61. Efficient Bounds In Constructive Solid Geometry May/June 1991 (Vol. 11, No. 3). pp. 6874 EfficientBounds in Constructive solid geometry. PDF. http://www.computer.org/cga/cg1991/g3068abs.htm

May/June 1991 (Vol. 11, No. 3) p p. 68-74 Efficient Bounds in Constructive Solid Geometry Stephen  Cameron Testing for intersection between geometric entities in ray casting is normally performed by intersecting a ray (a semi-infinite line) against the surface elements of a geometric model. Simple reasoning about the extent of each geometric entity significantly reduces the time required by such algorithms. If the ray and the geometric entities are boxed, one first tests to see whether the box around the ray and the box around a geometric entity overlap. Only if the boxes overlap does one continue to test to determine whether the ray and the entity overlap. A way to add boxes, called the S-bounds method, is described, and work to data on extending it is summarized. The method is useful for interference-detection and collision-detection problems. The full text of IEEE Computer Graphics and Applications is available to members of the IEEE Computer Society who have an online subscription and a web account

62. Constructive Solid Geometry Constructive solid geometry. Constructive solid geometry, or CSG forshort, is yet another way of representing solids. A CSG solid http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/model/csg.html

Constructive Solid Geometry Constructive Solid Geometry , or CSG for short, is yet another way of representing solids. A CSG solid is constructed from a few primitives with Boolean operators ( i.e. , set union, intersection and difference). Thus, a CSG solid can be written as a set equations and can also be considered a design methodology. CSG Primitives The standard CSG primitives consist of the block ( i.e. , cube), triangular prism, sphere, cylinder, cone and torus. These six primitives are in some normal or generic form and must be instantiated by the user to be used in his/her design. Moreover, the instantiated primitive may require transformations such as scaling, translation and rotation to be positioned at the desired place. Suppose the block primitive is defined by its "lower left" corner and "upper right" corner . To produce a rectangular box with center at and height and width 3 and length 5, a user may first scale the block primitive 1.5 times in the y - and z -direction and 2.5 times in the x -direction, and then translate the result to

63. CS3621 Introduction To Computing With Geometry Course Notes Boundary Representations Manifolds The WingedEdge Data Structure The Euler-PoincaréFormula Euler Operators Constructive solid geometry Interior, Exterior http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/notes.html

CS3621 Introduction to Computing with Geometry Notes Dr. C.-K. Shene Associate Professor Department of Computer Science Michigan Technological University You are visitor since July 1, 1998 Last update: December 9, 2002 Select the topics you wish to review: Unit 1: Course Overview Why Is Computing with Geometry Important? The Theme of this Course ... References Unit 2: Geometric Concepts Coordinate Systems, Points, Lines and Planes Simple Curves and Surfaces Homogeneous Coordinates Geometric Transformations ... References Unit 3: Solid Models Solid Representations: An Introduction Wireframe Models Boundary Representations Manifolds ... References Unit 4: Parametric Curves Parametric Curves: A Review Tangent Vector and Tangent Line Normal Vector and Curvature Continuity Issues ... References Unit 6: B-spline Curves Motivation B-spline Basis Functions Definition Important Properties Computation Examples B-spline Curves Definition Open Curves Closed Curves Important Properties ... Derivatives of a B-spline Curve Important Algorithms for B-spline Curves Knot Insertion Single Insertion Inserting a Knot Multiple Times De Boor's Algorithm De Casteljau's and de Boor's Algorithms ... References Unit 7: NURBS Curves (Updated!)

