Surface Triangulation Methods: From 2D to 3D

A Progressive Guide to Point Cloud & Mesh Reconstruction

Xin trân trọng cảm ơn PGS. TS. Nguyễn Tấn Khôi – giảng viên môn Mô hình hoá hình học (Đại học Bách khoa Đà Nẵng) – người đã truyền cảm hứng và định hướng tư duy, tạo động lực để tôi xây dựng repository này.

I would like to express my sincere gratitude to Assoc. Prof. Dr. Nguyễn Tấn Khôi, lecturer of Geometric Modeling at the University of Science and Technology – The University of Danang, whose inspiration and guidance motivated me to build this repository.

Authored by: Tran Nhat Minh

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📚 Table of Contents

1. Overview
2. 2D/2.5D Methods
3. 3D Foundation Methods
4. 3D Reconstruction Methods
5. Specialized Methods
6. Decision Guide

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🎓 Overview

Evolution of Methods

2D/2.5D (1970s-1980s)
    ↓
Delaunay 2D → Heightmaps
    ↓
3D Foundation (1980s-1990s)
    ↓
Convex Hull → Alpha Shapes → Delaunay 3D
    ↓
3D Reconstruction (1990s-2000s)
    ↓
Ball Pivoting → Greedy Projection
    ↓
Modern (2000s-Present)
    ↓
Poisson → Screened Poisson → Neural Methods

[PLACEHOLDER: Evolution timeline diagram]

Quick Comparison Table

Method	Era	Speed	Quality	Watertight	Complexity	Best For
Delaunay 2D	1970s	⚡⚡⚡⚡⚡	⭐⭐⭐	❌	⭐	Terrain
Heightmap	1980s	⚡⚡⚡⚡⚡	⭐⭐⭐	❌	⭐	Grid data
Convex Hull	1980s	⚡⚡⚡⚡⚡	⭐	✅	⭐	Bounding
Delaunay 3D	1980s	⚡⚡⚡⚡	⭐⭐	✅	⭐⭐	Foundation
Alpha Shapes	1994	⚡⚡⚡⚡	⭐⭐⭐⭐	⚠️	⭐⭐	Boundaries
Ball Pivoting	1999	⚡⚡⚡⚡	⭐⭐⭐⭐	⚠️	⭐⭐	Dense scans
Poisson	2006	⚡⚡	⭐⭐⭐⭐⭐	✅	⭐⭐⭐	High quality
Screened Poisson	2013	⚡⚡	⭐⭐⭐⭐⭐	✅	⭐⭐⭐	State-of-art
Marching Cubes	1987	⚡⚡⚡	⭐⭐⭐⭐⭐	✅	⭐⭐	Volume data

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📐 2D/2.5D Methods

When to use: Flat data, terrain, maps, elevation data

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1. Delaunay 2D Triangulation

[PLACEHOLDER: Delaunay 2D example - points to triangles]

📊 Overview

Property	Value
Year	1934 (Delaunay), 1970s (Computational)
Complexity	O(n log n)
Paradigm	Optimal 2D triangulation
Parameters	None (deterministic)

🎯 Core Principle

Delaunay Criterion: Maximize minimum angle → No point inside any triangle's circumcircle

Good Triangle (Delaunay)     Bad Triangle (Non-Delaunay)
       ●                            ●
      ╱ ╲                          ╱ ╲
     ╱   ╲                        ╱ ● ╲  ← Point in circle!
    ●─────●                      ●─────●

[PLACEHOLDER: Circumcircle criterion visualization]

✅ Strengths

• Mathematically optimal: Maximize minimum angle
• Extremely fast: < 1s for 10K points
• Deterministic: Same input → same output
• No parameters: No tuning needed
• Dual of Voronoi: Rich mathematical properties

❌ Weaknesses

• 2D ONLY: Cannot handle true 3D
• Projection loss: 3D → 2D loses information
• No overhangs: Z must be single-valued
• Wrong for 3D objects: Creates incorrect triangles

🔄 Evolution

Delaunay 2D (1970s)
    ↓
Constrained Delaunay (1980s) ← Can force edges
    ↓
Delaunay 3D (1990s) ← Tetrahedra
    ↓
Alpha Shapes (1994) ← Filtered Delaunay

💡 Key Insight

Delaunay 2D is the foundation for many modern methods:

