Decimation of Triangle Meshes

visualization and graphics research group

CIPIC

Decimation of Triangle Meshes

William J. Schroeder, Jonathan A. Zarge, William E. Lorensen

Presented by

Alden ChewSerban Porumbescu

visualization and graphics research group

CIPIC

What is the Problem?

• Want to visualize data interactively• Too many triangles• Too little hardware

visualization and graphics research group

CIPIC

High Level Approach

• Characterize the local vertex geometry and topology

• Evaluate decimation criteria for vertex removal

• Triangulate the resulting hole

visualization and graphics research group

CIPIC

Vertex Classification

•Feature edge: dihedral angle greater than user specified feature angle

•An interior edge vertex is a vertex with two feature edges

•A corner has one, three, or more feature edges

visualization and graphics research group

CIPIC

Vertex Removal

• Based on user specified distance to plane or distance to edge (boundary vertex)

visualization and graphics research group

CIPIC

Vertex Removal

• Removal of vertex creates a hole in the mesh– Triangulate

• Removal of feature edge:– Create a new feature edge– If two non-overlapping loops can be created,

triangulate the two loops

visualization and graphics research group

CIPIC

Triangulate Resulting Hole

• Triangulate using a recursive loop splitting procedure

• The stencil of the hole is called a loop• Loops are divided into two parts by a

split line • Split line

– A line between two non-adjacent vertices in the loop

visualization and graphics research group

CIPIC

Split Plane

• Split plane– The plane orthogonal to the average plane

through a split line

• Used for half space comparisons

visualization and graphics research group

CIPIC

Loop Splitting Procedure

• Need to create two non-overlapping loops

• A valid loop is entirely on one side of the split plane ….

• If the loop contain more than three vertices, recurse

• If the loop has three vertices, form a triangle

visualization and graphics research group

CIPIC

Split Line Selection

• Many split lines to choose from• Choose line that maximizes the aspect

ratio• The aspect ratio is the minimum

distance of the loop vertices to the split plane divided by the length of the split line

visualization and graphics research group

CIPIC

Special Cases

• Want to preserve topology • Don’t create duplicate triangles and

triangle edges

visualization and graphics research group

CIPIC

Sample Run From VTK (US Patent Number 5,559,388)

visualization and graphics research group

CIPIC

Skull

visualization and graphics research group

CIPIC

Blade

visualization and graphics research group

CIPIC

Hawaii

visualization and graphics research group

CIPIC

Mars