64. Solid Geometry BELIEVE ME NOT! - A SKEPTICs GUIDE. next up previous Next Algebra1 Up Geometry Previous The Pythagorean Theorem solid geometry. http://musr.physics.ubc.ca/~jess/hr/skept/Math/node5.html

B ELIEVE M E N OT! A S KEPTICs G UIDE Next: Algebra 1 Up: Geometry Previous: The Pythagorean Theorem: Solid Geometry Most of us learned how to calculate the volumes of various solid or 3-dimensional objects even before we were told that the name for the system of conventions and ``laws'' governing such topics was ``Solid Geometry.'' For instance, there is the cube , whose volume V is the cube (same chicken/egg problem again) of the length of one of its 8 edges . Similarly, a cylinder has a volume V equal to the product of its cross-sectional area A and its height h perpendicular to the base: V Ah . Note that this works just as well for any shape of the cross-section - square, rectangle, triangle, circle or even some irregular oddball shape. If you were fairly advanced in High School math, you probably learned a bit more abstract or general stuff about solids. But the really deep understanding that (I hope) you brought away with you was an awareness of the qualitative difference between 1-dimensional lengths , 2-dimensional areas and 3-dimensional volumes . This awareness can be amazingly powerful even without any ``hairy Math details'' if you consider what it implies about how these things change with scale Figure: Triangular, square and circular right cylinders.

65. Solid Geometry solid geometry. BT euclidean geometry FT geometrie dessolides Previous Item Next Item Search Help. http://www.nrc.ca/irc/thesaurus/solid_geometry.html

solid geometry BT euclidean geometry FT geometrie des solides [Previous Item] [Next Item] [Search] [Help]

66. Human Head Model In Constructive Solid Geometry (CSG) Human head model in Constructive solid geometry (CSG). Bartosz Sawicki,Jacek Starzynski. May 10, 2000. Abstract Constructive solid geometry. http://www.iem.pw.edu.pl/~sawickib/artykul1/

Human head model in Constructive Solid Geometry (CSG) Bartosz Sawicki, Jacek Starzynski May 10, 2000 Abstract: In this paper authors show the process of building human head model adapted for electromagnetic field calculations. Constructive Solid Geometry (CSG) is used to construct the model. Head is composed of basic primitives (such as plane, ellipsoid, sphere, tube) in such way, that it is looks similar to real human and its internal structure is similar too. Model contains four layers: scalp, skull, celebrospinal fluid and brain. Three-dimensional (3D) mesh generation is based on the Advancing Front Method implemented in Netgen. Some results of calculations are shown. Visualization in 3D is made by Virtual Reality Modeling Language (VRML). Introduction The human head is one of the most complicated nature achievements, so building numerical model of it is not a trivial problem. In starting point one must decide which features of the head are important. It is necessary for simplifying assumptions. At the current level of computer technology it is absolutely impossible to create a complete, detail model of the head. The most advanced technique is based on data from Computer Tomography slices. We can built a model containing over 500,000 triangles on surfaces and 2,000,000 tetrahedras in volume grid [ ]. It looks very nice, but if we want to make some simulating calculations at reasonable time, our model have to be simplified.

67. PinkMonkey.com Geometry Study Guide - CHAPTER 8 : SURFACE AREA AND VOLUME CHAPTER 8 SURFACE AREA AND VOLUME. 8.1 Introduction to solid geometry. All thegeometric shapes discussed in this book till now ie polygons, circles etc. http://www.pinkmonkey.com/studyguides/subjects/geometry/chap8/g0808101.asp

Support the Monkey! Tell All your Friends and Teachers Get Cash for Giving Your Opinions! Free College Cash 4U Advertise Here See What's New on the Message Boards today! Favorite Link of the Week. Your house from the sky! ... Tell a Friend Win a $1000 or more Scholarship to college! Place your Banner Ads or Text Links on PinkMonkey for $0.50 CPM or less! Pay by credit card. Same day setup. Please Take our User Survey CHAPTER 8 : SURFACE AREA AND VOLUME Figure 8.1 Shown in Figure 8.1 is a brick with length 10 cm, breadth 5 cm and height 4 cm. There cannot be a single plane which can contain the brick. A brick has six surfaces and eight vertices. Each surface has an area which can be calculated. The sum of the areas of all the six surfaces is called the surface area of the brick. Apart from surface area a brick has another measurable property. i.e. the space it occupies. This space occupied by the brick is called its volume . Every three dimensional (3-D) object occupies a finite volume. The 3 -D objects or geometric solids dealt within this chapter are Apart from defining these objects, methods to calculate their surface area and volume are also incorporated in this chapter.

