多边形网格处理（7）

7. Repairing

Definetion

Problem statement

  • Model repair, removing artifacts from a geometric model, generate output suitable for further processing by downstream applciations that require centain quality guarantees.

Application dependent

  • Depends on the particular application scenario:

    • “models”
    • “artiface”
    • “Suitable for further processing”
  • One application (CAD/CAM)
    • Models, trimmed NURBS surfaces to represent freeform surface geometry
    • Numerical fluid simulations needs a watertight, manifold triangle mesh as input (Downstream applications)
    • Intermediate stage: convert the NURBS surface into a triangle mesh. Introducing meshing artifaces
    • REPAIR: usually a tedious manual post-process

Repairing Guidelines

  • What is the upstream applications? Determines characteristics and defects of input.
  • What is the downstream applications? Determines requirements on output.
  • Based on this information. is it necessary to repair the input?
    • If necessary, is there an algorithm that does it directly?

      • If direct repair is not possibl, can several algorithms be used insequence?

        • If not, there is a gap in the state-of-the-art.

Defects and flaws

  • Isolated vertices and dangling edges (孤立的点和悬挂的边)
  • Singular edges (从流形定义上)
  • Singular vertices
  • Topological noise (tiny handles or tunnels, 环)
  • Orientation
  • Surface holes (Upsteam: Scanner)
  • Gaps (adjacent patches are separated by undesired gaps. Upstream: CAD systems)
  • Degenerate elements (退化的三角形)
  • Self-intersections (tessellation of multipatch CAD models; deformation, composing models out of multiple parts, merging patches reconstructed from partial scans)
  • Sharp feature chamfering (feature chamfering/aliasing)
  • Data noise

Up/Downstream applications

根据数据来源分类

  • 设计的模型

    • nonmanifoldness, gaps, intersections
    • caused by inaccuracies in modeling or produced by description processes.
  • Digitized
    • noise, holes, chamfered features, topological noise
    • due to limitations of the measurement process

根据conversion方法分类

For examples:

  • deviation of each triangulated patch from the original curved surface, gaps, intersections
  • Tessellation, near-degenerate polygons.

Downstream applications

  • Visualization: only significant holes is unaccpetable; noise, gaps and chamfered features can be adverse.
  • Modeling: without degeneracies; intersections are often acceptable; singularities and topological noise do not cause problems for some methods;others require or prefer clean manifold meshes.
  • Rapid prototyping: well-defined an interior and exterior volume; mesh has to be closed and free of intersections and singular non-manifold configurations.
  • Geometry processing: free of denegeracies and noise; aliasing effects like topological noise and chamfered features negatively affect and distrub several of these methods.
  • FEM: The highest requirements.

Types of Inputs

Registered range scans

  • A set of patches that represent overlapping parts of the surface SSS of a scanned object.
  • The main geometric problem: vary large overlap.
  • Each patch has its own connectivity that is usually not compatible to the connectivity of the other patches.

Fused range scans

  • Manifold meshes with boundaries (i.e., gaps, hoels, and islands)
  • Due to obstructions (遮挡) or bad surface properties (transparency or glossiness)

Triangle soups

  • sets of triangles with little or no connectivity information.
  • Due to the manual layout (assemble predefined elemetns without consistency constraints).

Triangulated NURBS patches

  • A set of connected triangle mesh patches.
  • Intersection, inconsistent normal orientations.

Contoured meshes

  • Meshes extracted from a volumetric dataset by MArching Cubes, Dual Contouring or other polygon mesh extraction algorithms.
  • Topological artifacts. Due to finite resolution.

Badly meshed manifolds

  • Degenerate elements (triangles, needles, triangle flips)
  • From tessellation of CAD models or output of Marching Cubes.

Approaches

Surface-oriented algorithms (基于曲面的)

  • Operate directly on the input data
  • Minimally perturb the input model (局部的)
  • Gaps, sanpping boundary elements (stitching)
  • Holes, filling
  • Intersection, explicitly splitting edges and triangles locally

Downside

  • Require the input model already satisfy certain quality requirements (网格质量已经较好，失真类型比较单一或局部)
  • 极少是全自动的，需要用户交互和人工后处理。
  • Due to numerical inaccuracies, certain types of artifacts cannot be resolved rebustly (intersections, large overlaps) 甚至会引入新的artifacts
  • Other artifaces, like gaps between two seperate solids cannot event be identified.

Consistent normal orientation

  • Consistently orienting the normals of an input moedl is part of most surface-oriented repair algorithms.
  • Usually the orientationof the normal is propagated along a minimum spanning tree between neighboring patches.

Surface-based Hole-filling

  • Smooth triangulation of a hole.

    • First, identify the holes and filled by a coarse triagulation.
    • Then, refine the patches (vertex densities, average edge lengths match the surroundings)
    • Finally, smoothed so as to blend with the geometry of the surounding mesh.

Conversion to manifolds

  • Identify all complex edges and singular vertices by counting the number of adjacent faces
  • Cut along these complex edges into separate manifold patches.

Gap closing

  • Identify gaps (the area between the pair of boundary edges).
  • Score measures.
  • Merged

Topology simplification

  • Detects handles
  • Remove the handles by cutting the input along a non-separating closed path and sealing the two resulting holes by triangle patches.

Volumetric algorithms

  • 把输入模型转换为itermediate volumetric representation，再把网格提取出来

    • 先把网格嵌入到体素等其他空间，grids，octrees，kd-trees，BSP-trees，Delaunay triangulations等
    • 处理
    • 提取
  • 体里面不会有空洞、自相交等。
  • 但是，体里面还有handles。此外，conversion带来信息丢失、还有连接关系的破坏。
  • 需要体素的数量比较多，提取的网格的密度大于输入网格的密度。
  • 用Marching cubes提取的网格质量较差，需要后处理。
  • 内存开销较大。

Volumetric repair on regular grids

  • Cartesian voxel grid

Volumetric repair on adaptive grids

  • Create an adaptive octree representation.
  • A sequence of morphological operations.
  • Reconstruction from the octree structure and samples.

Volumetric repair with BSP-trees

Volumetric repair on the dual grid

Summary

  • hybrid methods are receiving more and more attention.
  • Removal of self-intersections.
  • Is model repair a necessity that will disappear?
  • Automatic vs User interaction.

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