• Alpha Shapes filter Delaunay tetrahedra
• Constrained Delaunay adds constraints
• 3D Delaunay extends to tetrahedra

[PLACEHOLDER: Delaunay family tree diagram]

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2. Constrained Delaunay Triangulation

[PLACEHOLDER: CDT with forced edges highlighted]

📊 Overview

Property	Value
Year	1980s
Base	Delaunay 2D + Constraints
Parameters	Edge constraints, holes

🎯 Core Advancement

Standard Delaunay: Free triangulation Constrained Delaunay: Must preserve specified edges

Standard:                Constrained:
  ●───●                    ●───●
  │╲ ╱│                    │ ╱ │  ← Must keep this edge
  │ ╳ │    →               │╱  │
  │╱ ╲│                    ●───●
  ●───●

✅ Strengths (vs Standard Delaunay)

• Feature preservation: Roads, rivers, boundaries
• Hole support: Can create holes
• Multi-region: Handle islands

❌ Weaknesses (vs Standard Delaunay)

• Loses optimality: No longer maximizes angles
• More complex: Requires constraint input
• Still 2D only: Same limitations as base

🔄 Evolution to Delaunay 2D

Adds: Edge constraints, hole specification Keeps: Delaunay property where possible

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3. Heightmap / Grid Triangulation

[PLACEHOLDER: Regular grid to mesh]

📊 Overview

Property	Value
Year	1980s
Paradigm	Regular grid structure
Key Parameter	Grid resolution (20-512)

🎯 Core Principle

Regular grid of heights → Two triangles per cell

Grid:          Mesh:
4─5─6         4─5─6
│ │ │         │╱│╱│
1─2─3    →    1─2─3

✅ Strengths

• Extremely fast: No complex computation
• Game engine friendly: Regular structure
• Easy UV mapping: Grid → textures
• Simple LOD: Easy level-of-detail
• Memory efficient: Predictable structure

❌ Weaknesses

• Only Z=f(X,Y): Single-valued function
• No overhangs: Cannot handle cliffs, caves
• Uniform waste: Grid cells even where flat
• Interpolation artifacts: Cubic can create ripples

🔄 Evolution vs Delaunay

Delaunay 2D: Adaptive, irregular triangles Heightmap: Regular, uniform grid

Trade-off: Simplicity vs adaptivity

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🧊 3D Foundation Methods

When to use: True 3D data, complex geometry

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4. Convex Hull 3D

[PLACEHOLDER: Point cloud → convex hull]

📊 Overview

Property	Value
Year	1970s-1980s
Complexity	O(n log n)
Paradigm	Smallest convex envelope
Parameters	None (unique solution)

🎯 Core Principle

Convex Hull = Smallest convex shape containing all points

Like "shrink-wrapping" but ONLY convex surface.

✅ Strengths

• Extremely fast: O(n log n)
• Always watertight: Guaranteed closed
• Deterministic: Unique solution
• Never fails: Robust algorithm
• Foundation: Base for other methods

❌ Weaknesses

• Loses ALL concavity: Only convex
• Not shape-preserving: Creates new geometry
• Limited use: Only bounding volumes

🔄 Evolution Path

Convex Hull (1970s)
    ↓
Alpha Shapes (1994) ← Allows non-convex
    ↓
Power Crust (2001) ← Better thin features

💡 Key Insight

Convex Hull is the upper bound of all shape approximations:

• Alpha Shapes: α→∞ = Convex Hull
• Any tighter fit must be non-convex

[PLACEHOLDER: Alpha spectrum from tight to convex hull]

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5. Alpha Shapes

[PLACEHOLDER: Different alpha values comparison]

📊 Overview

Property	Value
Year	1994 (Edelsbrunner & Mücke)
Base	Delaunay 3D + Filtering
Key Parameter	Alpha (radius)
Complexity	O(n²) worst case

🎯 Core Principle

Alpha Shapes = Delaunay 3D tetrahedra + size filter

α → 0:    Points only
α small:  Detailed, holes
α medium: Shape outline
α → ∞:    Convex Hull

🔬 Algorithm Evolution

Delaunay 3D (base):

1. Create ALL tetrahedra (fills volume)
2. Result: Convex hull

Alpha Shapes (improvement):

1. Create ALL tetrahedra (same as Delaunay)
2. Filter: Remove "large" tetrahedra (α threshold)
3. Extract boundary
4. Result: Non-convex shape

✅ Strengths (vs Delaunay 3D)