68. The Constructive Solid Geometry Java Applet Home Page http://www.nbb.cornell.edu/neurobio/land/OldStudentProjects/cs490-96to97/indira/

69. AcadWiki - Constructive Solid Geometry Constructive solid geometry. Constructive solid geometry. Constructivesolid geometry (CSG) is the means by which such solids are formed. http://xarch.tu-graz.ac.at/autocad/wiki/ConstructiveSolidGeometry

Recent Changes Search Like Pages Back Links ... Constructive Solid Geometry Constructive Solid Geometry by Hin Jang http://xarch.tu-graz.ac.at/home/rurban/news/comp.graphics.algorithms/gfx/gfx6.html#csg Applying a series of Boolean operators on a set of primitives yields a complex solid. Constructive solid geometry (CSG) is the means by which such solids are formed. Each primitive, of which the block, cone, cylinder, sphere and right angular wedge are typical, is defined by a combination of finite half-spaces. Composite CSG primitives may also be subject to the Boolean operators of union, intersection and difference. The union of two primitives yields an object that encloses the space occupied by the primitives. Intersection yields an object that encloses the common space of the primitives. Difference yields an object that is the first primitive minus the space where the second intersected the first. The CSG model is stored in a tree with operators at the internal nodes and primitives at the leaves. As such, the shape of the object and the process of building the object is implicitly described in a single data structure. (...) From Gfx Algorithms Category Algorithms Last edited on 03/14/01.

70. Constructive Solid Geometry - Wikipedia Constructive solid geometry. From Wikipedia, the free encyclopedia.Constructive solid geometry, or CSG, is a modelling technique http://www.wikipedia.org/wiki/Constructive_Solid_Geometry

71. UKTV - Sin With Our Permission To Solid Geometry solid geometry C4 / 1x30m / 28 November 2002 / 1035pm Writer/DirectorDenis Lawson / Producer Gill Parry Drama. Newlywed Phil http://www.memorabletv.com/bfs4.htm

The Sections TV USA TV UK UK Sitcoms UK Comedy ... Quiz Shows Other Features Episode Guides TV's Greatest Hits The Hall of Fame Soapworld ... British Fiction The Memorable TV Guide to UK TV S5 - SIN WITH OUR PERMISSION to SOLID GEOMETRY PREVIOUS NEXT SIN WITH OUR PERMISSION ATV / 1x60m-e / 1981 / 26 May Writer: J.C. Wilsher / Producer: Colin Rogers / Director: Paul Harrison Scifi drama. A New Town of the future is under constant surveillance from Closed Circuit Television. With:- PAUL EDDINGTON as Harry Dudley / GREGORY FLOY as James Walton / ROBIN BAILEY as Dr Perry / KATE FAHY as Angela Birley / SALLY BAXTER as Jenny Tevitt SIR ARTHUR CONAN DOYLE'S SHERLOCK HOLMES BBC1 / 16x50m-e / 1968 Producer: David Goddard Period crime drama series. More cases of Victorian super sleuth Sherlock. A continuation of 1966's Sherlock Holmes but with Peter Cushing replacing Douglas Wilmer. With:- PETER CUSHING as Sherlock Holmes / NIGEL STOCK as Dr Watson SIRENS ITV1 / 2x120m / 13-14 October 2002 Writer: Chris Lang / Director: Nick Laughland / Producer: Margaret Mitchell Crime Drama. DC Jan Pearson is working on the police team hunting for a serial rapist. She has an affair with her sister’s boyfriend and then he emerges as a chief suspect.

