Cumincad : CUMINCAD Papers : Search Results

CumInCAD is a Cumulative Index about publications in Computer Aided Architectural Design
supported by the sibling associations ACADIA, CAADRIA, eCAADe, SIGraDi, ASCAAD and CAAD futures

PDF papers
References

Hits 1 to 20 of 2362

Reformat results as: short short into frame detailed detailed into frame

_id	67d2
authors	Kajiya, J.T. and Kay, T.L.
year	1986
title	Ray tracing complex scenes
source	Computer Graphics, 20 4, 269-78
summary	A new algorithm for speeding up ray-object intersection calculations is presented. Objects are bounded by a new type of extent, which can be made to fit convex hulls arbitrarily tightly. The objects are placed into a hierarchy. A new hierarchy traversal algorithm is presented which is efficient in the sense that objects along the ray are queried in ancient order. Furthermore , we demonstrate that it is currently possible to raytrace scenes containing hundreds of thousands of objects.
series	journal paper
last changed	2003/04/23 15:50

_id	56af
authors	Nakamae, E., Takao, I., Nishita, T. and Takita, S.
year	1989
title	Compositing 3D Images with Antialiasing and Various Shading Effects
source	IEEE Computer Graphics & Applications 9 no. 2: 21-29
summary	A method is proposed for compositing 3-D images produced by different programs, taking depth order into consideration. The method can add the following effects to composited images: antialiased images with scaling are displayed by a simple algorithm; the algorithm can add shading effects due to various types of light, such as area sources and skylight; and ray tracing can be performed in localized regions, producing realistic results without the computational expense of ray tracing the whole image. In addition to the above processes, such shading effects as fog and texture mapping can be processed with conventional methods. Thus, it becomes possible to display complex scenes with various shading effects, using relatively small computers. The multiscanning method used for antialiasing and a data structure for processing it are described. Examples are presented to demonstrate the capability of the system.
series	journal paper
last changed	2003/04/23 15:14

_id	7670
authors	Sawicki, Bogumil
year	1995
title	Ray Tracing – New Chances, Possibilities and Limitations in AutoCAD
source	CAD Space [Proceedings of the III International Conference Computer in Architectural Design] Bialystock 27-29 April 1995, pp. 121-136
summary	Realistic image synthesis is nowadays widely used in engineering applications. Some of these applications, such as architectural, interior, lighting and industrial design demand accurate visualization of non-existent scenes as they would look to us, when built in reality. This can only be archived by using physically based models of light interaction with surfaces, and simulating propagation of light through an environment. Ray tracing is one of the most powerful techniques used in computer graphics, which can produce such very realistic images. Ray tracing algorithm follows the paths of light rays backwards from observer into the scene. It is very time consuming process and as such one could not be developed until proper computers appeared, In recent years the technological improvements in computer industry brought more powerful machines with bigger storage capacities and better graphic devices. Owing to increasing these hardware capabilities successful implementation of ray tracing in different CAD software became possible also on PC machines. Ray tracing in AutoCAD r.12 - the most popular CAD package in the world - is the best of that example. AccuRender and AutoVision are an AutoCAD Development System (ADS) applications that use ray tracing to create photorealistic images from 3D AutoCAD models. These ,internal"' applications let users generate synthetic images of threedimensional models and scenes entirely within AutoCAD space and show effects directly on main AutoCAD screen. Ray tracing algorithm accurately calculates and displays shadows, transparency, diffusion, reflection, and refraction from surface qualities of user-defined materials. The accurate modelling of light lets produce sophisticated effects and high-quality images, which these ray tracers always generates at 24-bit pixel depth,"providing 16,7 million colours. That results can be quite impressive for some architects and are almost acceptable for others but that coloured virtual world, which is presented by ray tracing in AutoCAD space in such convincing way, is still not exactly the same as the real world. Main limitations of realism are due to the nature of ray tracing method Classical ray tracing technique takes into account the effects of light reflection from neighbouring surfaces but, leaves out of account the ambient and global illumination arising out of complex interreflections in an environment. So models generated by ray tracing belong to an "ideal" world where real materials and environment can't find their right place. We complain about that fact and say that ray tracing shows us "too specular world", but (...) (...) there is anything better on the horizon? It should be concluded, that typical abilities of today's graphics software and hardware are far from exploited. As was observed in literature there have been various works carried along with the explicit intention of overcoming all these ray tracing limitations, These researches seem to be very promising and let us hope that their results will be seen in CAD applications soon. As it happens with modelling, perhaps the answer will come from a variety of techniques that can be combined together with ray tracing depending on the case we are dealing with. Therefore from the point of view of an architects that try to keep alive some interest on the nature of materials and their interaction with form, "ray tracing" seems to be right path of research and development that we can still a long way follow, From the point of view of the school, a critical assimilation of "ray tracing" processes is required and one that might help to determinate exactly their distortions and to indicate the correct way of its development and right place in CAAD education. I trust that ray tracing will become standard not only in AutoCAD but in all architectural space modelling CAD applications and will be established as a powerful and real tool for experimental researches in architectural design process. Will be the technological progress so significant in the nearest future as it is anticipated?
series	plCAD
last changed	2000/01/24 10:08

