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The difference can be imperative with respect to manufacturability. It is often necessary to know whether a mesh is a closed mesh which represents a volumetric solid, or an open mesh that just represents a 2-dimensional surface. As an analogy, consider that even though we can store the equation of a line on a computer, in order to display that line, the computer must at some point convert the line into a series of discrete pixels on a screen to display. Non-manifold geometry is essentially geometry that cannot exist in the "real world". In Grasshopper, the two basic types of information required to define a mesh are geometry and connectivity; in other words, a set of points in rhino-space vertices and set of corresponding point-associations faces. The Mesh Edges component can be used to help determine this. Zooming into a NURBS surface retains a smooth curve, while a mesh element has a fixed resolution It is interesting to note that while NURBs surfaces are stored as mathematical equations, the actual visualization of these surfaces requires meshes. Without connectivity information, a mesh is unstructured and therefore still undefined. Meshes, on the other hand, are comprised of a discrete number of exactly defined vertices and faces. A mesh is considered Grand Jester Online Slot | PLAY NOW | StarGames Casino if there are well-defined sides to the mesh. These 'flipped faces' can cause problems in visualizations and renderings, as well as manufacturing or 3D-printing. This does not necessarily make it "bad geometry" but it is something to be aware of due to complications it may present for tools and operations for example: Some modeling software therefore treats the UV coordinates of a mesh vertex as an attribute like vertex color which can be manipulated and changed. There must be a dynamically updated rendering of a form that is changing in shape but not in face connectivity A discretized approximation of a curved geometry would suffice A low-resolution geometry must be systematically smoothed or articlated using computational methods to arrive at a higher-resolution model. Solid mesh geometry is also required for Boolean operations discussed in following section. The lack of UV coordinates, however, allows meshes the flexibility to handle more complicated geometry with a single mesh, instead of resorting to a polysurface in the case of NURBS. A mesh can also be considered Non-Manifold if it includes any vertices which are shared by faces that do not share edges or any edges with a valence greater than 2, creating a junction of at least 3 faces. Non-manifold geometry is essentially geometry that cannot exist in the "real world". The same set of vertices can have different connectivity information, resulting in different topology. Manifold vs Non-Manifold Non-manifold geometry is essentially geometry that cannot exist in the "real world". These are usually assigned and not completely defined by the mesh itself. Homeomorphism The points of a mesh can be moved without altering the connectivity information.

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