ATCM 6317 Procedural Animation Procedural Methods in 3D Computer Animation Dr. Midori Kitagawa

3D models Types of 3D models Polygons NURBS

Types of 3D models and their use computer animation, games 3D printing, engineering, manufacturing, computer aided design (CAD) scientific visualization, medical visualization, effect animation (e.g. clouds) Surface models Solid models Volume models

Surface model Always has a crisp surface with no thickness. Can be closed or open. Composed of polygons or surface patches.

Solid model Used in 3D printing, engineering, manufacturing, computer aided design (CAD), etc.

Solid model A solid model always has a crisp surface that divides the entire universe into two regions: the inside of the model and the outside of the model. A solid model is closed while a surface model can be open or closed. The interior of a solid model is homogeneous.

Volume model Used in scientific visualization, medical visualization

Volume model Consists of: a data set of a physical characteristic (e.g, density, electric charge and temperature) measured at various locations in the space of interest, or a field defined by mathematical equations.

Volume model The interior of a volume model is heterogeneous. Can have fuzzy surface.

Volume model Without converting into a surface or solid model, a volume model needs to be rendered by a special renderer. When surfaces are extracted from volume models, the volume models are called metaballs, implicit surfaces, blobby models or soft objects.

Metaballs Polygonization of an Isosurface Isosurface is the set of all points in space where a given function is equal to a chosen constant threshold. http://www.siggraph.org/education/materials/HyperGraph/modeling/metaballs/metaballs.htm http://www.phnet.fi/public/realsoft/modeling/metaball/metaball.html

Metaballs Polygonization of an isosurface Polygonization of the surface is a set of polygons that approximate the form of the surface to the best of their resolution. http://www.siggraph.org/education/materials/HyperGraph/modeling/metaballs/metaballs.htm

Metaballs

Types of 3D models A surface model can represent an egg’s broken shell or complete shell. A solid model can represent an egg’s complete shell and the space enclosed by the sell. A volume model can represent an egg’s various parts -- shell, york, white, etc.

Polygons Plane figure bounded by three or more straight edges. Used most frequently in 3D computer animation because they can be rendered faster than surface patches.

Polygons Good polygons are: single closed convex simple and planar.

Polygons Closed single simple planar polygons are almost always rendered correctly but open, non-single, non-simple, or skew polygons often causes rendering problems. If concave polygons are rendered incorrectly, triangulate a concave polygon into convex polygons. Triangulation eliminates skew (non-planar) polygons.

Polygons vs patches Polygon has straight edges and a flat surface. Surface patch has edges defined by curves (e.g. Bezier and NURBS) and curved surface.

NURBS curve Non-Uniform Rational B-Spline (NURBS) curve. Control vertices define the shape of a NURBS curve.

NURBS curve Offers a high degree of local curve control by using weights. The higher the weight of a control vertex, the more the curve segment is pulled towards that control vertex.

NURBS curve Sharp turn can be created at a control vertex by duplicating the control vertex or increasing the weight of the control vertex.

NURBS patch Defined by NURBS curves arranged in two directions U and V. Inherits all the characteristics of NURBS curves.

Mesh Mesh is a collection of polygons that can be converted to a surface patch.