Triangle Models Polygon Modeling Polygons Dominate Whats Bad

Triangle Models

Polygon Modeling

Polygons Dominate

What’s Bad About Polygons?

Polygons Aren’t Great

Polygon Meshes

Polygonal Data Structures

Triangle Meshes

Triangle Soup

Triangle Soup

Triangle Soup Evaluation

Vertex-Face Mesh

Vertex-Face Evaluation

Add more data

Some problems

Half-edge

Collision Methods for Triangle Models

Bounding Volumes

Bounding Volume Hierarchies

BVH-Based Collision Detection

Observations

Trade-off in Choosing BV’s Sphere AABB OBB 6 -dop Convex Hull

Bounding Volume Hierarchies (Example: Spheres, PSS)

Bounding Volume Hierarchies (Example: AABB)

Bounding Volume Hierarchies (Example: k-DOPs, k=6, 14, 18, 26)

Bounding Volume Hierarchies (Example: k-DOPs, k=6, 14, 18, 26)

Bounding Volume Hierarchies (Example: k-DOPs, k=6, 14, 18, 26)

Bounding Volume Hierarchies (Example: k-DOPs, k=6, 14, 18, 26)

Bounding Volume Hierarchies (Example: k-DOPs, k=6, 14, 18, 26)

Methods for Building Sphere. Trees

Building an OBBTree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree: Fitting

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree

Building an OBB Tree: Summary

Tree Traversal Disjoint bounding volumes: No possible collision

Tree Traversal Overlapping bounding volumes:

Tree Traversal

Tree Traversal Hierarchy of tests

Separating Axis Theorem

Implications of Theorem

OBB Overlap Test: An Axis Test

OBB Overlap Test: Axis Test Details

OBB Overlap Test: Axis Test Details

Implementation: RAPID