_id	e65f
authors	Haines, Eric A. and Greenberg, Donald P.
year	1986
title	The Light Buffer: A Shadow-Testing Accelerator
source	IEEE Computer Graphics and Applications. September, 1986. vol. 6: pp. 6-16 : col. ill. includes bibliography
summary	In one area of computer graphics, realistic image synthesis, the ultimate goal is to produce a picture indistinguishable from a photograph of a real environment. A particularly powerful technique for simulating light reflection - an important element in creating this realism - is called ray tracing. This method produces images of excellent quality, but suffers from lengthy computation time that limits its practical use. This article presents a new method to reduce shadow testing time during ray tracing. The technique involves generating light buffers, each of which partitions the environment with respect to an individual light source. These partition descriptions are then used during shadow testing to quickly determine a small subset of objects that may have to be tested for intersection. The results of timing tests illustrate the beneficial performance of these techniques. The tests compare the standard ray-tracing algorithm to light buffers of varying resolution
keywords	realism, synthesis, ray tracing, algorithms, computer graphics, shadowing
series	CADline
last changed	2003/06/02 13:58

_id	6728
authors	Rossignac, Jaroslaw R. and Requicha, Aristides A. G.
year	1986
title	Depth- Buffering Display Techniques for Constructive Solid Geometry
source	IEEE Computer Graphics and Applications. September, 1986. vol. 6: pp. 29-39 : ill. some col. includes bibliography
summary	Solid modelers based on constructive solid geometry (CSG) typically generate shaded displays directly from CSG by using ray-casting techniques, which do not require information on the faces, edges, and vertices that bound a solid. This article describes an alternative - a simple new algorithm based on a depth-buffering or z-buffering approach. The z- buffer display algorithm operates directly on CSG, does not require explicit boundary data, and is easier to implement than ray casting. Ray-casting and z-buffering algorithms have comparable performances, but z-buffering is often faster for objects with complex surfaces, because it avoids expensive curve/surface intersection calculations. Because of their simplicity, depth-buffering algorithms for CSG are well- suited to hardware implementations, and may lead to machines simpler than those now being built for ray casting
keywords	geometric modeling, CSG, display, computer graphics
series	CADline
last changed	2003/06/02 13:58

_id	c3a4
authors	Chiarelli, Julia
year	2001
title	APORTES EN LA BÚSQUEDA DE LA INFLUENCIA DE LA LUZ EN EL REALISMO DE LA IMAGEN ARQUITECTÓNICA (Contributions in the Search of the Influence of the Light in the Realism of the Architectural Image)
source	SIGraDi biobio2001 - [Proceedings of the 5th Iberoamerican Congress of Digital Graphics / ISBN 956-7813-12-4] Concepcion (Chile) 21-23 november 2001, pp. 60-63
summary	The real world is very complex, there are textures, gradients of colors, shades and reflections that are difficult to represent in the computer . Investigation : The realism and real image / Two algorithms of illumination (radiosity ,ray tracing) / Commercial programs that allow me to generate synthesis images.
series	SIGRADI
email
last changed	2016/03/10 09:49

