Surfaces

A MESH represents an object's surface using planar facets. The mesh density, or number of facets, is defined in terms of a matrix of M and N vertices, similar to a grid consisting of columns and rows. M and N specify the column and row position, respectively, of any given vertex. You can create meshes in both 2D and 3D, but they are used primarily for 3D.

Use meshes if you need hiding, shading, and rendering capabilities that wireframes don't provide but do not need the physical properties that solids provide (mass, weight, center of gravity, and so on). Meshes are also useful if you want to create geometry with unusual mesh patterns, such as a 3D topographical model of mountainous terrain.

A mesh can be open or closed. A mesh is open in a given direction if the start and end edges of the mesh do not touch, as shown in the following illustrations.

AutoCAD provides several methods for creating meshes. You can enter the mesh parameters manually or use the 3D command, which simplifies the process of creating the basic surface shapes.

Create a Predefined 3D Surface Mesh

The 3D command creates the following 3D shapes: boxes, cones, dishes, domes, meshes, pyramids, spheres, tori (donuts), and wedges. These are meshes that are displayed as wireframes until you use HIDE, RENDER, or SHADEMODE. To view the objects you are creating with the 3D command more clearly, set a viewing direction with 3DORBIT, DVIEW, or VPOINT. The procedures for creating 3D shapes are similar to those for creating 3D solids.

In the following illustrations, the numbers indicate points you specify to create the mesh.

3DMESH

AutoCAD defines a polygon mesh by a matrix, the size of which is determined by M and N size values. M × N equals the number of vertices that you must specify.

Specify location for vertex (0, 0): Enter a 2D or 3D coordinate. AutoCAD defines the location of each vertex in the mesh by m and n, the row and column indices of the vertex. The limit is between 2 and 256 virtex

Create a Rectangular Mesh

With the 3DMESH command, you can create polygon meshes that are open in both the M and N directions (similar to the X and Y axes of an XY plane). You can close the meshes with PEDIT. You can use 3DMESH to construct very irregular surfaces. In most cases, you can use 3DMESH in conjunction with scripts or AutoLISP routines when you know the mesh points.

Create a Polyface Mesh

The PFACE command produces a polyface (polygon) mesh, with each face capable of having numerous vertices.

Creating a polyface mesh is similar to creating a rectangular mesh. To create a polyface mesh, you specify coordinates for its vertices. You then define each face by entering vertex numbers for all the vertices of that face. As you create the polyface mesh, you can set specific edges to be invisible, assign them to layers, or give them colors.

To make the edge invisible, enter the vertex number as a negative value.

You can control the display of invisible edges with the SPLFRAME system variable. If SPLFRAME is set to a nonzero value, the invisible edges become visible and can then be edited. If SPLFRAME is set to 0, the invisible edges remain invisible.

Create a Ruled Surface Mesh

With RULESURF, you can create a surface mesh between two objects. You use two different objects to define the edges of the ruled surface: lines, points, arcs, circles, ellipses, elliptical arcs, 2D polylines, 3D polylines, or splines. Pairs of objects to be used as the "rails" of a ruled surface mesh must both be either open or closed. You can pair a point object with either an open or a closed object.

You can specify any two points on closed curves to complete RULESURF. For open curves, AutoCAD starts construction of the ruled surface based on the locations of the specified points on the curves.

Create a Tabulated Surface Mesh

With the TABSURF command, you can create a surface mesh representing a general tabulated surface defined by a path curve and a direction vector. The path curve can be a line, arc, circle, ellipse, elliptical arc, 2D polyline, 3D polyline, or spline. The direction vector can be a line or an open 2D or 3D polyline. TABSURF creates the mesh as a series of parallel polygons running along a specified path. You must have the original object and the direction vector already drawn, as shown in the following illustrations.

Create a Surface of Revolution Mesh

Use the REVSURF command to create a surface of revolution by rotating a profile of the object about an axis. The axis can be a line or straight PLINE. The Profile can be a LINE, ARC, CIRCLE, PLINE, or SPLINE. REVSURF is useful for surfaces with rotational symmetry. Changes in SURFTAB1 (n) and SURFTAB2 (n) control the smoothness of the surface. The default is n = 6.

Create an Edge-Defined Surface Mesh

With the EDGESURF command, you can create a Coons surface patch mesh, as shown in the following illustration, from four objects called edges. Edges can be arcs, lines, polylines, splines, and elliptical arcs. They MUST form a closed loop and share endpoints. A Coons patch is a bicubic surface (one curve in the M direction and another in the N direction) interpolated between the four edges. Changes in SURFTAB1 (n) and SURFTAB2 (n) control the smoothness of the surface. The default is n = 6.

The variable SURFTYPE controls the tyoe of mathematical formula used to generate the meshes; SURFTYPE (5) uses a Quadratic B-Spline, SURFTYPE (6)uses a Cubic B-Spline and is the default, SURFTYPE (8) uses a Bezier Curve.