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12
A Fast and Efficient ProjectionBased Approach for Surface Reconstruction
 High Performance Computer Graphics, Multimedia and Visualization
, 2002
"... We present a fast and memory efficient algorithm that generates a manifold triangular mesh S with or without boundary passing through a set of unorganized points P ⊂ R³ with no other additional information. Nothing is assumed about the geometry... ..."
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We present a fast and memory efficient algorithm that generates a manifold triangular mesh S with or without boundary passing through a set of unorganized points P ⊂ R³ with no other additional information. Nothing is assumed about the geometry...
Mechanical Verification of a Square Root Algorithm Using Taylor’s Theorem
 In Formal Methods in Computer Aided Design (FMCAD'02
, 2002
"... Abstract. The IBM Power4 TM processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theore ..."
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Abstract. The IBM Power4 TM processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theorem, and then analyzing the Chebyshev series using Taylor series. Taylor’s theorem is proved by way of nonstandard analysis, as implemented in ACL2(r). Since Taylor series of a given order have less accuracy than Chebyshev series in general, we used hundreds of Taylor series generated by ACL2(r) to evaluate the error of a Chebyshev series. 1
Taylor's Formula with Remainder
 In Proceedings of the Third International Workshop of the ACL2 Theorem Prover and its Applications
, 2002
"... In this paper, we present a proof in ACL2(r) of Taylor's formula with remainder. ..."
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In this paper, we present a proof in ACL2(r) of Taylor's formula with remainder.
Decomposing spline surfaces into nonoverlapping regions for visible surface computation
 In Proc. of Indian Conference on Computer Vision, Graphics and Image Processing
"... Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics and machining applications in manufacturing. Most of the earlier work has focused on discrete methods b ..."
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Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics and machining applications in manufacturing. Most of the earlier work has focused on discrete methods based onpolygonization or raytracing and hidden curve removal. In this paper we present an algorithm for decomposing a given surface into regions such that each region is either completely visible or hidden from a given viewpoint. Initially, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of visibility curves obtained byprojection of silhouette and boundary curves and decomposing the surface into nonoverlapping regions. 1
Anytime Reaction Planning In Probabilistic Logic
, 1992
"... This thesis describes a probabilistic approach to the definition of the quality of reaction plans, as a basis for anytime reactive planning for domains that are not fully predictable. The reaction plans are generated by a planner based on a possible models representation of actions, which allows co ..."
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This thesis describes a probabilistic approach to the definition of the quality of reaction plans, as a basis for anytime reactive planning for domains that are not fully predictable. The reaction plans are generated by a planner based on a possible models representation of actions, which allows coping with missing, ambiguous and contextdependent information. These plans have the structure of deterministic automata whose states represent actions to be executed, and whose transitions are labeled by possible models representing properties of the world. Due to the use of probabilistic logic, the probability to make a transition from one state to another can be computed from the data of apriori probabilities of events in the domain, and from the probability of actions achieving different possible effects. Markov chain theory enables us to study properties of these reaction plans considered as stochastic processes, and provides a framework for a dynamic evaluation of their quality with r...
Global Visibility and Hidden Surface Removal Algorithms for Free Form Surfaces
"... Computing the visible portions of freeform surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics and machining applications in manufacturing. Most of the earlier work has focused on discrete method ..."
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Computing the visible portions of freeform surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics and machining applications in manufacturing. Most of the earlier work has focused on discrete methods based on polygonization or raytracing, hidden curve removals and local visibility computations based on Gauss maps. In this paper we present an efficient and accurate algorithm for hidden surface and global visibility computations on free form surfaces. Given a viewpoint, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of "visibility curves" obtained by projection of silhouette and boundary curves and decomposing the surface into nonoverlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The nonoverlapping and visible portions o...
JOURNAl Of
, 2005
"... www.elsevier.com/locate/jpowsour Effect of Sn concentration on the corrosion (esistanceof PbSn alloys in H2S04 solution ..."
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www.elsevier.com/locate/jpowsour Effect of Sn concentration on the corrosion (esistanceof PbSn alloys in H2S04 solution
THE GLOBAL POSITIONING SYSTEM AND THE IMPLICIT FUNCTION THEOREM ∗
"... Abstract. This paper provides an example of the implicit function theorem to the accuracy of global positioning system (GPS) navigation. The implicit function theorem allows one to approximate the timing accuracy required by the GPS navigation system to locate a user within a certain degree of preci ..."
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Abstract. This paper provides an example of the implicit function theorem to the accuracy of global positioning system (GPS) navigation. The implicit function theorem allows one to approximate the timing accuracy required by the GPS navigation system to locate a user within a certain degree of precision.
Inverse Functions in ACL2(r)
"... ACL2(r) supports the definition of realvalued functions. In this paper, we introduce a theory of inverse functions into description of inverse functions, to a still abstract but more tractable treatment of the inverse of continuous functions. A macro is introduced to simplify the introduction of co ..."
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ACL2(r) supports the definition of realvalued functions. In this paper, we introduce a theory of inverse functions into description of inverse functions, to a still abstract but more tractable treatment of the inverse of continuous functions. A macro is introduced to simplify the introduction of concrete inverse functions. We illustrate the approach by defining some inverse functions in ACL2, including the square root, natural logarithm, inverse sine, and inverse cosine functions.