### Part 1

```SKM 4200
Computer Animation
Chapter 4: Animation
(3D Computer Animation – Part 1)
3D Computer Animation
Understanding Polygons
• Polygons are is a closed 2D shape formed by straight lines (edges)
• The building blocks of a polygon… For example, a cube (adapted from
[1]):
vertex
The breakdown…
• Vertex: Has no Length, Width or Height. In short, it has ZERO dimensions;
edge
• Edge: Has ONE dimension… Length;
• Face (i.e. the polygon): TWO dimensions… Width and Length;
face/polygon
• The number of vertices (plural of vertex) is always equals to the
number of edges
• Question: What is the minimum number of edges to make a
polygon? ____ (please fill in the blank… )
3D Computer Animation
Note:
Four-side polygons are referred
polygons with more than 4-sides
are n-gons [1]. The ‘n’ represents
the number of sides…
http://www.mathsteacher.com.au/year7/ch09
_polygons/05_polygon/Image11206.gif
3D Computer Animation
Understanding Polygons (continued)
• Planar polygons
– When all the vertices lie on the same plane (a plane is like the floor we
stand on. It has no curves and infinitely (straightly) extends in each
direction )
– A triangle is always planar 
• Non-planar polygons
– When the vertices lie on different planes
– Polygons other than triangles can be non-planar
Planar
Non-planar
http://softimage.wiki.softimage.com/xsidocs/poly_basic_PolygonMeshes.htm
3D Computer Animation
3D Primitives
• Instant 3D objects… with polygons as building blocks
• 3D Primitives: cube, cylinder, sphere, cone, polyhedron, wedge etc.
• Some 3D packages offer different types of primitives
For polyhedron, goto:
http://en.wikipedia.org/wiki/Polyhedron
http://docs.autodesk.com/ACD/2011/ENU/filesAUG/WS1a9193826455f5ffa23ce210c4a30acaf-68e7.htm
3D Computer Animation
Polygon Meshes
• A polygon mesh is a 3D object composed of one or more
polygons
– A group of polygons forming a model
– The 3D primitives are examples of polygon meshes 
• The 3D cube primitive:
The breakdown…
• Vertex: Has no Length, Width or Height. In short, it has ZERO dimensions;
• Edge: Has ONE dimension… Length;
• Face (polygon): Has TWO dimensions… Width and Length;
• The 3D mesh/model (the CUBE): Has ALL THREE… Height, Width and Length.
Reference  [1]
3D Computer Animation
• Closed polygon meshes
– Edges are shared by all faces
– An example is the cube, sphere and (closed) cones
and cylinders, etc.
– No hole to get into the mesh…
• Open polygon meshes
– Not all faces share the edges
– Can result in a 2D look (for a leaf?)… but it’s 3D of
course
– The outside edges are referred to as ‘boundary edges’
or ‘border edges’ [1]
3D Computer Animation
• An example of an open polygon mesh
Boundary/Border Edges
http://files.turbosquid.com/Preview/Content_2
010_12_08__22_43_43/Leaf_red_mesh_2.jpgce
037a0c-b7c8-480a-a5fe-fd6d447db19dLarger.jpg
3D Computer Animation
Modeling 
• Two modeling approaches will be discussed
– BOX MODELING
– EXTRUSION
3D Computer Animation
Box modeling
• Modeling begins with a box (a cube primitive)
• Artist then scales the object, moves
(translates) vertices and edges, and adds more
– This results in the 3D shape they want to create
dia.org/wikibooks/en
_Step6.jpg
2.jpg
3D Computer Animation
Extrusion modeling
• Extrude basically means to push or thrust out
– Modeling begins with an edge or a polygon, or
even a primitive
– Then you extrude new polygons from what you
started with
3D Computer Animation
• A basic tutorial on how to model a car can be
found here: A basic tutorial of how to box model
a
car
can
be
found
at
http://en.wikibooks.org/wiki/Wings_3D/Tutorials/Box_modeli
• Some videos
–
–
–
–
Box modeling -1
Box modeling-2
Extrude modeling-1
Extrude modeling-2
3D Computer Animation
Orthogonal Drawings
3D Computer Animation
Orthogonal Drawings
TOP
PERSPECTIVE
FRONT
SIDE
3D Computer Animation
Orthogonal Drawings
- Normally used as reference for modeling
- Does not have perspective
- Normally set up as planes in the FRONT VIEW, SIDE VIEW
and TOP VIEW of a particular 3D modeling application
IMPORTANT NOTE!!!
• Make sure that each drawing have the same aspect ratio
• Make sure each are set up so the edges of each drawing
match each other where they would meet
3D Computer Animation
Mirroring
- Model one side of the character/object, and then
duplicate its ‘mirror’ to obtain the other side
- So you won’t have to remodel different sides of your
object/character
- Many 3D applications allow mirroring to be done
automatically
- So if you model one side, the other side automatically gets
modeled as well
• Video 1  Concept of mirroring
• Video 2  Head modeling animation
3D Computer Animation
Editing the Mesh
• Things you can basically edit
– Vertices
– Edges
– Faces
• Can either choose to edit one at a time, or as a group
http://en.wikipedia.org/wiki/Polygon_mesh
3D Computer Animation
Editing the Mesh
• Soft selection
– Allows you to control how strongly the vertices and polygons
surrounding selected parts (for editing) are affected
– Polygons from far away feel the effect of changing a face’s position;
then the change will create a smoother, less steep slope
– The mesh behaves like soft clay, and so this is typically called soft
selection
– VIDEO
3D Computer Animation
• Extruding
– A way of adding more polygons to a mesh
– Applicable to edges and faces only
– You can extrude more than once depending on
what you want to model 
3D Computer Animation
• Subdividing
– Adding edges (or subtracting them) can be done across the
entire mesh
• Adding edges however increases the number of vertices and also
the number of faces/polygons
– Subdividing allows you model to become more detailed
• Smoothing can then be applied…
• Smoothing averages out the vertices, so that it has fewer sharp
angles
• Simplifying
– The opposite of subdividing
– Involves deleting of unwanted components (e.g. vertices,
faces or edges)
3D Computer Animation
3D Computer Animation
• Boolean - SUBTRACT
– FIRSTLY, select the mesh you want to keep
– SECOND, select then the other mesh
– Then perform the subtract operation
– This will cause the second mesh to be “removed”
3D Computer Animation
• Boolean - INTERSECTION
– Combine both meshes that you want to have
intersection
– Then perform the intersection operation
3D Computer Animation
• Boolean - UNION
– As the name suggests… both meshes are united

– For the example given below… the two shapes
involved are a cube and a sphere…
3D Computer Animation
• Welding
– The vertices to be joined (welded) on the border
edges from two different meshes are specified
– Welding results in those vertices and the edges to
combine into one
3D Computer Animation
• Bridging
– A new edge will be drawn between the selected
vertices, so that new bridging polygons are
created between the border edges of the two
meshes
3D Computer Animation
• Polygon Count
– The more polygons you have, the more detail a
mesh will be 
– Will take up more processing power to manipulate
the mesh
• The longer it will take to render
3D Computer Animation
• Normals
– Polygons have a back face and a front face
– When a primitive is created, the side of the faces that you can see are the front faces.
You can also think of this as the direction that the polygon is pointed in
– This is called the normal
– To visualize it, imagine a line that points straight out, perpendicular to your polygon
– Normals are important for:
• Lighting - how it interacts with the model
• Rendering
References
[1] Chopine, A., “3D Art Essentials: The Fundamentals of 3D Modeling,
Texturing and Animation”, Focal Press, 2011.
```