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### Recognition of Blurred Pieces of Discrete Planes [chapter]

Laurent Provot, Lilian Buzer, Isabelle Debled-Rennesson
2006 Lecture Notes in Computer Science
Two recognition algorithms of such primitives are proposed: the first one is a geometrical algorithm and minimizes the Euclidean distance and the second one relies on linear programming and minimizes the  ...  It generalizes such planes, admitting that some points are missing and then permits to adapt to noisy discrete data.  ...  The first one is based on a structural approach: the computation of the convex hull of the given voxels is done while we search for the two parallel planes that mark out this convex hull and that minimize  ...

### A pipelined architecture for ray/bezier patch intersection computation

R.R. Lewis, Renwei Wang, D. Hung
2003 Canadian journal of electrical and computer engineering
We describe an algorithm for computing ray/Bézier patch intersections from a hardware design aspect.  ...  This algorithm uses patch subdivision and other geometrical techniques to find a given maximum number of intersection points nearest to the ray origin.  ...  in adapting the Nishita algorithm and in implementing the software version of the proposed algorithm.  ...

### View Synthesis using Convex and Visual Hulls

Y Wexler, R Chellappa
2001 Procedings of the British Machine Vision Conference 2001
A better way to do this is to compute the dual convex hull of the planes and use the resulting edges to divide the image into at most ¥ convex polygons as shown in figure 4(a), each corresponds to a facet  ...  Both algorithms approximate the world object. One uses the convex hull and the other uses the visual hull.  ...  Shortcomings Figure 1 : Convex and visual hulls of a simple scene. 1(a) Two bounding planes in each image define the convex hull. 1(b) The resulting convex hull is used as an approximation to the shape  ...

### Backward Error Analysis in Computational Geometry [chapter]

Di Jiang, Neil F. Stewart
2006 Lecture Notes in Computer Science
This analysis is relevant in the context of uncertain data, which may well be the practical context for computational-geometry algorithms such as, say, those for computing convex hulls.  ...  Indeed, the example mentioned can be viewed simply as an example of an unstable algorithm, for a problem for which computational geometry has already discovered provably stable algorithms.  ...  an ambiguous point is considered to part of a "left turn", and dropped from the computed convex hull.  ...

### Computing a View Frustum to Maximize an Object's Image Area [chapter]

2005 Graphics Tools---The jgt Editors' Choice
This paper presents a method to compute a view frustum for a 3D object viewed from a given viewpoint, such that the object is completely enclosed in the frustum and the object's image area is also near-maximal  ...  First, from the given viewpoint, a conveniently-computed view frustum is used to project the 3D vertices of the object to their corresponding 2D image points.  ...  Support for this research comes from NSF ITR grant "Electronic Books for the Tele-immersion Age" and NSF Cooperative Agreement no.  ...

### Planar Features and 6D-SLAM based on Linear Regression Kalman Filters with n-Dimensional Approximated Gaussians

Cihan Ulas, Hakan Temeltas
2014 IFAC Proceedings Volumes
The method uses the LFKF with n-dimensional approximated Gaussians by addressing the data association problem based on semantic data of plane-features.  ...  While the conventional feature based SLAM methods use point features as landmarks, only a few take the advantage of geometric information like corners, edges, and planes.  ...  Convex hull computation is carried out in 2D space; therefore the 3D plane points are primarily projected to 2D space.  ...

### Theory and Algorithm for Planar Datum Establishment Using Constrained Total Least-squares

Craig M. Shakarji, Vijay Srinivasan
2016 Procedia CIRP
First, we present an efficient algorithm for establishing planar datums that is based on a constrained minimization search based on the L2 norm after forming a convex surface from sampled points.  ...  Second, we highlight advantages of this planar datum, including the major advantage that the datum planes have full mechanical contact with the datum features in stable cases yet are automatically balanced  ...  nonmaterial side of the computed convex surface that minimizes the integral of squared distances from that surface, namely , where S is the convex surface and d is the distance from a point p on the surface  ...