• Non-convex: Captures concavities
• Adjustable detail: α parameter
• No spurious connections: Filters unwanted triangles
• Well-studied: Strong theory

❌ Weaknesses (vs Delaunay 3D)

• Parameter tuning: Needs α selection
• Not always watertight: May have holes
• Multiple components: Can fragment
• Still derivative: Based on Delaunay

🔄 Relationship to Delaunay 3D

	Delaunay 3D	Alpha Shapes
Tetrahedra	All kept	Filtered by α
Result	Convex hull	Non-convex possible
Parameters	None	Alpha (critical)
Output	Unique	Varies with α

💡 Alpha Selection

Formula: α = mean_edge_length × multiplier

Multiplier	Effect	Use Case
1.5	Very tight	Max detail
2.5	Balanced ⭐	Most cases
4.0	Loose	Gap filling
6.0+	Very loose	Near convex

[PLACEHOLDER: Alpha parameter effect series]

🔄 Evolution from Alpha Shapes

Alpha Shapes (1994)
    ↓
Weighted Alpha Shapes (2000s) ← Non-uniform points
    ↓
Robust Cocone (2002) ← Better normals
    ↓
Power Crust (2001) ← Thin features

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6. Delaunay 3D Tetrahedralization

[PLACEHOLDER: Tetrahedra filling space]

📊 Overview

Property	Value
Year	1980s-1990s
Output	Volume tetrahedra
Surface	Convex hull (boundary)

🎯 Core Principle

Extend 2D Delaunay to 3D:

• 2D: Triangles
• 3D: Tetrahedra (4 vertices each)

✅ Strengths

• 3D foundation: Base for many methods
• Well-studied: Rich theory
• Efficient: O(n log n) expected

❌ Weaknesses

• Only convex surface: Same as convex hull
• Not directly useful: Needs post-processing
• Volume filling: Creates interior tetrahedra

💡 Role in Ecosystem

Delaunay 3D is NOT a standalone method - it's a building block:

Delaunay 3D Tetrahedra
    ↓
Used by:
  • Alpha Shapes (filter tetrahedra)
  • Power Crust (medial axis)
  • Cocone (normal estimation)
  • Natural Neighbor (interpolation)

🔄 Relationship Map

Delaunay 2D ──extends──> Delaunay 3D
                              │
                    filters by size
                              ↓
                         Alpha Shapes
                              │
                    adds weighting
                              ↓
                    Weighted Alpha Shapes

[PLACEHOLDER: Delaunay family relationship diagram]

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🏗️ 3D Reconstruction Methods

When to use: Point clouds needing surface reconstruction

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7. Ball Pivoting Algorithm (BPA)

[PLACEHOLDER: Ball rolling animation]

📊 Overview

Property	Value
Year	1999 (Bernardini et al.)
Paradigm	Local geometric growth
Key Parameters	Ball radii (3 values typical)
Complexity	O(n) expected

🎯 Core Principle

Imagine a ball rolling on point cloud:

1. Ball touches 3 points → create triangle
2. Pivot around edge to find next point
3. Repeat until complete

Step 1: Seed      Step 2: Pivot     Step 3: Grow
  ●─────●           ●─────●           ●────●─────●
   ╲ ○ ╱             ╲ │○╱             ╲  ╱│╲ ○ ╱
    ╲ ╱               ╲│╱               ╲╱ │ ╲╱
     ●                 ●──●              ●───●

✅ Strengths

• Fast: 5-10× faster than Poisson
• Geometry preserving: No new vertices
• Natural results: No over-smoothing
• Low memory: No voxelization
• Simple concept: Easy to understand

❌ Weaknesses

• Requires uniform density: Points must be evenly spaced
• Cannot fill holes: Only connects existing points
• Radius sensitive: Wrong radii → poor results
• Not watertight: Depends on data completeness
• Needs normals: Or must estimate

🔄 Evolution

Ball Pivoting (1999) ← Original
    ↓
Variations:
  • Adaptive BPA (2000s) ← Variable radii
  • Parallel BPA (2010s) ← GPU acceleration
  • Robust BPA (2010s) ← Noise handling

💡 Radius Selection

Critical parameter: Ball size

Radius Type	Formula	Use Case
Small	avg_nn × 1.5	Details
Medium	avg_nn × 2.5 ⭐	Main structure
Large	avg_nn × 4.0	Gap filling