_id	ecaade2017_305
id	ecaade2017_305
authors	Luther, Mark B.
year	2017
title	The Application of Daylighting Software for Case-study Design in Buildings
doi	https://doi.org/10.52842/conf.ecaade.2017.1.629
source	Fioravanti, A, Cursi, S, Elahmar, S, Gargaro, S, Loffreda, G, Novembri, G, Trento, A (eds.), ShoCK! - Sharing Computational Knowledge! - Proceedings of the 35th eCAADe Conference - Volume 1, Sapienza University of Rome, Rome, Italy, 20-22 September 2017, pp. 629-638
summary	The application of different software, whether simple or complex, can each play a significant role in the design and decision-making on daylighting for a building. This paper, discusses the task to be accomplished, in real case studies, and how various lighting software programs are used to achieve the desired information. The message iterated throughout the paper is one that respects, and even suggests, the use of even the simplest software, that can guide and inform design decisions in daylighting. Daylighting can be complex since the position of the sun varies throughout the day and year as well as do the sky conditions for a particular location. Just because we now have the computing capacity to model every single minute of a day throughout a year, doesn't justify its task. Several projects; an architecture studio, a university office building, a school library and a gymnasium all present different tasks to be achieved. The daylighting problems, the objects and the software application and their outcomes are presented in this paper. Over a decade of projects has led to reflecting upon the importance of computing in daylighting, its staged approach and the result that it can achieve if properly applied.
keywords	Daylighting Design; Daylighting Analysis; Radiosity; Ray-tracing
series	eCAADe
email
last changed	2022/06/07 07:51

_id	2006_566
id	2006_566
authors	Rafi, Ahmad; Mohamad Izani Zainal Abidin; Avijit Paul and Aishah Abdul Razak
year	2006
title	Simulation of architectural lighting in a virtual environment - A case study on real and fake High Dynamic Range Images (HDRI)
doi	https://doi.org/10.52842/conf.ecaade.2006.566
source	Communicating Space(s) [24th eCAADe Conference Proceedings / ISBN 0-9541183-5-9] Volos (Greece) 6-9 September 2006, pp. 566-572
summary	The early findings of this research were presented in eCAADe 2005 International Conference, Lisbon primarily to highlight the concept of High Dynamic Range Images (HDRI) when representing architectural spaces in the form of still images. An experiment had been carried out to compare the results between HDRI rendering and ‘conventional’ lighting simulation algorithms namely ray tracing and radiosity. The results were based on static and using the same exposure factors, when capturing HDRI. This project, funded by Intensification Research Priority Area (IRPA) grant continues to present and report HDRI results in a simulation environment. In this paper, we first briefly explain on the concept of real and fake HDRI. Then a comparison experiment is conducted to compare these two methods and discuss the impact and effectiveness of the illumination computation in architectural simulation environment. In order to carry out the experiment, a few models of the architectural scenes were developed. These models were then textured with real photos and manipulated with ‘shaders’, and further rendered using fake and real HDRI techniques. As for the fake HDRI, two methods were developed. The first was using an image as the ambient map and different exposures were created by increasing the value of Hue, V of HSV and saturation. The second involved a series of digital photos with the selection of the brightest and darkest area using Adobe Photoshop to establish the scale of luminosity. A few camera movements were triggered and position for ‘real-time’ rendering simulation. The result of the experiment has shown a significant improvement on the rendering time and quality of the rendering. Finally this paper suggests the selection criteria for choosing real and fake HDRI, and how each technique can be best utilized for architectural representations in a simulation environment.
keywords	HDRI; simulation; Real HDRI;Fake HDRI; illumination computation
series	eCAADe
email
last changed	2022/06/07 07:59

_id	87d2
authors	Serrano, J.G., Coll, J., Melero, J.C. and Burry, Mark
year	1993
title	The Need to Step Beyond Conventional Architectural Software
doi	https://doi.org/10.52842/conf.ecaade.1993.x.v0u
source	[eCAADe Conference Proceedings] Eindhoven (The Netherlands) 11-13 November 1993
summary	The Sagrada Familia Church has appointed two groups of consultants to assist the translation of Gaudi's 1:10 scaled models of the nave into coherent information from which to build. One team has been undertaking the static analysis of the nave roof vault structure and the other the study of the complexities of Gaudi's composition in order to provide full-scale production templates and models for the walls. Both teams had begun using the same basic CAD package and both have had to move onto high-end and very expensive solid-modelling software normally used by mechanical engineers and vehicle designers. Both groups are collaborating together with different accents despite an improbable geographical separation. The original problem, one of intersecting ruled-surfaces accurately to reflect the geometries of the surviving fragments of the original models, has led to surprising possibilities which were not anticipated at the outset. Currently the potential of parametric variation and associative geometries are being investigated as a mirror for some of the intuitive design process and finite element analysis is being considered as a means of interactively analysing the structural implications for each study. The software being used also has a powerful ray-tracing module; rather than being simply a tool to produce eye-catching 'realistic' renderings it has proved to be invaluable in allowing the computer user to understand the spatial complexities of the components being studied. This paper discusses the merits of an architecture so demanding (despite having been designed at the beginning of this century) that it requires the most costly equipment in today's market and it will consider the proposition that in ordinary circumstances, an architecture too complex to be described using basic CAD tools is an architecture beyond our reach. The interdisciplinary nature of the diverse and powerful modules within the software referred to will be used to contest this proposition using the presence of both teams in schools of architecture as evidence.
series	eCAADe
last changed	2022/06/07 07:50

