## Fachbereich Informatik

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#### Erscheinungsjahr

- 2001 (21) (entfernen)

#### Dokumenttyp

- Bericht (12)
- Preprint (7)
- Wissenschaftlicher Artikel (2)

#### Schlagworte

- AG-RESY (9)
- RODEO (7)
- vibration (3)
- genetic algorithms (2)
- trajectory planning (2)
- Assembly (1)
- Force-Torque (1)
- Manipulation skills (1)
- Robotics (1)
- SIMERO (1)

We present a system concept allowing humans to work safely in the same environment as a robot manipulator. Several cameras survey the common workspace. A look-up-table-based fusion algorithm is used to back-project directly from the image spaces of the cameras to the manipulator?s con-figuration space. In the look-up-tables both, the camera calibration and the robot geometry are implicitly encoded. For experiments, a conven-tional 6 axis industrial manipulator is used. The work space is surveyed by four grayscale cameras. Due to the limits of present robot controllers, the computationally expensive parts of the system are executed on a server PC that communicates with the robot controller via Ethernet.

We introduce two novel techniques for speeding up the generation of digital \((t,s)\)-sequences. Based on these results a new algorithm for the construction of Owen's randomly permuted \((t,s)\)-sequences is developed and analyzed. An implementation of the new techniques is available at http://www.cs.caltech.edu/~ilja/libseq/index.html

We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a \(p\)-summability condition and for integration of functions from Lebesgue spaces \(L_p([0,1]^d)\) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Brassard, Høyer, Mosca, and Tapp (2000) on computing the mean for bounded sequences and complements results of Novak (2001) on integration of functions from Hölder classes.

We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hölder or Sobolev spaces. First we discuss optimal deterministic and randornized algorithms. Then we add a new aspect, which has not been covered before on conferences
about (quasi-) Monte Carlo methods: quantum computation. We give a short introduction into this setting and present recent results of the authors on optimal quantum algorithms for summation and integration. We discuss comparisons between the three settings. The most interesting case for Monte
Carlo and quantum integration is that of moderate smoothness \(k\) and large dimension \(d\) which, in fact, occurs in a number of important applied problems. In that case the deterministic exponent is negligible, so the \(n^{-1/2}\) Monte Carlo and the \(n^{-1}\) quantum speedup essentially constitute the entire convergence rate.

The simulation of random fields has many applications in computer graphics such as e.g. ocean wave or turbulent wind field modeling. We present a new and strikingly simple synthesis algorithm for random fields on rank-1 lattices that requires only one Fourier transform independent of the dimension of the support of the random field. The underlying mathematical principle of discrete Fourier transforms on rank-1 lattices breaks the curse of dimension of the standard tensor product Fourier transform, i.e. the number of function values does not exponentially depend on the dimension, but can be chosen linearly.

Interleaved Sampling
(2001)

The sampling of functions is one of the most fundamental tasks in computer graphics, and occurs in a variety of different forms. The known sampling methods can roughly be grouped in two categories. Sampling on regular grids is simple and efficient, and the algorithms are often easy to built into graphics hardware. On the down side, regular sampling is prone to aliasing artifacts that are expensive to overcome. Monte Carlo methods, on the other hand,
mask the aliasing artifacts by noise. However due to the lack of coherence, these methods are more expensive and not weil suited for hardware implementations. In this paper, we introduce a novel sampling scheme where samples from several regular grids are a combined into a single irregular sampling pattern. The relative positions of the regular grids are themselves determined by Monte Carlo methods. This generalization obtained by interleaving yields,significantly improved quality compared to traditional approaches while at the same time preserving much of the advantageous coherency of regular sampling. We demonstrate the quality of the new sampling scheme with a number of applications ranging from supersampling over motion blur simulation to volume rendering. Due to the coherence in the interleaved samples, the method is optimally suited for implementations in graphics hardware.

As opposed to Monte Carlo integration the quasi-Monte Carlo method does not allow for an (consistent) error estimate from the samples used for the integral approximation. In addition the deterministic error bound of quasi-Monte Carlo integration is not accessible in the setting of computer graphics, since usually the integrands are of unbounded variation. The structure of the high dimensional functionals to be computed for photorealistic image synthesis implies the application of the randomized quasi-Monte Carlo method. Thus we can exploit low discrepancy sampling and at the same time we can estimate the variance. The resulting technique is much more efficient than previous bidirectional path tracing algorithms.

In this work we propose a set of term-rewriting techniques for modelling object-oriented computation. Based on symbolic variants of explicit substitutions calculi, we show how to deal with imperative statements like assignment and sequence in specifications in a pure declarative style. Under our model, computation with classes and objects becomes simply normal form calculation, exactly as it is the case in term-rewriting based languages (for instance the functional languages). We believe this kind of unification between functions and
objects is important because it provides plausible alternatives for using the term-rewriting theory as an engine for supporting the formal and mechanical reasoning about object-oriented specifications.