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Real-Time Resolution of Self-Intersection in Dynamic Cylindrical Free-Form Deformation
April 2011 (vol. 17 no. 4)
pp. 515-526
Woojin Ahn, Korea Advanced Institute of Science and Technology, Daejeon
Doo Yong Lee, Korea Advanced Institute of Science and Technology, Daejeon
This paper presents a method of self-intersection detection and resolution for dynamic cylindrical-lattice-based free-form deformation (FFD). The lattice-based approach allows efficient computation of deformation of complex geometries. But excessive deformation can cause visual anomalies such as surface infiltration and distortion. This paper derives a geometrically intuitive sufficient condition to guarantee that the FFD function is a homeomorphism and there is no self-intersection. The FFD function is defined by linear and quadratic B-Spline functions with the control points of the cylindrical lattice cell. The sufficient condition is satisfied if each trilinear function of the nine prism-shaped pentahedrons derived from the cell has a positive Jacobian determinant. The positivity is satisfied if the 12 tetrahedrons derived from the pentahedron have positive volumes. Based on the sufficient condition, the proposed method converts the self-intersection problem into a point-face collision detection and response problem suitable for dynamic simulation. The efficiency and accuracy of the self-intersection detection algorithm is analyzed and compared with a previous method. The results show that the proposed technique allows simulation of excessive deformation of tubular objects in an efficient and realistic manner.

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Index Terms:
Free-form deformation, self-intersection, collision, simulation.
Woojin Ahn, Doo Yong Lee, "Real-Time Resolution of Self-Intersection in Dynamic Cylindrical Free-Form Deformation," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 4, pp. 515-526, April 2011, doi:10.1109/TVCG.2010.54
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