72. PCTrace - Constructive Solid Geometry 7. Constructive solid geometry Building blocks put together. Constructivesolid geometry or CSG allows us to play around with our http://www.cse.iitd.ernet.in/~parag/CG2/asign1/report/csg.html

7. Constructive Solid Geometry - Building blocks put together Constructive solid geometry or CSG allows us to play around with our primitives and build complex objects. CSG supports union, intersection and difference of two or more objects. Essentially a CSG tree gets built for each CSG object with the nodes being the primitives or CSG subtrees themselves. The various CSG operations are explained below. Union - An union CSG object C (where C = A union B) will contain all the points which belong to A OR B. A sample union specification is shown below - Figure 7 union object transform object transform The union can be of two primitives or of two CSG objects themselves or any combination thereof. The CSG tree which gets formed as a result of the above code is also shown. Some examples of CSG union are shown below - Intersection - An intersection CSG object C (where C = A intersection B) will contain all the points which belong to A AND B. Intersection is specified exactly in the same manner as an union and the tree formed is also similar. Some examples of CSG intersection are shown below - Difference - A Difference CSG object C (where C = A difference B) will contain all the points which belong to A AND NOT B). Difference is specified exactly

73. Constructive Solid Geometry (CSG) next up previous contents Next Solid modelling and building Up Modelling of manmadesolid Previous Primitive instancing Constructive solid geometry (CSG). http://www.ipf.tuwien.ac.at/fr/buildings/diss/node38.html

Next: Solid modelling and building Up: Modelling of man-made solid Previous: Primitive instancing Constructive Solid Geometry (CSG) It is the concept of CSG to provide solid 3D primitives which are described a set of parameters reflecting the object dimensions (Figure ). The CSG primitives are simple objects such as cubes, boxes, tetrahedrons or quadratic pyramids. They are considered to be bounded point sets in 3D space, and they can easily be combined using Boolean set operations ( union intersection and difference ) in order to represent more complex objects consisting of more than one primitive (cf. section ). In theory, the (bounded) primitives themselves can be considered to be the intersections of half spaces containing all points P for which the inequality is fulfilled, where f P ) is a characteristic function of the point P and f P ) = describes the bounding surface of the point set, e.g. a plane in 3D space ( halfspace models The most natural way to represent a CSG model is the CSG tree which can be defined as follows: where is an instance of one of the primitives of the primitive data base

74. About "Polyhedron: An Application In Solid Geometry" Polyhedron An application in solid geometry. Library Home FullTable of Contents Suggest a Link Library Help Visit this http://mathforum.org/library/view/5663.html

Polyhedron: An application in solid geometry Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://geocentral.net/polyhedron/ Author: Stelian Dumitrascu Description: Software based on "deduction-free geometry," which allows the user to perform various actions upon solids as if holding these solids in your hands. It simulates a number of tools, such as the ruler, protractor, setsquare, compass, bisector, saw, and eraser. You can manage them through a common menu. Solids can be revolved, visualized in different manners, cut, stacked, and so forth. There are 250 problems built into the program, involving such things as frameworks, toys, beetles, ants, and other unusual stuff. The problems of degree 5-6 (there are 6 degrees of complexity) are difficult enough even for the best students. Program available in ZIP format from this site, or in ARJ, ZIP, or TAR and GZIP from the Univ. of Waterloo site. Levels: High School (9-12) College Languages: English Resource Types: Problems/Puzzles Topic Tools Miscellaneous Math Topics: Polyhedra Suggestion Box Home The Math Library ... Search http://mathforum.org/

75. [opendx-users] Constructive Solid Geometry (CSG) opendxusers Constructive solid geometry (CSG). To opendx-users@watson.ibm.com;Subject opendx-users Constructive solid geometry (CSG); http://opendx.npaci.edu/mail/opendx-users/1999.08/msg00035.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index [opendx-users] Constructive Solid Geometry (CSG) To opendx-users@watson.ibm.com Subject : [opendx-users] Constructive Solid Geometry (CSG) From Date : 16 Aug 99 11:11:56 MST Reply-To opendx-users@watson.ibm.com Sender owner-opendx-users@watson.ibm.com Could someone please tell me how to construct the difference of two solids defined by implicit equations I have managed to construct the union and intersection of two solids by using the min and max function respectively in a compute module. Thanks, Sebastian Prev by Date: Next by Date: [opendx-users] Import/Series/Plotting question Prev by thread: Re: [opendx-users] Import/Series/Plotting question Next by thread: Index(es): Date Thread

