Basic Methods Used to Create Surface Models

Most surface modeling softwares are programmed with a matrix/list of an object’s or a part’s vertices and how they are linked to one another to form edges in the CAD database which can mathematically generate surfaces (from points, lines, and curves) between an object’s vertices.

During the process of creating surface models, some surface modelers save additional information that defines and indicates the inner/inside and outer/outside parts of a surface.

This is often accomplished by saving a “surface normal”—a leading or directional line that is normal or perpendicular to the outer part of the surface. This feature makes it easy to shade and render the model.

The basic methods used to create surface models, are as follows:

  • Extrusion and revolution
  • Mesh surfaces or meshes
  • NURBS-based surfaces, or spline approximations

1. Extrusion and revolution

It’s possible to define a surface by using a 2D shape or profile and the axis or course about which it revolves (circles around or moves about in an orbit) or extrudes (forms or takes shape by forcing through an opening).

Figures 1 and 2 below show a surface model that is created by revolution, and the axis of revolution and profile used to create it. Surface primitives (such as cylinders, planes, and cones) are sometimes used as building blocks and can be created from the revolution or extrusion of regular geometric entities.

Figure 1

Figure 1

Figure 2

Figure 2

The surface model (figure 1) above was created by revolving the profile (figure 2) about the axis (same figure 2). (Source: Technical Drawing with Engineering Graphics, 15th edition.)

2. Mesh surfaces or meshes

In the CAD database, vertices or matrix of vertices are used to define flat plane surfaces, and the 3D location of each vertex defines each individual mesh surface. Below, figure 5 shows the matrix/list of a mesh’s vertices, while figures 3 and 4 show the wireframe view and rendered view, respectively.

Mesh surfaces are very important in modeling uneven surfaces in which it isn’t necessary to use completely smooth surfaces. Instead of producing a mesh surface with a slightly bumpy appearance, some CAD modeling packages allow users to define surfaces by a smoothed representation.

Figure 3

Figure 3

Figure 4

Figure 4

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593, 6177,5594

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595, 6177,6601

596, 6177,6611

597, 6177,6621

598, 6177,6621

599, 6177,6616

600, 6177, 6611

601, 6177,6606

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Figure 5

A Mesh Surface: A mesh surface comprises a series of planar surfaces that are defined by a matrix or list of vertices (figure 5), a wireframe view (figure 3), and a rendered view (figure 4). (Source: Technical Drawing with Engineering Graphics, 15th edition.)

3. NURBS-based surfaces, or spline approximations

The mathematics that is behind and guides non-uniform rational B-spline curves also forms the basis for the method which is used to create surface models and surfaces in most surface modelling systems.

A set of vertices (in 3D) that are used to mathematically define smooth surfaces, are also used to define non-uniform rational B-spline (NURBS) surfaces.

The advantage that the surface modelers who use NURBS have is that, because rational curves and surfaces can be used to generate both free-form curves and analytical forms (such as cylinders, planes, lines, and arcs), the CAD database doesn’t necessarily have to be equipped with different techniques for creating surfaces by using a surface primitive, revolution, extrusion, or mesh.

Some extruded and revolved surfaces can be “lofted” or “swept”, and spline curves can be used as program or input for extruded and revolved surfaces.

“Lofting” is a term used to define any surface that fits into a series of curves that don’t intersect or meet at any point with each other. On the other hand, “sweeping” is a process whereby a surface is created by sweeping a cross section or curve along one or more “paths”.

In both cases—lofting or sweeping—the overall surface merges from the shape of one curve to the shape of the next curve, as shown in figures 6 and 7 below.

Figure 6

Figure 6

Figure 7

Figure 7

A lofted surface (figure 6) merges a series of curves that don’t intersect into a smooth surface, while a swept surface (figure 7) sweeps a cross section or curve along a curved path and merges the characteristics of both into a smooth surface model (Source: Technical Drawing with Engineering Graphics, 15th edition.)

Figure 8

Figure 8

Figure 9

Figure 9

NURBS surfaces can also be created by meshing curves that are perpendicular or cut across each other, as shown in figure 8 and 9 above. (Source: Technical Drawing with Engineering Graphics, 15th edition.)

Note

If you want to create a surface model, you don’t have to create an entire surface at once. Only entities (technically referred to as “patches”) would be enough, but you have to combine the entities or patches into a continuous model and to create complex surfaces.

Each patch can be approximated or interpolated just like a spline curve can, and surface patches are connected together by employing mathematical methods to merge the approximated edges of the patches and eventually create smooth joints.

It is important to note that sometimes or where necessary, trimming is used to create complex surface patches. For instance, a modeler might start out with a circular patch but trim it to a triangular patch and eventually merge it with other surface patches.

Some surface modeling systems use Boolean operations, while others don’t. It can be difficult to use the systems that don’t employ Boolean operations (or proficient tools for trimming surfaces) to create a feature such as a rectangular hole through a curved surface because the exact shape of the surface and hole has to be defined by assigning or fixing its edges.

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