1. Connection Constrained 3D Collage Zhe Huang 1, Jiang Wang, Rynson W.H. Lau, Hongbo Fu City University of Hong Kong 1. Author’s email: igamenovoer@gmail.com

2. Motivation: Building Complex 3D Structures Transformer Futuristic Objects

3. Motivation: Building Complex 3D Structures Collage Algorithm Element Database Coarse Shape (or Proxy Space) Complex Structure

4. Related Works Unstructured 3D Collage 3D Collage [Gal et al. 2007] Animation Collage [Theobalt et al. 2007] Structured Mechanical Collage Structured Mechanical Collage [Huang et al. 2014]

5. What is a well connected collage? Connector Pairwise Relationship Well Connected (male-to-female / male-to-male) Improperly IntersectedDisconnected Plausible Configuration

6. What is a well connected collage? A collage is well connected if and only if each pair of elements is in plausible configuration Well Connected CollageDefected Collage Improperly Intersected

7. Greedy Approach (Huang et al.2014) Algorithm: Elements are added one by one, by connecting to the existing collage Problem: Fail to find a solution when it exists. input elements = step 1step 2step 3 ? A good configuration

8. A B Put into Elements Proxy Space p1 p2 p1 v d Element must be within the proxy space: Our Approach: Element Placement using Mixed Integer Programming

9. A B Convex Decomposition Well Connected Improperly Intersected Disconnected Our Approach: Element Placement using Mixed Integer Programming Pairwise Configuration Space

10. p1 p2 A B Put into Elements Proxy Space Elements must be in plausible configuration x1 x2 x3 x1,x2,x3 = Connection Selection Variables x1==1 Element A is positioned in c1 M= large constant x1==0No constraint Our Approach: Element Placement using Mixed Integer Programming

11. Result Put into Elements Proxy Space In-proxy constraint: A B p1 p2 Connection Selections: The two elements must connect Our Approach: Element Placement using Mixed Integer Programming

12. Our Approach: Placing More Elements Put into Elements Proxy Space y1 y1, y2 = Disconnection Selection Variables Allow selecting disconnection space y1

13. Disregarding some element s1,s2,s3 = element selection variable s1 s2s3 Our Approach: Placing More Elements Put into Elements Proxy Space z3 z1,z2,z3 = Improper Intersection Selection Variables z1 z2 If well-connected collage is impossible, we allow: Using improper intersection

14. Our Approach: Placing More Elements Put into Elements Proxy Space Energy Function to Minimize: Encourage to select more elements Encourage to use more connectors Discourage improper intersection (refer to the paper for detail).

15. Iterative Collage Construction How to determine element orientation? Element Database Proxy Space Greedy Construction (Huang el al. 2014) Greedy Construction (Huang el al. 2014) Re-arrange the elements using Mixed Integer Programming Re-arrange the elements using Mixed Integer Programming

16. Iterative Collage Construction How to limit computational complexity? In each step, add and re-arrange a fixed number of elements

17. Results: compare with greedy approach (Huang et al. 2014) Ours Huang et al. 2014 Ours Huang et al. 2014

18. Results: more

19. Thank You For inquiry, please email to the author (igamenovoer@gmail.com)