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Fast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic

A. Knoll, Y. Hijazi, A. Kensler, M. Schott, C. Hansen, H. Hagen
2009 Computer graphics forum (Print)  
A similar algorithm can also be implemented stacklessly, allowing for efficient ray tracing on the GPU.  ...  Nonetheless, implemented efficiently using a stack-driven iterative algorithm and SIMD vector instructions, these methods can achieve interactive performance for common algebraic surfaces on the CPU.  ...  Hart [Har96] proposed a robust method for ray tracing algebraics by defining signed distance functions from an arbitrary point to the surface.  ... 
doi:10.1111/j.1467-8659.2008.01189.x fatcat:nasyvep56fbvngkthp2wmahny4

A higher dimensional formulation for robust and interactive distance queries

Joon-Kyung Seong, David E Johnson, Elaine Cohen
2006 Proceedings of the 2006 ACM symposium on Solid and physical modeling - SPM '06  
This topological information provides an elegant way to efficiently find a global minimum distance solution for spatially coherent queries. Additionally, we extend this approach to a 3D case.  ...  We present an efficient and robust algorithm for computing the minimum distance between a point and freeform curve or surface by lifting the problem into a higher dimension.  ...  In this paper, a symbolic-numeric hybrid approach is presented to exploit both advantages.  ... 
doi:10.1145/1128888.1128916 dblp:conf/sma/SeongJC06 fatcat:edvkta62hvg77b3xue22ssylse

A predictor–corrector-type technique for the approximate parameterization of intersection curves

Bert Jüttler, Pavel Chalmovianský
2006 Applicable Algebra in Engineering, Communication and Computing  
We describe a method to approximate a segment of the intersection curve of two implicitly defined surfaces by a rational parametric curve.  ...  An SQP-type method is used to solve the optimization problem numerically. Two different predictor steps, which are based on simple extrapolation and on a differential equation, are formulated.  ...  In the case of algebraic space curves, several computational techniques relying on symbolic and hybrid symbolic-numeric algorithms exist.  ... 
doi:10.1007/s00200-006-0031-8 fatcat:ofmvls7m5bcytb6t44xeyk4p7y

Distortion Theory of Stereographic Draping with Flexible Fabric on General Surface: Part I-Geometric Analysis

Roger Ng, Winnie Yu
2006 Sen'i Gakkaishi  
Stereographic Draping is a mathematical model of garment draping that unfolds a 3-D garment surface to the corresponding flat garment patterns.  ...  Mathematically, Stereographic Draping on a general surface is very difficult to be analyzed.  ...  The authors would like to take this opportunity to express our gratitude such research funding.  ... 
doi:10.2115/fiber.62.74 fatcat:bdaybcspsre5rgej5xmzkggjm4


J. C. Henson, W. M. G. Malalasekera
1997 Numerical Heat Transfer, Part A Applications  
Numerical solutions found with both algorithms are in good agreement with published benchmark results which used contemporary methods to determine the radiative transport in a unit cube.  ...  m 2 G S i j volume-to-surface total exchange area, m 2 I intensity of radiation, W/m 2 sr Henson, Greek Symbols  extinction coefficient, 1/m  emissivity  absorption coefficient, 1/m    , , coordinates  ...  Comparisons are made with calculations from a hybrid zonal/Monte Carlo code to ensure a valid set of numerical solutions, and both numerical methods are first verified against solutions by Hsu and Farmer  ... 
doi:10.1080/10407789708913877 fatcat:zagyo352yzf73bipijoeh5rxb4

Affine Arithmetic-Based B-Spline Surface Intersection with GPU Acceleration

Hongwei Lin, Yang Qin, Hongwei Liao, Yunyang Xiong
2014 IEEE Transactions on Visualization and Computer Graphics  
Because the B-spline surface intersection is a fundamental operation in geometric design software, it is important to make the surface intersection operation robust and efficient.  ...  As is well known, affine arithmetic is robust for calculating the surface intersection because it is able to not only find every branch of the intersection, but also deal with some singular cases, such  ...  ACKNOWLEDGMENTS The authors are very grateful to the reviewers for their invaluable advice. This work was supported by the Natural Science Foundation of China (Nos. 61379072, 60970150, and 60933008).  ... 
doi:10.1109/tvcg.2013.237 pmid:24356361 fatcat:46baef5tsferhg5ijs4gixbrrq

Optimally Fast Soft Shadows on Curved Terrain with Dynamic Programming and Maximum Mipmaps [article]

Dawoon Jung
2020 arXiv   pre-print
To add support for accurate planetary ephemerides and interactive features, we integrated the engine into celestia.Sci, a general space simulation software.  ...  We present a simple, novel method of efficiently rendering ray cast soft shadows on curved terrain by using dynamic programming and maximum mipmaps to rapidly find a global minimum shadow cost in constant  ...  While several acceleration techniques for computing ray-terrain intersections exist [21, 31] , such techniques typically are problematic when ray casting the surface of a curved base surface such as a  ... 
arXiv:2005.06671v1 fatcat:svb5i6b32fhjffp67vduyelgoy


