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Solid mesh geometry is also required for Boolean operations discussed in following section. Meshes, on the other hand, are comprised of a discrete number of exactly defined vertices and faces. Common conditions that result in a non-manifold mesh include: The network of vertices generally cannot be defined by simple UV coordinates, and because the faces are discrete the amount of precision is built into the mesh and can only be changed by refining the mesh and added more faces. 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. Meshes can be favorable in situations where: In this primer, we are interested in its basic application with respect to parametric workflows that afford us the opportunity to create and control mesh geometry. Meshes can be favorable in situations where: If none of the edges of a mesh have a valence of 1 if the E1 output is null , then we know that all the edges are 'Interior Edges' and the mesh does not have an external boundary edge, and is therefore a closed mesh. 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 new mesh has the same topology as the original. 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. In general, however, moving a single control point in a NURBS surface creates a more global change in geometry. 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. 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. Homeomorphism The points of a mesh can be moved without altering the connectivity information. Meshes can be favorable in situations where: All this would mean is that they are constructed out of the same number of points and that the points are structured by the same set of faces.

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