Coordinate representation of order types requires exponential storage
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
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Proceedings of the eleventh annual symposium on Computational geometry
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Optimal Net Surface Problems with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Finite-resolution computational geometry
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Algorithms for Computing the Maximum Weight Region Decomposable into Elementary Shapes
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Effect of corner information in simultaneous placement of K rectangles and tableaux
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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Given a fixed origin o in the d-dimensional grid, we give a novel definition of digital rays dig(op) from o to each grid point p. Each digital ray dig(op) approximates the Euclidean line segment op between o and p. The set of all digital rays satisfies a set of axioms analogous to the Euclidean axioms. We measure the approximation quality by the maximum Hausdorff distance between a digital ray and its Euclidean counterpart and establish an asymptotically tight Θ(log n) bound in the n x n grid. The proof of the bound is based on discrepancy theory and a simple construction algorithm. Without a monotonicity property for digital rays the bound is improved to O(1). Digital rays enable us to define the family of digital star-shaped regions centered at o which we use to design efficient algorithms for image processing problems.