Meshes

- Light weight flexible alternative to NURBS
- Used in everything from rendering, visualization, digital fabrication, 3d printing
- Made up of mesh triangles or mesh quads – no more than 4 sides are allowed

What is a mesh

- collection of triangles/quadrilaterals that represent surface or solid geometry
- made up of
- vertices – points of a mesh, a list in grasshopper
- edges – (Valence = # Edges a face is adjacent to)
- Valence 1 – naked edge, external boundary of mesh
- Valence 2 – interior edges
- Valence 3 – non-manifold edges, geometry that cannot exist in the real world.

- faces – polygons, an ordered list of 3-4 vertices.
- mesh traingle
- mesh quad

- colors
- normals
- of vertices
- of faces

How to create a mesh

- Geometry – a list of vertices
- Connectivity – a system of grouping those vertices in to faces
- From NURBS – using Mesh Surface or Mesh Brep component

Why Meshes?

- Joining NURBS will result in a polysurface, with different sections of the geometry having different UV parameters and curve defitions
- Geometry cannot be defined by simple UV coordinates, and since faces are discrete, the amount of precision is built into the mesh. Lack of UV coordinates allows meshes to handle more complicated geometry.

Why NURBS?

- When curvature or smoothness must be represented with high fidelity
- Geometry must be converted into a manufactured solid
- final form must be able to be easily edited manually

Mesh operations

- Smoothing – can be achieved by increasing number of faces in process of subdividing.
- Strength
- # of iterations
- displacement limit

- Blur – only affects vertex colors, and used to reduce jagged appearance of colored meshes.
- Triangulate – each quad face is replaced with two triangle faces
- Weld – vertices are shared, combining them into one.