76. CONSTRUCTIVE SOLID GEOMETRY First Previous Next Last Index Text. Slide 7 of 14. http://www.cs.jhu.edu/~wolff/course600.461/week2.1/sld007.htm

First Previous Next Last ... Text Slide 7 of 14

77. CONSTRUCTIVE SOLID GEOMETRY CONSTRUCTIVE solid geometry. Combine different geometricshapes to produce a desired object shape. +. =. http://www.cs.jhu.edu/~wolff/course600.461/week2.1/tsld007.htm

CONSTRUCTIVE SOLID GEOMETRY Combine different geometric shapes to produce a desired object shape. Previous slide Next slide Back to first slide View graphic version

78. CNC System That Reads Solid Geometry Cuts Programming Time 50% Case Study Mold Craft. CNC system that reads solid geometry cutsprogramming time 50%. By Jerry Fireman. Switching to a CNC system http://www.unisysworld.com/monthly/2002/09/cnc.shtml

Quick Search: Unisys World Unisys World Print September 2002 UNISYS WORLD PRINT This month's issue Archives UNISYS WORLD ONLINE Unisys Corp. News White Papers Careers Column OpinionWire ... ARS Analyst Outlook SUBSCRIPTIONS Subscription Center U.S. (free trial) Outside U.S. E-Mail Newsletter OTHER RESOURCES Vendor Directory Contact Us Media Kit SISTER PUBLICATIONS Enterprise Networking Magazine Networking News This Month's Issue Subscription Center ... Subscription Center ADVERTISERS Case Study: Mold Craft CNC system that reads solid geometry cuts programming time 50% By Jerry Fireman Switching to a CNC system capable of directly reading solid models from popular CAD systems has cut programming time 50 percent at Mold Craft by eliminating the need to fine-tune part geometry. After importing IGES surfaces into the CAM software used in the past, extensive manual touch-up work was required to fix problem areas. The new CAM system uses the Parasolid solid modeling engine so it can read native solid model geometry from many CAD systems such as the Solid Edge program used at Mold Craft. The ability to import perfect geometry allows programmers to focus on optimizing 3-D machining tool path. The net result, for a typical complicated mold cavity, is a reduction in programming time from five to two and a half days. Mold for a six-pack bottle carrier, using a CNC mill application.

79. 12.4 CSG (constructive Solid Geometry) Translate this page 12.4 CSG (constructive solid geometry). Jedes Objekt wird beschriebendurch einen binären Baum, dessen Blätter beschriftet sind http://www-lehre.informatik.uni-osnabrueck.de/~cg/2000/skript/12_4_CSG_construct

12.4 CSG (constructive solid geometry) (Vereinigung), (Durchschnitt), (Differenz).

80. Constructive Solid Geometry-Modell Translate this page Begriff, Constructive solid geometry-Modell. internationaler, Constructivesolid geometry-Modell. Begriff. Akronym, CSG. Synonyme. Erläuterung, http://www.blien.de/ralf/cad/db/csg.htm

CAD-Lexikon Volumenmodell Struktur Index CAD-Web Begriff Constructive Solid Geometry-Modell internationaler Constructive Solid Geometry-Modell Begriff Akronym CSG Synonyme Bei der Volumenbeschreibungsmethode nach dem Prinzip der Constructive Solid Geometry operationen (Bool'sche Mengenoperationen), als deren Operanden ein bestimmter Vorrat Als Bool' sche Operationen stehen "Vereinigung", "Differenz", "Schnittmenge" und "Komplement" zu Verfügung. Beispiel Beispielgraphik Quelle Eingabedatum weitere Infos: Volumenmodell

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