3.0 - Meshes Flashcards
What do Meshes consist of?
Vertices, Edges and Faces
Structural Engineering uses of meshes, name 4…
- Finite Element Analysis
- Regular diameter and spacing of rebar meshes
- Meshes of steel ties for roofs
- Gridshells
Name 3 more from other disciplines…
- Computer Graphics (e.g. games)
- Medical Imaging
- Terrain/Topography
- Photo realistic and real-time rendering
- Additive Manufacturing
- Simulation of bodies for physics engines
Name the 3 Different Mesh Types…
- Tri-Mesh (Triangular)
- Quad-Mesh (4 sided)
- NGon/Poly-mesh (Mixture of Tri & Quad)
How are Vertices and Face stored?
Vertices are the same as networks (using index then coordinate).
Faces use the index and then the vertices that create the face (in the correct cyclic order).
How are edges stored?
The index is followed by the the vertices in the direction that they are connected.
What are half edges and how are they stored?
Splits edges in half so faces that share an edge can be independently generated.
The direction is important - still cyclic but two half edges between the same vertices must travel in opposite directions.
What are the positives of halfedges?
- Guaruntees consistency
- More computationally efficient
What is the biggest downside to half edge data structure and what alternative can be used?
Can only have 2 faces per edge.
The alternative datastructure is called a Winged-Edge Mesh (not discussed as its complex)
What do single half edges represent?
Boundaries and holes in meshes as only physical faces are mapped.
What can be done to make it easier to query any vertex?
By adding the face index next to the Vertex Index to Coordinate Data Structure:
{0: [1,0], [0]
1: [1,1], [0,2]
…
How can face edges be used to identify what edges surround what face.
Start at one vertex and work your way round the half-edges:
1-2 then 2-0 then 0-1 will match a face index if one is present.
What is the difference between a Structured and Unstructured Mesh?
Structured Mesh - Vertices and faces are laid out in a regular, mathematical or parametric grid (either in Cartesian or polar/spherical coordinates).
Unstructured Mesh - Doesn’t have any regularity and is often triangulated with mesh refinement near to corners or sharp edges (therefore range of face sizes).
How does the Delaunay Triangulation method work?
No vertex is inside the circles formed by another set of 3 vertices.
This creates triangles of maximum internal angles (good for FEE).
NB: Can be done in 3D using spheres.
What is Ruppert’s Algorithm and how can it produce accurate FEE results?
It is a refinement of Delaunay Triangulation but produces faces that are more equilateral.
Can only define boundary vertices with triangles contructed internally.
Any thin triangles have new points placed at centre.
A minimum internal angle can be imposed (15-20 degrees usually gives a good mesh).
