A SURFACE INTERSECTION ALGORITHM BASED ON LOOP DETECTION

1991 ◽  
Vol 01 (04) ◽  
pp. 473-490 ◽  
Author(s):  
MICHAEL E. HOHMEYER
Keyword(s):  
Gauss Map ◽  
Algebraic Surfaces ◽  
Boundary Representation ◽  
Intersection Curve ◽  
Closed Loops ◽  
Detection Algorithms ◽  
Surface Intersection ◽  
Loop Detection ◽  
Intersection Algorithm ◽  
New Strategies

A robust and efficient surface intersection algorithm that is implementable in floating point arithmetic, accepts surfaces algebraic or otherwise and which operates without human supervision is critical to boundary representation solid modeling. To the author's knowledge, no such algorithms has been developed. All tolerance-based subdivision algorithms will fail on surfaces with sufficiently small intersections. Algebraic techniques, while promising robustness, are presently too slow to be practical and do not accept non-algebraic surfaces. Algorithms based on loop detection hold promise. They do not require tolerances except those associated with machine associated with machine arithmetic, and can handle any surface for which there is a method to construct bounds on the surface and its Gauss map. Published loop detection algorithms are, however, still too slow and do not deal with singularities. We present a new loop detection criterion and discuss its use in a surface intersection algorithms. The algorithm, like other loop detection based intersection algorithms, subdivides the surfaces into pairs of sub-patches which do not intersect in any closed loops. This paper presents new strategies for subdividing surfaces in a way that causes the algorithms to run quickly even when the intersection curve(s) contain(s) singularities.

An Efficient Algorithm for Circular Blending of Edges

2001 ◽  
Author(s):  
Sharad K. Jaiswal ◽  
A. Ghosal ◽  
B. Gurumoorthy
Keyword(s):  
Efficient Algorithm ◽  
Tangent Plane ◽  
Characteristic Direction ◽  
Intersection Curve ◽  
Generation Algorithm ◽  
Variable Radius ◽  
Surface Intersection ◽  
Explicit Evaluation

Abstract This paper describes a method for constructing circular blends using geometric tools. The algorithm presented in this paper is based on marching along a characteristic direction on the tangent plane to the Voronoi surface of the two surfaces being considered for blending. Starting from any point on the edge to be blended, the algorithm converges to the spine curve. The characteristic direction of marching lies on the plane containing the points in assignment and the tangent plane to the Voronoi surface. The spine curve generation algorithm presented in this paper, does not require computing offsets of surfaces or an explicit evaluation of surface-surface intersection (SSI). The algorithm presented is computationally simple and fast, and can be used for constant and variable radius circular blending of surfaces, each of which is G2 continuous. The algorithm can also be used to obtain the surface-surface intersection curve by setting the radius of blend to zero.

scholarly journals A line/trimmed NURBS surface intersection algorithm using matrix representations

2016 ◽  
Vol 48 ◽  
pp. 1-16 ◽  
Author(s):  
Jingjing Shen ◽  
Laurent Busé ◽  
Pierre Alliez ◽  
Neil Dodgson
Keyword(s):  
Nurbs Surface ◽  
Matrix Representations ◽  
Surface Intersection ◽  
Intersection Algorithm

An efficient surface–surface intersection algorithm based on geometry characteristics

2004 ◽  
Vol 28 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Xueyi Li ◽  
Hong Jiang ◽  
Song Chen ◽  
Xiaochun Wang
Keyword(s):  
Surface Intersection ◽  
Intersection Algorithm

Microelectromechanical Hybrid Gyroscope Design of Closed-Loop Detection Circuit Based on FPGA

2013 ◽  
Vol 562-565 ◽  
pp. 172-177
Author(s):  
Dun Zhu Xia ◽  
Cheng Yu ◽  
Shou Rong Wang ◽  
Hong Sheng Li
Keyword(s):  
Closed Loop ◽  
Rotation Frequency ◽  
Digital Design ◽  
Closed Loops ◽  
Noise Interference ◽  
Scale Factors ◽  
Detection Circuit ◽  
Loop Detection ◽  
Sinusoidal Functions ◽  
Cross Axis

This paper presents a new microelectromechanical hybrid gyroscope (MHG) with three equilibrium rings. This structure can eliminate the error caused by the double rotation frequency of the driving shaft successfully. The MHG kinematic equations with three equilibrium rings are derived in this paper. Meanwhile, a new digital design and simulation of the MHG closed-loop detection circuit are proposed based on FPGA. The noise interference is weakened by using differential mode signal detection and the resources of FPGA are decreased by the loop diode demodulation in this paper. The cross axis coupling of the decoupled system is about 2.4%. The phase margin is 70deg and the magnitude margin is 22db after correction. The transcient response simulation is tested when the inputs are sinusoidal functions. The bandwidth and scale factors of x-axis and y-axis closed loops are analyzed in the paper. The bandwidth can reach about 70Hz and the scale factors of x-axis and y-axis closed loops are 0.1467V/o/s and -0.1467V/o/s respectively.

scholarly journals A Condition Number Analysis of a Line-Surface Intersection Algorithm

2008 ◽  
Vol 30 (2) ◽  
pp. 1064-1081 ◽  
Author(s):  
Gun Srijuntongsiri ◽  
Stephen A. Vavasis
Keyword(s):  
Condition Number ◽  
Surface Intersection ◽  
Intersection Algorithm

scholarly journals Role of Deep Learning in Loop Closure Detection for Visual and Lidar SLAM: A Survey

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1243
Author(s):  
Saba Arshad ◽  
Gon-Woo Kim
Keyword(s):  
Deep Learning ◽  
Detailed Comparison ◽  
Loop Closure ◽  
Loop Closure Detection ◽  
Detection Algorithms ◽  
Mobile Objects ◽  
Localization And Mapping ◽  
Loop Detection ◽  
Scene Representation ◽  
Matching Strategy

Loop closure detection is of vital importance in the process of simultaneous localization and mapping (SLAM), as it helps to reduce the cumulative error of the robot’s estimated pose and generate a consistent global map. Many variations of this problem have been considered in the past and the existing methods differ in the acquisition approach of query and reference views, the choice of scene representation, and associated matching strategy. Contributions of this survey are many-fold. It provides a thorough study of existing literature on loop closure detection algorithms for visual and Lidar SLAM and discusses their insight along with their limitations. It presents a taxonomy of state-of-the-art deep learning-based loop detection algorithms with detailed comparison metrics. Also, the major challenges of conventional approaches are identified. Based on those challenges, deep learning-based methods were reviewed where the identified challenges are tackled focusing on the methods providing long-term autonomy in various conditions such as changing weather, light, seasons, viewpoint, and occlusion due to the presence of mobile objects. Furthermore, open challenges and future directions were also discussed.

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