Connectivity shapes Martin Isenburg Stefan Gumhold Craig Gotsman

Connectivity shapes Martin Isenburg Stefan Gumhold Craig Gotsman Presented by Anna Repina 26. 05. 2017 1

Structure • Motivation • Related works • Method: Shape from Connectivity Connectivity from Shape Constructing hierarchy • Applications • Limitations • Conclusion • Future work 2

Motivation Polygonal mesh Mesh geometry Mesh connectivity 3

Related works Face Fixer: Compressing Polygon Meshes with Properties Martin Isenburg, Jack Snoeyink A New Voronoi-Based Surface Reconstruction Algorithm Nina Amenta, Marshall Bern, Manolis Kamvysselisy 4

Shape from connectivity 5

What is it – connectivity shape? • First Key idea Set of vertices Set of edges 6

Limitation on the properties • 7

Family of connectivity shapes • Family of the CS Main problem is To avoid unwanted local minimum 8

How to choose the optimal parameter? • 9

Algorithm: How to compute (*)? • Current solution 10

Connectivity from shape 11

12

13

Constructing hierarchy 14

Applications 15

Applications 16

Limitations • The shapes doesn’t contain explicit geometric information • Couldn’t generate the identical shape for the connectivity • Connectivity shape not unique 17

Conclusion • 18

Future work • Find the precise relationships between the sizes of vertices and boundaries • Find the global minimum which is maximizes the volume of the shape • Find the relation between natural geometry and natural connectivity 19

Thank you! 20

Q&A • On the 7 th slide. Why in this paper used the unit length for all edges to represent the shape ? • We could imagine that our edges are springs, which are connected at the vertices. Then the edges having unit length corresponds to the spring system being in its equilibrium state. 21

Q&A • Slide 3. Why do we get the connectivity shape as an embedding on the sphere? why couldn't we do it directly? • Embedding on the sphere is an itermediate stage. We could represent the geometry features here. Just for easier representation of a spring system. 22

Q&A • The same slide. Could we use another topology of a mesh, for example tor? Will the method work if we will have a gap in the original mesh? • Yes, we could use another presentation of the mesh. Sphere is just the easiest one. But if we will have a holes, i think we could just use some boundary conditions, to avoid problems in reconstruction. 23

Q&A • 24

Q&A • 25

Q&A • Slide 13. How to choose the optimal number of vertices? • It was depended on authors choice. 26