidal voronoi tessellation—energy smoothness and fast computation. ACM Trans. Graph. 28, 4 (Aug. 2009)
Solution? CVTs (Centroidal Voronoi Tessellations[2])
Scale Placement
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Produces mostly hexagons
[2] Liu, Y., Wang, W., Lévy, B., Sun, F., Yan, D., Lu, L., and Yang, C. 2009. On centroidal voronoi tessellation—energy smoothness and fast computation. ACM Trans. Graph. 28, 4 (Aug. 2009)
Solution? CVTs (Centroidal Voronoi Tessellations[2])
Scale Placement
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Orientation
Determine vector field on surface, and propagate to the Voronoi Tessellation
Scale Placement
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Orientation
Orientations allow for anisotropy
Scale Placement
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How do we guide the CVT?
Scale Placement
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How do we guide the CVT? Solution – use a lateral line
Scale Placement
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Scale Placement
The artist draws the lateral line
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Scale-sites spawn from the lateral line
Scale Placement
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Scale-sites spawn from the lateral line
Scale Placement
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Scale-sites spawn from the lateral line
Scale Placement
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Scale Placement
Vector field initialized from the lateral line’s tangents
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Scale Placement
Vector field initialized from the lateral line’s tangents
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Scale Placement
Initial scale distribution
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Scale Placement
Applying anisotropic Lloyd’s algorithm
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Example of dense CVT
Scale Placement
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Part 2: Scale geometry synthesis
Scale Synthesis
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- Replace scale regions with artist-provided geometry
- Connect geometry together in a watertight fashion
- Conform geometry to original surface
Scale Synthesis
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- Replace scale regions with artist-provided geometry
- Connect geometry together in a watertight fashion
- Conform geometry to original surface
Scale Synthesis
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Cut the proxy model using the boundary of the scale region
Scale Synthesis
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Triangle stitching to match boundary
Scale Synthesis
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Move the cut proxy-model to the mesh, and deform it to fit the surface
Scale Synthesis
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Repeat for each scale region, then connect together to form a watertight network of scales
Scale Synthesis
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Results
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Results
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Results
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Results
High genus scales
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- Does not require a global 2D mesh parameterization
- Allows for arbitrary scales including high-genus or long/thin
shapes incompatible with displacement mapping
- Allows intuitive control through the lateral line
- Provides a watertight, topologically 2-manifold surface well
suited for post-processing such as subdivision and simplification
Conclusions
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