Polygonal 3D Modeling - Common Box and Edge Modeling Workflows

In an earlier article, we introduced seven of the basic 3D modeling techniques used in today's computer graphics industry. While writing that article, we noticed that the sections on box and contour modeling were getting to be quite a bit longer than we intended.

Ultimately, we decided it'd be best to break off the majority of that information into a separate article. In this piece, we'll focus on some the specific tools and processes used in polygonal 3D modeling.

In polygonal modeling, an artist creates a digital representation of a 3D object with a geometric mesh composed of faces, edges, and vertices. Faces are usually quadrilateral or triangular, and make up the surface of the 3D model. Through the use of the following techniques, a modeler methodically transforms a primitive 3D mesh (usually a cube, cylinder, or sphere) into a complete 3D model:

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Extrusion is a method of adding geometry to a polygon primitive, and one of the primary tools a modeler uses to begin shaping a mesh.

Through extrusion a modeler manipulates the 3D mesh by either collapsing a face in upon itself (to create an indentation), or by extruding the face outward along its surface normal—the directional vector perpendicular to the polygonal face.

Extruding a quadrilateral face creates four new polygons to bridge the gap between its starting and ending position. Extrusion can be difficult to visualize without a concrete example:

  • Consider a simple pyramid shape, with a quadrilateral (4-edged) base. A modeler might transform this primitive pyramid into a house-like shape by selecting the base of the pyramid and extruding it in the negative Y direction. The pyramid's base is shifted downward, and four new vertical faces are created in the space between the base and the cap. A similar example might be seen in modeling the legs of a table or chair.
  • Edges can also be extruded. When extruding an edge, it is essentially duplicated—the duplicate edge can then be pulled or rotated away from the original in any direction, with a new polygonal face automatically created connecting the two. This is the primary means for shaping geometry in the contour modeling process.
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Subdivision is a way for modelers to add polygonal resolution to a model, either uniformly or selectively. Because a polygonal model typically starts from a low-resolution primitive with very few faces, it is almost impossible to produce a finished model without at least some level of subdivision.

  • A uniform subdivision divides the entire surface of a model evenly. Uniform subdivisions are usually completed on a linear scale, meaning every polygonal face is subdivided into four. Uniform subdivision helps to eliminate "blockiness," and can be used to evenly smooth the surface of a model.
  • Edge Loops - Resolution can also be added by selectively placing additional edge loops. An edge loop can be added across any contiguous set of polygonal faces, subdividing the selected faces without needlessly adding resolution to the rest of the mesh. Edge loops are typically used to add resolution in regions of a model that require a level of detail disproportionate to nearby geometry (the knee and elbow joints of a character model are a prime example, as are lips and eyes).

    Edge loops can also be used to prepare a surface for extrusion or uniform subdivision. When a surface is uniformely subdivided, any hard edges are rounded and smoothed—if a subdivision is required but the modeler would like to maintain certain hard edges, they can be maintained by placing an edge loop on either side of the edge in question. This same effect can be achieved through the use of a bevel, discussed below.
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Bevels or Chamfers

If you've been around the engineering, industrial design, or woodworking fields at all, the word bevel might already hold some weight for you.

By default, the edges on a 3D model are infinitely sharp—a condition that virtually never occurs in the real world. Look around you. Inspected closely enough, almost every edge you encounter will have some sort of taper or roundness to it.

A bevel or chamfer takes this phenomenon into account, and is used to reduce the harshness of the edges on a 3D model:

  • For example, each edge on a cube occurs at a 90 degree convergence between two polygonal faces. Beveling those edges creates a narrow 45 degree face between the converging planes to soften the edge's appearance and helps the cube interact with light more realistically. The length (or offset) of the bevel, as well its roundness can be determined by the modeler.
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Also referred to as "pushing and pulling vertices," most models require some level of manual refinement. When refining a model, the artist moves individual vertices along the x,y, or z axis to fine tune the contours of the surface.

A sufficient analogy for refinement might be seen in the work of a traditional sculptor: When a sculptor works, he first blocks out the large forms of the sculpture, focusing on the overall shape of his piece. Then he revisits each region of the sculpture with a "rake brush" to fine tune the surface and carve out the necessary details.

Refining a 3D model is very similar. Every extrusion, bevel, edge-loop, or subdivision, is typically accompanied by at least a little bit of vertex-by-vertex refinement.

The refinement stage can be painstaking and probably consumes 90 percent of the total time a modeler spends on a piece. It might only take 30 seconds to place an edge loop, or pull out an extrusion, but it wouldn't be unheard of for a modeler to spend hours refining the nearby surface topology (especially in organic modeling, where surface changes are smooth and subtle).

Refinement is ultimately the step that takes a model from a work in progress to a finished asset.