Typical: Use 3 radii: [small, medium, large]

[PLACEHOLDER: Different radii comparison]

🆚 vs Alpha Shapes

	Ball Pivoting	Alpha Shapes
Approach	Local growth	Global → filter
Speed	Faster	Slower
Quality	Natural	Adjustable
Foundation	Direct geometry	Delaunay-based

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8. Greedy Projection Triangulation

[PLACEHOLDER: Greedy growth visualization]

📊 Overview

Property	Value
Year	2000s
Paradigm	Greedy frontier expansion
Base	Similar to BPA but different strategy

🎯 Core Principle

Greedy expansion from seed triangle:

1. Start with one triangle
2. For each edge on frontier: find best next point
3. Add triangle greedily (locally optimal)
4. Repeat

Like BPA but:
  BPA: Ball constraint (geometric)
  Greedy: Best angle (heuristic)

✅ Strengths (vs BPA)

• Simpler parameters: No radius tuning
• Faster in some cases: Greedy is quick
• More flexible: Adapts to density

❌ Weaknesses (vs BPA)

• Less robust: Greedy can fail
• Quality varies: No geometric guarantee
• Not widely used: BPA more popular
• Still needs normals: Same as BPA

🔄 Position in Evolution

Ball Pivoting (1999)
    ↓
Greedy Projection (2000s) ← Alternative approach
    ↓
Both influenced by:
    ↓
Advancing Front (CFD mesh generation)

💡 Use Case

Greedy Projection is a variant, not evolution:

• Use BPA for most cases (more robust)
• Use Greedy if BPA radius tuning fails

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9. Poisson Surface Reconstruction

[PLACEHOLDER: Smooth watertight result]

📊 Overview

Property	Value
Year	2006 (Kazhdan, Bolitho, Hoppe)
Paradigm	Global optimization (PDE solver)
Key Parameters	Depth (8-11), density threshold
Complexity	O(n log n) with octree

🎯 Core Principle

Mathematical elegance: Solve Poisson equation

Problem: Point cloud + normals
         ↓
Formulate: ∇·N = ∇·∇χ = Δχ  (Poisson equation)
         ↓
Solve: Find indicator function χ
         ↓
Extract: Isosurface at χ = 0.5

Physical intuition: Normals are "vector field" → Find surface whose gradient matches

[PLACEHOLDER: Poisson concept - vector field to surface]

🔬 Technical Breakthrough

Key innovations:

1. Octree spatial structure: Adaptive resolution
2. Global optimization: Not local like BPA
3. Watertight guarantee: Always closed surface
4. Automatic hole filling: Implicit in formulation

✅ Strengths

• Highest quality: Globally optimal
• Always watertight: Guaranteed
• Automatic hole filling: No manual intervention
• Noise robust: With proper parameters
• Mathematically rigorous: PDE-based

❌ Weaknesses

• Slow: Depth 10 can take minutes
• Memory intensive: High depth needs RAM
• Requires good normals: Critical input
• May create geometry: Can add artifacts
• Parameter sensitive: Needs tuning

⚙️ Key Parameters

1. Depth (Most Critical)

Controls octree resolution:

Depth	Grid	Quality	Speed	Use Case
8	256³	⭐⭐⭐	⚡⚡⚡	Preview
9	512³	⭐⭐⭐⭐	⚡⚡	Standard ⭐
10	1024³	⭐⭐⭐⭐⭐	⚡	High quality
11	2048³	⭐⭐⭐⭐⭐	🐢	Research

[PLACEHOLDER: Depth comparison visual]

2. Density Threshold

Filters low-density regions:

Threshold	Effect	Use Case
0.01	Keep detail	Clean data
0.05	Balanced ⭐	Standard
0.10	Heavy filter	Noisy data

🔄 Evolution

Poisson (2006) ← Original, globally optimal
    ↓
Streaming Poisson (2007) ← Large datasets
    ↓
Screened Poisson (2013) ← Better data fit
    ↓
Parallel Poisson (2010s) ← GPU acceleration

💡 Revolutionary Impact

Before Poisson: Messy, holes, manual work After Poisson: Smooth, watertight, automatic

Influence: 3D scanning, reconstruction, printing

[PLACEHOLDER: Before/after Poisson revolution comparison]

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10. Screened Poisson Reconstruction

[PLACEHOLDER: Screened vs standard comparison]

