1. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences NearReal-TimeCutting Paul F. Neumann

2. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Virtual Reality Surgical Simulators Simulate the functionality of surgical instruments such as blades and scissors A general 3D cutting algorithm is a one of challenging problems. Simulators must maintain an interactive frame rate.

3. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Previous Cutting Algorithms 1988 Tearing (Terzopoulos and Fleischer) 1992 Particle Systems (Szeliski and Tonnesen) 1992 Radial Projection on FEM (Pieper et al.) 1995 2D FEM Template (Song and Reddy) 1997 3D FEM with Bilinear Cutting Plane (Mazura and Seifert) 1997 Boolean Operations (Delp et al.) 1998 Hybrid Elastic Model (Colin et al.) My Goal: To develop an interactive cutting algorithm on a mass-spring system with a polygonal surface.

4. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Mass-Spring System Very popular PBM platform Vertices as mass points Edges as vector springs Dynamic system which permits insertions and deletions Distributes mass appropriately Conserves surface area

5. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Vector Springs Invented by Alan Millman at EVL Maintain their orientation and length Easy to subdivide

6. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Algorithm Overview 1) Samples blade’s path. 2) Reconstructs the path with a series of parallelograms. 3) Intersects and subdivides springs and triangles. 4) Recomputes mass and spring stiffness coefficients.

7. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Reconstructing Cutting Path Discretely samples path. Drop samples if roughly co-planar. Fit parallelogram through two selected samples by averaging orientation and adding offset. Parallelograms lag behind current position.

8. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Intersection

9. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Subdivision New interior springs must compute their rest direction through vector addition of their neighbors. Intersection Spring Subdivision Triangle Subdivision Further Subdivision

10. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Mass Distribution: Localized Approximation Mass proportional to surface area at rest. New vertices and their neighbors have their mass values recomputed after subdivision. Spring rest direction vectors outline the undeformed triangle area.

11. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Cutting Example

12. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Cutting Example

13. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Cutting Example

14. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Cutting Example

15. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Cutting Example

16. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Cutting Example

17. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Variations Suction CutterTearing Scissors

18. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Video Tape

19. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences Discussion Geometry dependence. Lag in response time. Rounds to nearest vertex. Collision Detection Small parallelograms within a triangle aren’t processed.

20. College of Health and Human Development Sciences, University of Illinois at Chicago Dept. of Ophthalmology and Visual Sciences More Information A more detailed paper is included on your Application cdrom. Web Site: www.bvis.uic.edu/paul/ CAL Demonstration right after session