_id	5f23
authors	Vineeta, Pal
year	1999
title	Integrated Computational Analysis of the Visual Environment in Buildings
source	Carnegie Mellon University, Pittsburgh
summary	Despite significant advances in the area of computational support for lighting design, lighting simulation tools have not been sufficiently integrated into the lighting design process. There is a significant body of designers who rely solely on their individual experience and do not use predictive simulation tools. Even when simulation tools are utilized, it is for design verification or presentation rather than for design support. A number of factors are thought to contribute to this lack of integration of simulation tools into the design process: a) Most existing tools rely on the problematic assumption implying the appropriateness of simplified models for the less complex early design and detailed simulation for the more complex later stages of design; b) They do not support an active exploration of design variables to satisfy desired performance criteria; c) They are not integrated with other building performance simulation models. This thesis addresses the above shortcomings by contributing to the field of visual analysis in the following areas, pertaining to the development of active, integrated design and performance simulation environments: - Implementation of a consistent and coherent, physically-based modeling approach, combining radiosity and ray-tracing methods for the simulation of light propagation. - Provision of design support both in terms of evaluation support for interpreting large amounts of computed data with diverse performance indices, and in terms of active design support to explore the relationships between the design variables and performance indices. - Integration of the lighting simulation module within a larger software environment (SEMPER) for the prediction and evaluation of multiple performance indicators (for energy, light, acoustics, etc.) in buildings.
series	thesis:PhD
last changed	2003/02/12 22:37

_id	678e
authors	Aish, Robert
year	1986
title	Three-dimensional Input and Visualization
source	Computer-Aided Architectural Design Futures [CAAD Futures Conference Proceedings / ISBN 0-408-05300-3] Delft (The Netherlands), 18-19 September 1985, pp. 68-84
summary	The aim of this chapter is to investigate techniques by which man-computer interaction could be improved, specifically in the context of architectural applications of CAD. In this application the object being designed is often an assembly of defined components. Even if the building is not actually fabricated from such components, it is usually conceptualized in these terms. In a conventional graphics- based CAD system these components are usually represented by graphical icons which are displayed on the graphics screen and arranged by the user. The system described here consists of three- dimensional modelling elements which the user physically assembles to form his design. Unlike conventional architectural models which are static (i.e. cannot be changed by the users) and passive (i.e. cannot be read by a CAD system), this model is both 'user generated' and 'machine readable'. The user can create, edit and view the model by simple, natural modelling activities and without the need to learn complex operating commands often associated with CAD systems. In particular, the user can view the model, altering his viewpoint and focus of attention in a completely natural way. Conventional computer graphics within an associated CAD system are used to represent the detailed geometry which the different three-dimensional icons may represent. In addition, computer graphics are also used to present the output of the performance attributes of the objects being modelled. In the architectural application described in this chapter an energy- balance evaluation is displayed for a building designed using the modelling device. While this system is not intended to offer a completely free-form input facility it can be considered to be a specialist man-machine interface of particular relevance to architects or engineers.
series	CAAD Futures
email
last changed	2003/11/21 15:15

_id	c5af
authors	Bobrow, Daniel G. and Stefik, Mark J.
year	1986
title	Perspective on Artificial Intelligence Programming
source	Science. February, 1986. vol. 231: pp. 951-956
summary	Programming systems for artificial intelligence application use specialized languages, environments, and knowledge-based tools to reduce the complexity of the programming task. Language style based on procedure, objects logic rules, and constraints reflect different models for organizing programs and facilitate program evaluation and understandability. To make programming easier, multiple styles can be integrated as sublanguages in programming environment. Programming environments provide tools that analyze programs and create informative displays of their structure. Programs can be modified by direct interaction with these displays. These tools and languages are helping computer scientists to regain a sense of control over systems that have become increasingly complex
keywords	programming, AI
series	CADline
last changed	2003/06/02 13:58

