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Ray-tracing triangular trimmed free-form surfaces

W. Sturzlinger
1998 IEEE Transactions on Visualization and Computer Graphics  
For trimmed surfaces an irregular adaptive subdivision is constructed to quickly eliminate all parts outside the trimming curve from consideration during rendering.  ...  A hierarchical subdivision of the surface with associated tight bounding volumes provides for quick identification of the surface regions likely to be hit by a ray.  ...  Many thanks to the anonymous reviewers for their constructive suggestions. Thanks also to Jörg Peters for the 288-patch model.  ... 
doi:10.1109/2945.722295 fatcat:gbdq54pgtzf2zdr4v7gulcd3wi

Nonlinear subdivision through nonlinear averaging

S. Schaefer, E. Vouga, R. Goldman
2008 Computer Aided Geometric Design  
As an application we show how to apply our nonlinear subdivision algorithms to intersect some common transcendental functions.  ...  We investigate a general class of nonlinear subdivision algorithms for functions of a real or complex variable built from linear subdivision algorithms by replacing binary linear averages such as the arithmetic  ...  Acknowledgements We would like to thank Nira Dyn for her help and advice with this paper as well as for suggesting [11] as a reference.  ... 
doi:10.1016/j.cagd.2007.07.003 fatcat:kdtze4qrnvchpf7txw6pp7do2q

Recursive subdivision of polygonal complexes and its applications in computer-aided geometric design

Ahmad H. Nasri
2000 Computer Aided Geometric Design  
A method for subdividing polygonal complexes and identifying conditions to control their limit curves is presented.  ...  We formulate this problem and establish a general theory which has a number of applications in CAGD such as the generation of subdivision surfaces through predefined arbitrary network of curves.  ...  Acknowledgements This work was supported by a research grant from the American University of Beirut. The author would like to thank Prof. Abdallah Lyzzaik for his valuable comments.  ... 
doi:10.1016/s0167-8396(00)00015-7 fatcat:3dnlrk4ipvdutlpwxuryf5r3mq

Taxonomy of interpolation constraints on recursive subdivision surfaces

Ahmad H. Nasri, Malcolm A. Sabin
2002 The Visual Computer  
It addresses surface interpolation constraints, building upon the concepts and categories introduced in the first paper, on interpolation constraints on recursive subdivision curves.  ...  This is the second of two papers which describe and classify situations which any complete study of interpolation constraints for a recursive subdivision surface needs to consider.  ...  Thanks are due to the American University of Beirut, the Lebanese National Council for Scientific Research, and the Royal Society of London for supporting this work.  ... 
doi:10.1007/s003710100155 fatcat:m5vbcowrdfgaflpw6df7ti5dhq

Trimming implicit surfaces

Galina Pasko, Alexander Pasko
2004 The Visual Computer  
The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm.  ...  These twodimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface.  ...  Alexander Belyaev for proposing an application example and for his help with its implementation. The comments by an anonymous reviewer helped improve the paper.  ... 
doi:10.1007/s00371-004-0250-6 fatcat:b6esu3kd3rcshkb3vpcxpelmoq

Fillet Operations with Recursive Subdivision Surfaces [chapter]

Zheng Xu, Kunio Kondo
2001 Geometric Modelling  
Recursively subdividing polyhedral networks, often called polyhedral subdivision, has become one of the basic tools in Computer Aided Geometric Design(CAGD) for modeling complex surfaces.  ...  After fillet operations, we tried two basic recursive subdivision methods Doo-Sabin and Catmull-Clark to generate surfaces.  ...  Nasri extended Doo-Sabin method to generate a surface which interpolates some or all vertices of a polyhedron [4] ,Morc-over, he proposed an algorithm to generate subdivision surfaces which interpolate  ... 
doi:10.1007/978-0-387-35490-3_19 fatcat:rc3r7t5yhrgdli6ene535gpvj4

Page 9500 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Summary: “In this paper we present a symbolic algorithm for parametrically blending with G'-continuity a collection of rational surfaces with rational clipping intersections.  ...  This paper introduces new families of uniform non-stationary subdivision schemes for free-form curve and surface design.  ... 

