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Create Surfaces

May 20, 2011

3D meshes uses planar embedded surfaces as its surface. Defined from the the vertex position of initial mesh network-axis and secondary network-axis (the direction of M and N), in which Vertex of initial mesh network-axis points to the M direction, and N direction points to secondary network-axis. Similar to the function of X and Y axis on XY plane, M and N are designated individually to the vertex position of row and column, Meshes are available both in 2D and 3D spaces, mainly used in 3D spaces.

Meshes can help solving the problem of using features like hide, shade and render other than physical properties (weight, quality, center of gravity) that is unavailable in using wireframe. You can also create irregular geometric drawings with meshes, such as a 3D topographical model of mountainous terrain.

Either closed or open meshes can be created, the following pictures show each meshes open or closed individually in M and N direction:

Various methods are used for creating mesh, both using keyboard way to specify mesh parameter or operating 3D command to draw planar mesh, The size of M and N of a mesh determines the number of lines drawn on each direction.

Create 3D surfaces

You can create a three dimensional face, which consists of a section of a plane in three dimensional space. You define a three dimensional face by specifying the x,y,z coordinates of three or more corners. After you specify the fourth point, the program continues to prompt you for additional faces by alternating prompts for the third point and fourth point to allow you to build a complex three dimensional object. Each three or four sided plane is created as a separate three dimensional face object.

To create a three dimensional face

1. Choose Draw > Surfaces > 3D Face.

2. Specify the first point of the three-dimensional face.

3. Specify the second, third, and fourth points.

4. Specify the third and fourth points for additional faces.

5. To complete the command, press Enter.

Surfaces toolbar

Command line 3DFACE

TIP Any or all edges of a three dimensional face can be invisible to allow you to more accurately model objects with holes in them. As the program prompts you for the corner points, in the prompt box, choose Invisible Edge to make the next edge invisible.

An example of a three dimensional model created using three dimensional faces.

Create 3D Meshes

3D command is widely used for creating objects as boxes, cones, dishes, meshes, pyramids, spheres, donuts and wedges. Before hiding 3D entities, all the meshes are displayed in wireframe.

Use DVIEW or VPOINT to view the entity once you have created a 3D entity, or performed View-3D Orbit from View menu options to view the 3D entity in full perspective. The following picture displays entities as meshes with specified vertexes.

Creating rectangular meshes

You can create a three dimensional rectangular mesh consisting of four sided polygons. You determine the size of the mesh by specifying the number of vertices along the primary (Mdirection) and secondary (N direction) mesh axes and then specifying the coordinates for each vertex.

To create a rectangular mesh

1. Choose Draw > Sufaces > 3D Mesh.

2. Specify the number of vertices along the primary mesh axis.

3. Specify the number of vertices along the secondary mesh axis.

4. Specify the coordinates for each vertex.

5. Specifying the coordinates for the last vertex completes the mesh and ends the command.

Surfaces toolbar

Command line 3DMesh

TIP Although creating rectangular meshes manually can be exacting, they are useful for representing complex surfaces such as three dimensional terrain models. The 3D Mesh tool is most useful when combined with scripts or LISP programs that mathematically calculate the coordinates of the vertices.

An example of a three dimensional terrain model created using rectangular meshes.

The following picture shows the polygon mesh with coordinates specified for each vertex.

Create Polygon Meshes

You can create a polygon mesh consisting of faces connecting three or more vertices.

You first determine the coordinates of each vertex and then define each face by entering the vertex numbers for all the vertices of that face. As you create each face, you can control the visibility and color of each edge and assign each edge to specific layers.

When creating meshes, a positive vertex means an invisible edge. System variable SPLFRAME controlles whether to show the invisible edges or not. If set SPLFRAME on, any assumed surfaces and invisible edges are displayed as those visible meshes.

To create a polyface mesh

1. Type pface and then press Enter.

2. Specify the coordinates of each vertex.

After each vertex that you specify, the next vertex number is displayed, and you are prompted for the coordinates of the vertex. Specify the coordinates, and then press Enter. Continue to specify the coordinates for each numbered vertex.

1. To finish specifying vertex coordinates, press Enter.

2. Specify the vertex numbers that define the first face.You specify the face by entering the vertex numbers that were defined when you specified coordinates in step 2. Each face can be composed of three or more numbered vertices.

3. To finish defining the first face, press Enter.

4. Specify the next face by entering its vertex numbers.

5. To complete the command, press Enter.

Command line PFACE

TIP To make an edge invisible, type the vertex number as a negative value.

Create Ruled Surface

RULESURF creates a polygon mesh representing the ruled surface between two curves. The entities you select define the edges of the ruled surface. The entities include the point, line, spline, circle, arc or polyline. If the first entity is a closed one, the other one must be closed two or a point. If the first entity is a point, the other one should be a closed or open entity. There is only one point as a boundary curve on a ruled surface.

