Polygon Meshes- Important Steps

When working with polygon meshes, it is important to ensure that the mesh representation is consistent.

– All polygons are closed.

– Each edge is used at least once and not more than twice.

– Each vertex is referenced by at least two edges

Polygon Meshes - Pointers to an edge list

Polygon Meshes - Pointers to a vertex list

Polygon Meshes

A polygon mesh is a set of bounded polygons (vertices, edges, and faces) such that each edge is shared by at most 2 polygons

Polygon meshes can be represented in several ways

– Explicit representation

   P={(x1,y1,z1),........,(xn,yn,zn)}

Surface Modeling | Graphics Designing

Surface Modeling

Several methods are available to model surfaces

 

– Polygon meshes
• Surface is represented as a set of bounded planar surfaces
– Parametric polynomial curves
• Surface is defined by 3 equation in a parameter, t, one for each principal axis (x, y, z)

– Parametric bivariate polynomial surface patches
• Similar to parametric polynomial curves but this time each equation has two variables
– Quadratic surfaces
• Surface is implicitly defined by an equation f(x, y, z) = 0