Reconstruction of Branching Surface and Its Smoothness by Reversible Catmull-Clark Subdivision [chapter]

Kailash Jha
2009 Lecture Notes in Computer Science  
In the current research a new algorithm has been developed to get surface from the contours having branches and a final smooth surface is obtained by reversible Catmull-Clark Subdivision.  ...  This process is repeated for all layers having branching problems. In the next step, 3D composite curves are converted into different polyhedrons by the help of the contours at adjacent layers.  ...  In reference [20] an algorithm has been developed to obtain branching surfaces by energy based skinning of compatible 2-D curves obtained by energy-based approximation.  ... 
doi:10.1007/978-3-642-01973-9_85 fatcat:jke7aywmhfdj7edxauuiw2pgye

Splines and geometric modeling [chapter]

Chandrajit Bajaj
2004 Handbook of Discrete and Computational Geometry, Second Edition  
An algorithm for the local interpolation of a cubic curve mesh by a piecewise bi quartic C 1 surface is described.  ...  Peters Pet93 gives an algorithm for re ning an irregular mesh of points into a bivariate C 1 surface.  ... 
doi:10.1201/9781420035315.ch53 fatcat:e7evq2b77ba5lj3vxlcxwxxzda

Page 5328 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews  
Micchelli, The design of curves and surfaces by subdivision algorithms (pp. 115-153). E. Cohen [Elaine Cohen] and C. L.  ...  Gmelig Meyling, An algorithm for smooth interpolation to scattered data in R?  ... 

Improving Ray Tracing Precision by Object Space Intersection Computation

H. Dammertz, A. Keller
2006 2006 IEEE Symposium on Interactive Ray Tracing  
ABSTRACT Instead of computing intersections along a ray, an algorithm is proposed that determines a point of intersection in object space.  ...  In addition the method lends itself to a simple solution of the self-intersection problem. Considering the obtained precision the algorithm is efficient, simple to use, and to implement.  ...  ACKNOWLEDGEMENTS We would like to thank Ingo Wald for the fruitful scientific discussion.  ... 
doi:10.1109/rt.2006.280211 fatcat:gcjau3jbsbb5jfhrw773t6hsbi

Interactive ray tracing of free-form surfaces

Carsten Benthin, Ingo Wald, Philipp Slusallek
2004 Proceedings of the 3rd international conference on Computer graphics, virtual reality, visualisation and interaction in Africa - AFRIGRAPH '04  
However, existing algorithms for ray tracing free-form surfaces are much too slow for interactive use.  ...  In this paper we present a simple and generic approach for ray tracing free-form surfaces together with specific implementations for cubic Bézier and Loop subdivision surfaces.  ...  The second category of algorithms typically uses a recursive refinement algorithm: If the ray might intersect the current primitive, refine it into a set of new primitives and recurse for each of them.  ... 
doi:10.1145/1029949.1029968 dblp:conf/afrigraph/BenthinWS04 fatcat:wz2jk4vwsvbhha4p5q64s2jxa4

Component-based polygonal approximation of soft objects

Kyung Ha Min, In-Kwon Lee, Chan-Mo Park
2001 Computers & graphics  
polygonal approximation using subdivision surface schemes.  ...  While the conventional polygonization methods decompose space into small-sized cells and compute many pieces of polygons for the cells, this new method polygonizes a soft object by smoothing an initial  ...  Gerard Jounghyun Kim for his kind review and Sung-Min Pak for his implementation of the human body model.  ... 
doi:10.1016/s0097-8493(00)00128-x fatcat:poqdrnixcrcr5d342w6enwhppu

A survey of subdivision-based tools for surface modeling [chapter]

Ioana Boier-Martin, Denis Zorin, Fausto Bernardini
2005 Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing  
Subdivision surfaces have emerged as a powerful representation for surface modeling and design.  ...  In this paper we survey existing subdivision-based modeling methods with emphasis on interactive tools for styling and decoration of 3D models.  ...  and Refinement steps: Algorithm 1 (snapping and refinement): Given a domain mesh M and an intersection curve c(t) in M Repeat For each vertex v of a triangle intersected by c do 1.  ... 
doi:10.1090/dimacs/067/01 dblp:conf/dimacs/Boier-MartinZB03 fatcat:5pqdfabmvzbj5aktapk2enku2u

Page 67 of Journal of Research and Practice in Information Technology Vol. 21, Issue 2 [page]

1989 Journal of Research and Practice in Information Technology  
Interpolative hidden surface removal method for polyhedra M.S. Cottingham Monash University, Melbourne, Victoria. All hidden surface removal methods involve sorting facets into some order.  ...  Warnock’s algorithm (Warnock, 1969) avoids this by recursively subdividing the image space until each region contains only one visible facet or is only one pixel in size.  ... 
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