### FLOATING-POINT ARITHMETIC FOR COMPUTATIONAL GEOMETRY PROBLEMS WITH UNCERTAIN DATA

D. JIANG, N. F. STEWART
2009 International journal of computational geometry and applications
It is the purpose of this paper to show that these suggestions, based on an example showing failure of a certain algorithm for computing planar convex hulls, are misleading, and why this is so.  ...  This analysis is relevant in the context of uncertain data, which may well be the practical context for computational-geometry algorithms such as, say, those for computing convex hulls.  ...  an ambiguous point is considered to part of a "left turn", and dropped from the computed convex hull.  ...

### Interactive Cutaway Illustrations

J. Diepstraten, D. Weiskopf, T. Ertl
2003 Computer graphics forum (Print)
In this paper we discuss different approaches to generate cutaway illustrations. The purpose of such a drawing is to allow the viewer to have a look into an otherwise solid opaque object.  ...  Traditional methods to draw these kinds of illustrations are evaluated to extract a small and effective set of rules for a computer-based rendering of cutaway illustrations.  ...  Acknowledgments We would like to thank the anonymous reviewers for helpful comments to improve the paper.  ...

### Unsupervised upright orientation of man-made models

Yong Jin, Qingbiao Wu, Ligang Liu
2012 Graphical Models
The models are to be iteratively rotated by using the recently presented TILT technique, in order to ensure that their projections have optimal low-rank observations.  ...  We present a novel unsupervised approach for finding the upright orientation of man-made models by using a low-rank matrix theorem based technique.  ...  By utilizing advanced convex optimization tools from matrix rank minimization, their approach is able to find an ''upright'' version of the image texture by computing an optimal transformation in a certain  ...

### Estimation of minimum volume of bounding box for geometrical metrology

Chelishchev Petr, Sørby Knut
2020 International Journal of Metrology and Quality Engineering
As showed in the paper, the solution of the minimum bonding box is not based on faces located near the edges; therefore, we can save computation time by excluding them from the convex polyhedron data set  ...  The algorithm is based on the convex hull operation and established theories about a minimum bounding box circumscribing a convex polyhedron.  ...  The authors wish to thank Dr. Christoph A. Thieme, NTNU, Trondheim, for valuable advices and comments.  ...

### Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes

U.A. Khan, S. Kar, J.M.F. Moura
2009 IEEE Transactions on Signal Processing
The paper develops DILOC, a distributive, iterative algorithm that locates M sensors in R^m, m≥ 1, with respect to a minimal number of m+1 anchors with known locations.  ...  DILOC uses the barycentric coordinates of a sensor with respect to its neighbors that are computed using the Cayley-Menger determinants.  ...  APPENDIX I CONVEX HULL INCLUSION TEST We now give an algorithm that tests if a given sensor, , lies in the convex hull of nodes in a set, , using only the mutual distance information among these nodes  ...

### Page 5231 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews
However, this approach results in inconsistent systems of inequalities if the convex hulls do intersect. An iterative scheme based on minimizing the error in the linear systems can still be used.  ...  In this paper, the author presents a different approach based on minimizing the sum of (arbitrary) norm distances to the separating hyperplane of points lying on the wrong side of the plane.  ...

### Fundamental Matrices from Moving Objects Using Line Motion Barcodes [article]

Yoni Kasten, Gil Ben-Artzi, Shmuel Peleg, Michael Werman
2016 arXiv   pre-print
Prior methods searched for corresponding epipolar lines using points on the convex hull of the silhouette of a single moving object.  ...  Computing the epipolar geometry between cameras with very different viewpoints is often very difficult.  ...  This research was supported by Google, by Intel ICRI-CI, by DFG, and by the Israel Science Foundation.  ...

### A novel Approach to Human Gait Recognition using possible Speed Invariant features

Anup Nandy, Rupak Chakraborty, Pavan Chakraborty, G.C. Nandi
2014 International Journal of Computational Intelligence Systems
This drawback inspires us to compute the area of each region by constructing a convex hull of the feature points in order to obtain certain key speed invariant features.  ...  Initially, all the feature points are represented as the sides of an n-sided polygon for calculating the area of each region.  ...  Acknowledgements We owe our sincere thanks and gratitude to Prof Yasushi Yagi and his whole research team for sharing with us the valuable OU-ISIR  Gait database without which the work could not  ...
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