1 INTRODUCTION  
1.1 Geodesic Queries  
1.2 Polyhedral vs. Smooth Geodesic Problem  

2 BACKGROUND  
2.1 Smooth Setting  
2.2 Polyhedral Setting  

3 PDE-BASED METHODS  

4 COMPUTATIONAL GEOMETRY METHODS  

5 METHODS FOR GEODESICS TRACING  

6 MESHING  

7 EVALUATION  

8 CONCLUDING REMARKS