If you select a closed polylines, the ruled surface begins at the last vertex and proceeds backward along the polyline segments. If you select open curves, selecting objects at the same side of the two objects to create ruled surface, selecting objects at different side of the two objects to create crossed ruled surface, shown as follows:

To create a ruled surface mesh

1. Choose Draw > Surfaces > Ruled Surface.

2. Select the first defining object.

3. Select the second defining object.

Surfaces toolbar

Command line RULESURF

 Select the first (A) and second (B) defining objects The resulting ruled surface mesh

TIP To control the density of the mesh, change the values for the Number of M Direction Surfaces. Choose Tools > Draft Settings, and then click the 3D Settings tab. Under Surface Settings, change the Number Of M Direction Surfaces value.

Create Tabulated Surface

Creates a polygon mesh defined by a path and a direction vector.The path curve defines the surface of the polygon mesh. The objects like a line, arc, circle, ellipse, or 2D or 3D polyline can be used as outline curves for defining polygons. Both lines and open 2D or 3D polylines are used as direction vector.

Tabulated surface meshes are used as a serial of paralleled polygon on spec ified path, you should draw direction vector and origine object before creating a Tabulated Surface.

To create an extruded surface mesh

1. Choose Draw > Surfaces > Tabulated Surface.

2. Select the object to extrude.

3. Select the extrusion path.

Surfaces toolbar

Command line TABSURF

 Select the object to extrude (A) and the extrusion path (B) The resulting extruded surface mesh

TIP To control the density of the mesh, change the values for the Number of M Direction Surfaces. Choose Tools > Draft Settings, and then click the 3D Settings tab. Under Surface Settings, change the Number Of M Direction Surfaces.

NOTE An extruded mesh is different from an extruded solid. If you want to extrude an object and convert it to a three dimensional solid, use the Extrude command.

Create Revolved Surfaces

Use REVSURF command to create a surface of revolution by rotating a profile of the object about an axis. The object to be revolved can be a line, arc, circle, ellipse, elliptical arc, closed polyline, polygon, closed spline or torus. REVSURF is useful for surfaces with rotational symmetry.

You can create a surface of revolution, which is a three dimensional polygon mesh that approximates the surface generated by rotating a two dimensional profile around an axis. You select the two objects that define the profile and the axis. You also specify the starting angle and the number of degrees to revolve the profile.

Revolving the profile 360 degrees creates a closed three dimensional mesh. The Number Of M Direction Surfaces value determines the mesh density (the number of mesh segments) in the M direction (around the axis of revolution). The N Direction Mesh Density value determines the mesh density (the number of mesh segments) in the N direction (along the axis of revolution).

To create a revolved surface mesh

1. Choose Draw > Surfaces > Revolved Surface.

2. Select the object to revolve.

3. Select the object to be used as the axis of revolution.

4. Specify the starting angle.

5. Specify the number of degrees to revolve the object.

Surface toolbar

Command line REVSURF

 Select the object to be revolved (A) and the axis of revolution (B) The resulting revolved surface mesh

TIP To control the density of the mesh, change the values for the Number of M Direction Surfaces. Choose Tools > Draft Settings, and then click the 3D Settings tab. Under Surface Settings, change the Number Of M Direction Surfaces.

Create Edge-Defined Surface Meshes

You can create a surface called a Coons surface patch, a mesh connecting four edges.You select the entities that define the edges. Edge entities can be arcs, lines, or polylines. The four edge entities must form a closed loop and share endpoints. A patch is a bicubic surface (one curve extends in the M-direction and the other in the N-direction) interpolated between the four adjoining edges. You can select the edges in any order. The first edge you select determines the M-direction of the mesh.

To create an edge defined Coons surface patch mesh

1. Choose Draw > Surfaces > Edge Surface.

2. Select the first edge.

3. Select the second, third, and fourth edges.

Surface toolbar

Command line EDGESURF

 Select the objects to be used as the four edges (A, B, C, and D) The resulting Coons surface patch mesh

TIP To control the density of the mesh, change the values for the Number of M Direction Surfaces. Choose Tools > Draft Settings, and then click the 3D Settings tab. Under Surface Settings, change the Number Of M Direction Surfaces.

Commands Reference

3DMESH: Creates a free-form polygon mesh

EDGESURF: Creates a three-dimensional polygon mesh

REVSURF: Creates a revolved surface about a selected axis

RULESURF: Creates a ruled surface between two curves

TABSURF: Creates a tabulated surface from a path curve and a direction vector

System Variables Reference

SURFTAB1: Sets the number of tabulations to be generated for the RULESURF and TABSURF commands

SURFTAB2: Sets the mesh density in the N direction for the REVSURF and EDGESURF commands

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