_id	63d0
authors	Carrara, Gianfranco and Novembri, Gabriele
year	1986
title	Constraint-bounded design search
source	Computer-Aided Architectural Design Futures [CAAD Futures Conference Proceedings / ISBN 0-408-05300-3] Delft (The Netherlands), 18-19 September 1985, pp. 146-157
summary	The design process requires continual checking of the consistency of design choices against given sets of goals that have been fulfilled. Such a check is generally performed by comparing abstract representations of design goals with these of the sought real building objects (RBO) resulting from complex intellectual activities closely related to the designer's culture and to the environment in which he operates. In this chapter we define a possible formalization of such representations concerning the goals and the RBO that are usually considered in the architectural design process by our culture in our environment. The representation of design goals is performed by expressing their objective aspects (requirements) and by defining their allowable values (performance specifications). The resulting system of requirements defines the set of allowable solutions and infers an abstract representation of the sought building objects (BO) that consists of the set of characteristics (attributes and relations) which are considered relevant to represent the particular kind of RBO with respect to the consistency check with design goals. The values related to such characteristics define the performances of the RBO while their set establishes its behaviour. Generally speaking, there is no single real object corresponding to an abstract representation but the whole class of the RBO that are equivalent with respect to the values assumed by the considered characteristics. The more we increase the number of these, as well as their specifications, the smaller the class becomes until it coincides with a single real object - given that the assessed specifications be fully consistent. On the other hand, the corresponding representation evolves to the total prefiguration of the RBO. It is not therefore possible to completely define a BO representation in advance since this is inferred by the considered goals and is itself a result of the design process. What can only be established in advance is that any set of characteristics assumed to represent any RBO consists of hierarchic, topological, geometrical and functional relations among the parts of the object at any level of aggregation (from components to space units, to building units, to the whole building) that we define representation structure (RS). Consequently the RS may be thought as the elementary structures that, by superposition and interaction, set up the abstract representation that best fit with design goals.
series	CAAD Futures
last changed	1999/04/03 17:58

_id	876b
authors	Christiansson, Per
year	1986
title	Structuring a Learning Building Design System
source	Advancing Building Technology, CIB International Congress (10th : 1986 : Washington D. C.). 9 p. : ill. includes bibliography
summary	It is now vital to aim at formulating computer system modules that possess a high ability to adapt their behavior to fundamental human values and a complex and unstandardized (not uniform) building process but at the same time put constraints on them so that we don't end up with a confusion of computerized routines hard to access, control and understand. In the paper formulations are made of basic artifact skeletons outgoing from the properties to give integrated CAD systems and to those rules by which the growth of the systems are governed. System learning domains including conceptual modelling tools are presented aiming at supporting professional skill, creativity and integration between process actors. The basis for system implementation is frames, descriptive language (PROLOG) and relational databases with regard taken to future possibilities to parallel processing
keywords	modeling, learning, integration, database, AI, design, systems, frames
series	CADline
last changed	1999/02/12 15:07

_id	a9b1
authors	Cohen, M.F., Greenberg, D.P. and Immel, D.S. (et al)
year	1986
title	An Efficient Radiosity Approach for Realistic Image Synthesis
source	IEEE Computer Graphics and Applications March, 1986. vol. 6: pp. 26-35 : col. ill. includes bibliography.
summary	The radiosity method models the interaction of light between diffusely reflecting surfaces and accurately predicts the global illumination effects. Procedures are now available to simulate complex environments including occluded and textured surfaces. For accurate rendering, the environment must be discretized into a fine mesh, particularly in areas of high intensity gradients. The interdependence between surfaces implies solution techniques which are computationally intractable. This article describes new procedures to predict the global illumination function without excessive computational expense. Statistics indicate the enormous potential of this approach for realistic image synthesis, particularly for dynamic images of static environments
keywords	computer graphics, radiosity, rendering, algorithms
series	CADline
last changed	2003/06/02 14:42

