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

College of Health and Human Development Sciences, University of Illinois at Chicago

Dept. of Ophthalmology and Visual Sciences

Near Near

Real-TimeReal-Time

CuttingCutting

Paul F. Neumann



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.



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.



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



Vector Springs

• Invented by Alan Millman at EVL

• Maintain their orientation and length

• Easy to subdivide



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.



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.



Intersection



Subdivision

New interior springs must compute their rest directionthrough vector addition of their neighbors.

Intersection SpringSubdivision

TriangleSubdivision

FurtherSubdivision



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.



Cutting Example



Cutting Example



Cutting Example



Cutting Example



Cutting Example



Cutting Example



Variations

Suction Cutter Tearing

Scissors



Video Tape



Discussion

• Geometry dependence.

• Lag in response time.

• Rounds to nearest vertex.

• Collision Detection

• Small parallelograms within a

triangle aren’t processed.



More Information

A more detailed paper is included on

your Application cdrom.

Web Site:

www.bvis.uic.edu/paul/

CAL Demonstration right after session

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

Documents