📊 Overview

Property	Value
Year	2013 (Kazhdan & Hoppe)
Base	Poisson + Screening term
Key Addition	Data fitting term

🎯 Core Advancement

Standard Poisson equation:

Δχ = ∇·N

Screened Poisson equation:

Δχ + λP = ∇·N + λP
     ↑
  Screening term: Pull surface toward data

Physical meaning:

• Poisson: Smooth global solution
• Screened: Smooth + close to input data

✅ Improvements Over Standard Poisson

• Better data fidelity: Stays closer to input
• Less over-smoothing: Preserves details
• Fewer artifacts: Less spurious geometry
• Still watertight: Maintains closure
• Same speed: No performance cost

❌ Weaknesses (Same as Poisson)

• Still slow for large datasets
• Still needs good normals
• Still parameter sensitive

🆚 When to Use Each

Use Poisson When	Use Screened Poisson When
Data very noisy	Data relatively clean
Need maximum smooth	Need preserve detail
Large holes to fill	Small gaps only
Medical imaging	3D scanning

🔄 Evolution Path

Poisson (2006)
    ↓
Observation: Sometimes too smooth
    ↓
Screened Poisson (2013) ← Add data term
    ↓
Current state-of-the-art for PDE-based reconstruction

💡 State-of-the-art Status

Screened Poisson is currently the best PDE-based method for:

• High-quality 3D scanning
• Photogrammetry
• LiDAR reconstruction
• Any application needing watertight + detailed

[PLACEHOLDER: Quality comparison across methods]

---

🎛️ Specialized Methods

11. Marching Cubes

[PLACEHOLDER: Volume to surface extraction]

📊 Overview

Property	Value
Year	1987 (Lorensen & Cline)
Domain	Volume data (voxels)
Input	3D scalar field
Output	Isosurface mesh

🎯 Core Principle

Extract surface from volume data:

1. Divide space into cubes (voxels)
2. For each cube: check which corners are inside/outside
3. Use lookup table (256 cases) to create triangles
4. Assemble into mesh

Volume Data → Threshold → Triangle cases → Mesh

✅ Strengths

• Guaranteed watertight: Always closed
• Handles any topology: Genus-n surfaces
• Well-studied: Decades of refinement
• Efficient: Linear in voxels

❌ Weaknesses

• Requires volume data: Not for point clouds
• Memory intensive: O(resolution³)
• Staircase artifacts: At low resolution
• Many triangles: Can be inefficient

🔄 Evolution

Marching Cubes (1987) ← Original
    ↓
Marching Tetrahedra (1991) ← Simpler cases
    ↓
Dual Contouring (2002) ← Sharp features
    ↓
Flying Edges (2015) ← Faster algorithm

💡 Domain

Different domain than other methods:

• Most methods: Point cloud → Surface
• Marching Cubes: Volume → Surface

Use for: Medical imaging (CT/MRI), implicit surfaces, signed distance fields

[PLACEHOLDER: Medical imaging example]

---

12. Power Crust

📊 Overview

Property	Value
Year	2001 (Amenta et al.)
Base	Weighted Voronoi
Status	Research, less practical

🎯 Core Concept

Uses medial axis transform:

• Compute "poles" (furthest Voronoi vertices)
• Power diagram on poles
• Extract crust

✅ Strengths (Theoretical)

• Better thin features than Alpha Shapes
• Provable guarantees
• Good for theory

❌ Weaknesses (Practical)

• Complex implementation
• Not in standard libraries
• Superseded by Poisson for practical use

💡 Historical Importance

Power Crust showed that provable reconstruction is possible, but Poisson is more practical.

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🎯 Decision Guide

Quick Decision Tree

START

Is data 2D/2.5D (terrain, flat)?
├─ YES → Delaunay 2D or Heightmap
└─ NO → Continue

Is data volumetric (voxels)?
├─ YES → Marching Cubes
└─ NO → Continue

Need FAST preview?
├─ YES → Ball Pivoting or Alpha Shapes
└─ NO → Continue

Need WATERTIGHT (3D printing, simulation)?
├─ CRITICAL → Poisson or Screened Poisson
└─ NOT CRITICAL → Continue

Is point cloud DENSE and UNIFORM?
├─ YES → Ball Pivoting (fast, accurate)
└─ NO → Poisson (robust, quality)

DEFAULT: Try Ball Pivoting → If unsatisfied → Poisson

[PLACEHOLDER: Interactive flowchart]

