Edge-flows in Three Steps

Mesh design lies at the root of 3d modeling. It is the arrangement of vertexes (or points), edges and faces in the construction of a 3d surface. While you are dealing with all three of these basic elements of modeling (vertexes, edges, and faces), how well you design your mesh is what makes a model good or bad.

Polygon modeling is largely about creating and editing edges. The topology (or geometric features) of the surface you are modeling drives the decision making about where your edges should be, how large or small they are, and what their direction is. Even sculpting in ZBrush and Mudbox depends on the underlying geometry to be good for optimum results, such as edge orientation and polygon distribution.

Modelers learn very early on that a surface is best described by perpendicular and parallel edge-flow. This is accomplished by analyzing the major silhouette features of the subject, interpreting these features into a bi-directional flow of edges, and constructing the model using keeping these envisioned edge-flows in mind.

Silhouette Analysis

The silhouette describes the model in profile and defines the readable profile shapes of the model. It is important to place edges along the defining silhouette features of a surface to maintain an accurate representation of the object in the mesh. Straps, armor and other costume features on a character are an example of silhouette design features to consider for a character.

Ultimately the level of detail required by the subject is determined by the character or object design, in consideration of the polygon rendering budget. Guidelines should be established by an art lead or director.  Many details can be handled by a normal map or a displacement map. These are usually very small details that do not have a lot of relief that would require silhouette treatment.

Every subject has a set of features that require well-placed geometry to describe.

Features and details cannot be described without an accurately placed edge, so the first step in this part of the process is finding those features that require definition and planning to place edges at their extremes to describe the features. The changes along the silhouette and other major features should be considered as well as low points, high points, holes, and extrusions.

When the edges in the geometry flow with the features of a surface, the most accurate and clean representation of the surface can be achieved.
When the geometry does not flow well with the surface features, smoothing artifacts like those visible in the ripple mesh at left are visible.

The straight vertical and horizontal arrangement of the edges in the square ripple on the left does not adapt well to the concentric wave shape the topology of the object is taking. In the example to the right, the same shape is described with the edges flowing in the same direction as the topology. Because of this, the annoying edge artifacts are eliminated and the shape renders cleanly. This simple principle is one major key to building good models. The edges should flow along and across the changes in the surface. This method (along and across) leads to a bi-directional interpretation of the surface which lies at the base of good mesh design.

One good exercise is to find a small sculpture or object you can write or make marks on, and draw lines along these features. Look for the highs, lows, sharp or soft edges, contours, raised areas, shapes that extrude from others, how they intersect and what features best describe what is going on on the surface.


Bi-directional Edgeflow

The second fundamental step in this process is to apply a generally perpendicular and parallel approach for governing edge-flow. This means to interpret the previous exercise, which took a look at major lines and features, and visualizes what would be happening in the perpendicular directions to these features. This is because models are largely created using quads or square shaped polygons with edges flowing with the contours and cutting across them.

The cylinder is an example of very basic bi-directional edge-flow. Edges flow in perpendicular directions in geometrically simplified objects.

The simplest example of this is the above cylinder primitive where the edges of the polygons that make up the cylinder have a consistent bi-directional flow. Besides the simplicity of the primitive shape, it is the perpendicular arrangement of edges in two perpendicular directions, (Height and Circumference) that describes this shape so efficiently and smoothly. It is of course much harder to build perpendicular arrangements as topology becomes more complex or organic.

As you take the feature markup you created and from there visualize a bi-directional flow of edges to describe those features, you can begin to see how the edges will flow around your model.

Another major factor that determines edge-flow direction is how the model will deform as it is animated or posed. This consideration includes the range of motion of things like joints that bend, muscles that bulge or contract, and facial features that will need to appear or disappear during facial animation and expressions. Typical areas that will need extra or specific edge treatment can be elbows, shoulders, fingers, hips, knees, etc. Facial topologies tend to have radial edge-flows around the eyes and mouth because the compression and expansion required by facial poses in these areas.


As you apply this thinking to your meshes, you will find that your meshes tend to become arrangements of quadrangle sections that flow into and out of each other. Before long, edge-loops appear.


Edge-loops are chains of connected edges along quadrangle-based geometry. They are used to describe the defining silhouettes of the subject being modeled. If it’s helpful, think of edge-loops in terms of shapes and cross-sections. The red lines above represent just a few edge-loops that exist on this model.


Edge-loops can represent cross-sections on cylindrical shapes, but many of them are not. Keep in mind that this is a very simplified explanation since silhouettes should be managed from as many angles as possible to build successful models. Remember, the more detail required by the topology and the rigging requirements, the more edges and edge-loops are required.


Keep in mind that you may need to optimize the geometry of your models after or during this edge-looping process. Once the edge-loops are created it is usually a fairly simple process to select and collapse groups of edges where necessary. We will cover this process later in more detail in a future article and tutorial.


As you apply this thinking to your meshes, you will find that your models will more accurately represent your subject and lend themselves to the other CG processes that your models will need to fulfill their production designs. These principles apply to creating models to be sculpted further in ZBrush, and models that are the result of the re-topo process once the high res ZBrush or Mudbox sculpture is done.