Peng-Fei Zhang, Shu-Xi Gong, S. F. Zhao
2009 Electromagnetic Waves  
A hybrid method is developed to compute the radiation pattern of antennas on large complex three-dimension carriers.  ...  A dipole placed on different carriers are taken as the examples to show the validity of the hybrid method, and the radiation patterns computed by the proposed method are in good agreement with those by  ...  NUMERICAL RESULTS To illustrate the validity of the proposed method, numerical results are generated for a dipole in two different geometries.  ... 
doi:10.2528/pier08112506 fatcat:rk4yei7xdvdtplrgfg3hxhwqkq

An efficient surface intersection algorithm based on lower-dimensional formulation

Shankar Krishnan, Dinesh Manocha
1997 ACM Transactions on Graphics  
A good surface intersection algorithm should, in theory, b e able to detect all such features of the intersection curve and trace them correctly in an e cient manner.  ...  The surface intersection problem gets further complicated due to numerical errors present in all niteprecision computations Hof89 .  ...  We thank Mike Hohmeyer for lending his implementation of Seidel's linear programming algorithm. We are also very grateful to G. Angelini,  ... 
doi:10.1145/237748.237751 fatcat:r4zs3qiucjfzjn7auple63g5te

Analysis of electromagnetic scattering from a cavity with a complex termination by means of a hybrid ray-FDTD method

R. Lee, Tse-Tong Chia
1993 IEEE Transactions on Antennas and Propagation  
Our results are compared against those found from a hybrid combination of the modal method and the method of moments.  ...  In this paper, we present a hybrid method which combines the,most attractive features of the low-and high-frequency techniques.  ...  Also, we wish to thank the reviewers for providing some very useful suggestions for this paper.  ... 
doi:10.1109/8.267356 fatcat:r3ktb4v4rrea7fvtuq5bdosdzm

Three-dimensional finite difference method and hybrid modeling of earthquake ground motion

Ivo Oprsal
2002 Journal of Geophysical Research  
1] A new two-step hybrid technique (hybrid) has been developed to estimate the earthquake ground motion in three-dimensional (3-D) local models excited by external sources.  ...  The first step of the hybrid requires an arbitrary 3-D method (e.g., finite difference (FD), discrete wave number, ray, or analytical solution) to compute three-component excitation on a grid box surrounding  ...  Albarède and A. Dainty and reviews of R. Graves  ... 
doi:10.1029/2000jb000082 fatcat:xyduj6tfzvd67ldjtndtf6cz7i

Fast and accurate collision detection for haptic interaction using a three degree-of-freedom force-feedback device

A. Gregory, M.C. Lin, S. Gottschalk, R. Taylor
2000 Computational geometry  
At run time, we use hybrid hierarchical representations and exploit frame-to-frame coherence for fast proximity queries.  ...  We describe a new overlap test, which is specialized for intersection of a line segment with an oriented bounding box for haptic simulation and takes 42-72 operations including transformation costs.  ...  Acknowledgements We are grateful to Army Research Office, National Science Foundation, National Institute of Health National Center for Research Resources and Intel Corporation for their support and the  ... 
doi:10.1016/s0925-7721(99)00041-3 fatcat:nf4plf427zhkvpuqar3qob5gm4

Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast [chapter]

Pavel Emeliyanenko, Eric Berberich, Michael Sagraloff
2009 Lecture Notes in Computer Science  
Our hybrid method inherits the ideas of subdivision and curve-tracking methods.  ...  We present an algorithm to visualize distinct connected arcs of an algebraic curve efficiently and precise (at a given resolution), irrespective of how close to each other they actually pass.  ...  Figure 7 depicts an intersection of a Dupin Cyclide with 10 algebraic surfaces of degree 3 computed using [3] .  ... 
doi:10.1007/978-3-642-10331-5_57 fatcat:6gcbq6teobbzrluqljytpv5pbm

Automated generation of hybrid system models for reachability analysis of nonlinear analog circuits

Hyun-Sek Lukas Lee, Matthias Althoff, Stefan Hoelldampf, Markus Olbrich, Erich Barke
2015 The 20th Asia and South Pacific Design Automation Conference  
Our method provides a guaranteed bound on the number of linearization locations that have to be explicitly computed for such a nonlinear circuit.  ...  A reachable set contains the union of all possible system trajectories for a set of uncertain states and as such can be used to provably check whether undesired behavior is possible or not.  ...  Symbols replace the PWL models of this linearized netlist. When computing the system equations for a specific location, numerical parameters according to their active regions replace those symbols.  ... 
doi:10.1109/aspdac.2015.7059096 dblp:conf/aspdac/LeeAHOB15 fatcat:jg5xnl2ldbflxfztbf6v5oi7jq

Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

Xiaowu Li, Lin Wang, Zhinan Wu, Linke Hou, Juan Liang, Qiaoyang Li
2017 Symmetry  
For some special cases where the First-Order method does not converge, we combine it with Newton's second-order iterative method to present the hybrid second-order algorithm.  ...  We also give some numerical examples to illustrate its faster convergence than the existing methods.  ...  Acknowledgments: We take the opportunity to thank anonymous reviewers for their thoughtful and meaningful comments. This work is supported by the National Natural Science  ... 
doi:10.3390/sym9080146 fatcat:lagkanba6bfjzhdk4vgmv3rqxq
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