_id	d37c
authors	Haines, Eric A. and Greenberg, Donald P.
year	1986
title	The Light Buffer: A Ray Tracer Shadow Testing Accelerator
source	Comput. Graph. and App., vol. 6, no. 9, pp. 6-16, IEEE, Sept. 1986
summary	The basic ideas presented are classifying objects from the light's viewpoint, and caching shadowing objects. The classification scheme uses a modified z-buffer to create lists of objects in sorted order for each "pixel" the light sees and determining depths beyond which no light passes. The other technique presented is caching the object that was last intersected by a shadow ray and immediately testing this object for the next shadow ray for the same light at the same location in the ray tree. Shadow caching is simple and applicable to almost any ray tracer. Dieter Bayer implemented the light buffer for POV-Ray.
series	other
email
last changed	2003/04/23 15:14

_id	8e43
authors	Katz, R., Chang, E. and Bhateja, R.
year	1986
title	Version Modeling concepts for Computer-Aided Design Databases
source	ACM SIGMOD Intl. Conf On Management of Data
summary	We describe a semantic object-oriented data model for representing how a complex design database evolves over time. Structural relationships, introduced by the data management system, are imposed on the objects created by existing CAD tools. The relationships supported by the model are (1) version histories, (2) time-varying configurations, and (3) equivalences among objects of different types. We describe mechanisms for (1) identifying current versions, (2) supporting dynamic configuration binding, and (3) verifying equivalence relationships. The data model is being implemented in a Version Server, under development at the University of California, Berkeley.
series	other
last changed	2003/04/23 15:14

_id	682d
authors	Kim, Uk
year	1986
title	Model for an Integrated Design Evaluation System using Knowledge Bases
doi	https://doi.org/10.52842/conf.acadia.1986.204
source	ACADIA Workshop ‘86 Proceedings - Houston (Texas - USA) 24-26 October 1986, pp. 204-215
summary	Computer-aided architectural design (CAAD) systems need to be integrated so that one unified system can generate and do various analysis and evaluation of building models. A data system can not solve this problem because all design concepts can not be stored in the database before the design is completed. As design stage proceeds, design concept and necessary information for analysis and evaluation become complex and detailed. In order to accommodate increasing entities and new relationships between them, knowledge-based systems are integrated into the database of building models. frame structure and production rules are adopted to represent knowledge about the database, and to represent evaluation rules respectively. The system is implemented in Prolog on an Apollo workstation.
series	ACADIA
last changed	2022/06/07 07:52

_id	0e5e
authors	Kociolek, A.
year	1986
title	CAD in Polish Building
source	Computer-Aided Architectural Design Futures [CAAD Futures Conference Proceedings / ISBN 0-408-05300-3] Delft (The Netherlands), 18-19 September 1985, pp. 235-245
summary	There is little CAAD in Polish architectural design offices, and only recently have practising architects discovered the computer. On the other hand, CAAD has been used for some time in research and development based at universities or in large design organizations. This chapter gives a broad picture of the computerization of building design in Poland, a complex process which concerns planning and financing, hardware, software, CAD practice, standardization, training, education, etc. Here architectural applications are treated on an equal basis, together with other applications representing design disciplines involved in design, such as structural and mechanical engineering. The underlying philosophy of this chapter is a belief that proper and well-balanced computerization of design in building which leaves creative work to human beings should result in better design and eventually in improvements in the built environment. Therefore integration of the design process in building seems more important for design practice than attempts to replace an architect by a computer, although the intellectual attraction of this problem is recognized.
series	CAAD Futures
last changed	1999/04/03 17:58

_id	4e59
authors	Koparkar, P. A. and Mudur, S.P.
year	1986
title	Generation of Continuous Smooth Curves Resulting from Operations on Parametric Surface Patches
source	Computer Aided Design. May, 1986. pp. 193-206 : ill. includes bibliography
summary	In recent years a number of techniques based on the subdivision principle have been suggested for detecting the curves resulting from the intersection of two parametrically defined surface patches. Silhouette curves of surfaces can also be detected using analogous techniques. Usually the output is a set of pixels or line segments which form the complete curve, though not necessarily in an ordered manner. This paper presents data structures for maintaining the result of subdivision, and algorithms for tracing the curves in a continuous fashion. Using a few iterations of the Newton-Raphson technique the curve points may be refined to any required precision. For each point on the curve the nonlinear equations are chosen by looking at the local topological nature of the curve so as to guarantee convergence of the Newton-Raphson technique in one or two iterations
keywords	curved surfaces, parametrization, curves, intersection, relaxation, geometric modeling, computational geometry
series	CADline
last changed	2003/06/02 14:41

For more results click below: