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Tridiagonal Matrix Formulation for Inextensible Hair Strand Simulation

This paper proposes a method to simulate inextensible hair strands using tridiagonal matrix formulation in which
distance constraints are formulated as a linear system. The proposed method avoids constructing a full matrix
explicitly. Instead, it takes advantage of the chain topology and serial indexing to formulate symmetric tridiagonal
matrix. Furthermore, we use a linear distance constraint so that the constraint gradient can be easily formulated.
With this matrix-free formulation, memory usage can be extremely lowered. Since the formulated matrix is diagonally
dominant, we can solve it by an efficient direct solver. Comparing error (i.e., stretch of constraints) of the
proposed constraint solver to ones of the position-based solver with different number of iterations, we show that
error of the proposed method is much smaller than those of position-based solver. Also the simulation result shows
mush less numerical damping compared to Dynamic Follow-The-Leader method. By implementing in GPU, we
demonstrate that our proposed method is simple and efficient.

Dongsoo Han,
Nov 18, 2013, 10:59 AM