3D Modeling I (week 2) Instructor: Ya Lu Lin

Polygonal Modeling

I. Polygon Components

A polygon is an n-sided shape, defined by its corners (vertices) and the straight lines between them (edges). When you model with polygons you usually use triangles or quadrilaterals ("quads"), although Maya supports polygons with more sides. An individual polygon is often called a face, and is thought of as the filled area defined by its vertices and edges.

Vertex - A vertex is a point in 3D space. Three or more connected vertices make a face.

Edge - Edges connect vertices by drawing a straight line between them. A single edge can be moved, scaled, or rotated.

Face - A face is made up of three or more connected edges. A face with three sides is a triangle, with four sides is a quad, and with more than four sides is a n-gon.

UV- UVs are the two-dimensional coordinates that are required to display or render a texture on a mesh. A UV directly corresponds to a vertex on the mesh.

Border edges - edges that are not shared (they are on the outside edge of a shell)

NormalsFace normals

The order of vertices around the face determine the direction of the face (whether a side of the polygon is the front or the back). This can be important because technically polygons are only visible from the front, though by default Maya automatically makes all polygons double-sided so you can see them from the back. You can turn this double-sided behavior off for meshes.

The front of a polygon's face is graphically represented using a vector called the polygon's normal. A normal is a line representing the direction perpendicular to a polygonal surface.

When you shade or render polygons, the normals determine how light reflects from the surface.

Vertex normals

Vertex normals represent the visual smoothing between polygon faces. Unlike face normals, they are not intrinsic to the polygon, but rather reflect how Maya renders the polygons in smooth shaded mode.

Vertex normals appear as lines projecting from the vertex, one for each face that shares the vertex.

When the vertex normals all point in the same direction (called soft or shared vertex normals), there is a softer transition between the faces in smooth shaded mode.

When the vertex normals point in the same directions as their faces (called hard vertex normals), the transition between faces is hard, creating a faceted appearance.

Meshes and shells

Polygons can share vertices and edges with other polygons. You can use a large number of connected polygons to form shapes.

A mesh is a collection of polygons (a mesh is also sometimes called a polyset or a polygonal object). A mesh can contain different types of polygons (triangles, quads, n-sided).

Often a mesh consists only of connected polygons, however it can also be several disjoint sets of connected polygons, called shells.

II. 2-manifold, non-manifold, and invalid polygonal geometry

2-manifold topology basically means you can unfold the geometry so that it lies flat without overlapping pieces.

Non-manifold geometry cannot be unfolded into a continuous flat piece. Some tools and actions cannot work with non-manifold geometry, including Boolean operations and Reduce.

In the first example (the "T" shape), more than two faces share an edge. This is known as multiply connected geometry.

In the second example (the "bowtie" shape), two faces share a single vertex without also sharing an edge.

This shape is also possible where two three-dimensional shapes share a vertex (such as two cubes meeting at a single point).

In the third example, a single shape has non-contiguous normals (without border edges). This is a less obvious example of nonmanifold geometry.

The following operations can produce nonmanifold geometry:

Extrude Edge.

Normals > Reverse (without extracting geometry).

Merge Vertices.

Delete Face.

Collapse (Face or Edge).

You can automatically make nonmanifold geometry 2-manifold (including the less obvious case of adjacent faces with opposite normals) using Polygons > Cleanup.

Invalid geometry

Invalid geometry includes vertices that are not on an edge and edges that are not part of a face.

Planar and non-planar polygons

A polygon is planar if all its points lie in a certain plane. A triangle is always planar, because its three points define a plane.

A polygon is non-planar if it has more than three vertices, and any of those vertices are not in the same plane.

In general planar polygons are preferable to non-planar. Maya has options that keep you from creating non-planar polygons (Polygons > Tool Options > Keep New Faces Planar), tools to "fix" non-planar polygons (Edit Polygons > Split Polygons Tool), and display options that can identify non-planar polygons (in Display > Custom Polygon Display).