A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (International Series of Numerical Mathematics)
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2009 papers
ACM SIGGRAPH 2010 papers
Globally optimal direction fields
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Designing and fabricating mechanical automata from mocap sequences
ACM Transactions on Graphics (TOG)
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Solving mixed-integer problems, i.e., optimization problems where some of the unknowns are continuous while others are discrete, is NP-hard. Unfortunately, real-world problems like e.g., quadrangular remeshing usually have a large number of unknowns such that exact methods become unfeasible. In this article we present a greedy strategy to rapidly approximate the solution of large quadratic mixed-integer problems within a practically sufficient accuracy. The algorithm, which is freely available as an open source library implemented in C++, determines the values of the discrete variables by successively solving relaxed problems. Additionally the specification of arbitrary linear equality constraints which typically arise as side conditions of the optimization problem is possible. The performance of the base algorithm is strongly improved by two novel extensions which are (1) simultaneously estimating sets of discrete variables which do not interfere and (2) a fill-in reducing reordering of the constraints. Exemplarily the solver is applied to the problem of quadrilateral surface remeshing, enabling a great flexibility by supporting different types of user guidance within a real-time modeling framework for input surfaces of moderate complexity.