---

Method Selection Matrix

By Data Type

Data Type	First Choice	Second Choice	Avoid
Terrain/DEM	Heightmap	Delaunay 2D	Ball Pivoting
Dense 3D scan	Ball Pivoting	Screened Poisson	Delaunay 2D
Sparse points	Alpha Shapes	Poisson (low depth)	Ball Pivoting
Medical CT/MRI	Marching Cubes	Poisson	Heightmap
Photogrammetry	Screened Poisson	Ball Pivoting	Delaunay 2D
Game terrain	Heightmap	-	Poisson (slow)
3D printing	Screened Poisson	Poisson	Any non-watertight

By Priority

Speed ⚡:

1. Convex Hull / Delaunay 2D
2. Heightmap
3. Alpha Shapes
4. Ball Pivoting

Quality 🏆:

1. Screened Poisson (depth 10)
2. Standard Poisson (depth 10)
3. Ball Pivoting (well-tuned)
4. Alpha Shapes

Watertight ✅:

1. Screened Poisson
2. Standard Poisson
3. Marching Cubes

---

Evolution Summary

2D/2.5D Timeline

1970s: Delaunay 2D
  ↓
1980s: Constrained Delaunay, Heightmaps
  ↓
Still used today for terrain, GIS

3D Foundation Timeline

1980s: Convex Hull, Delaunay 3D
  ↓
1994: Alpha Shapes ← Major advancement
  ↓
2001: Power Crust ← Theoretical peak

3D Reconstruction Timeline

1987: Marching Cubes ← Volume domain
  ↓
1999: Ball Pivoting ← Fast, practical
  ↓
2006: Poisson ← Quality revolution
  ↓
2013: Screened Poisson ← Current state-of-art
  ↓
2020s: Neural methods (future)

[PLACEHOLDER: Complete timeline visualization]

---

Key Insights

Paradigm Shifts

1. 1970s-1980s: Geometric algorithms (Delaunay, Convex Hull)
2. 1990s: Refinement (Alpha Shapes, BPA)
3. 2000s: Global optimization (Poisson)
4. 2010s: Refinement (Screened Poisson)
5. 2020s: Learning-based (Neural implicit surfaces)

Trade-offs

Axis	Fast End	Quality End
Speed vs Quality	Delaunay, BPA	Poisson depth 10
Local vs Global	BPA, Alpha	Poisson
Simple vs Complex	Convex Hull	Screened Poisson
Memory	BPA	Poisson depth 11

Method Relationships

Delaunay 2D ─extends─> Delaunay 3D ─filters─> Alpha Shapes
                            │
                            └─surface─> Convex Hull

Ball Pivoting ──similar──> Greedy Projection

Poisson ──improves─> Screened Poisson

Marching Cubes ← Different domain (volume)

[PLACEHOLDER: Method relationship graph]

---

📚 Summary

Core Methods (Must Know)

1. Delaunay 2D: Foundation of 2D triangulation
2. Alpha Shapes: Non-convex 3D boundaries
3. Ball Pivoting: Fast 3D reconstruction
4. Poisson: Quality 3D reconstruction
5. Screened Poisson: State-of-the-art

Historical Impact

Method	Impact
Delaunay 2D	Foundation of computational geometry
Alpha Shapes	Made non-convex reconstruction practical
Ball Pivoting	Made fast 3D scanning viable
Poisson	Revolutionized reconstruction quality
Screened Poisson	Current state-of-the-art

Future Directions

Current: PDE-based (Poisson family)
    ↓
Emerging: Neural implicit surfaces
    • Neural Radiance Fields (NeRF)
    • Occupancy Networks
    • DeepSDF
    ↓
Future: Hybrid approaches
    • Classical + Learning
    • Best of both worlds

---

🎨 Image Placeholders

Images needed:

1. Evolution timeline diagram
2. Delaunay 2D step-by-step
3. Circumcircle criterion
4. Alpha shapes spectrum (different α)
5. Ball pivoting animation
6. Poisson depth comparison (8, 9, 10)
7. Screened vs standard Poisson
8. Method relationship graph
9. Decision flowchart
10. Quality comparison gallery
11. Use case examples per method
12. Before/after reconstructions

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Version: 2.0 Last Updated: 2026-02-05 Scope: Comprehensive overview from 2D to state-of-the-art 3D

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