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Topic: Solid geometry

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 Solid geometry   (Site not responding. Last check: 2007-11-07)
The Pythagorean s had dealt with the sphere and regular solid s, but the pyramid, prism, cone and cylinder were but little known until the Platonist s took them in hand.
The Geometry of the Sphere This material was the text for part of the Advanced Mathematics course in the High School Teachers Program at the IAS/Park City Mathematics Institute at the Institute for Advanced Study during July of 1996.
Solids that are sufficiently heated may sublimate into a gas or melt into a liquid.
www.serebella.com /encyclopedia/article-Solid_geometry.html   (582 words)

 Constructive solid geometry - Wikipedia, the free encyclopedia
Constructive solid geometry (CSG) is a technique used in solid modeling.
Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine objects.
When CSG is procedural or parametric, the user can revise their complex geometry by changing the position of objects or by changing the Boolean operation used to combine those objects.
en.wikipedia.org /wiki/Constructive_solid_geometry   (398 words)

 Encyclopedia: Constructive solid geometry   (Site not responding. Last check: 2007-11-07)
Solid modeling studies unambiguous representations, that is, models, of solid objects suitable for computer processing.
In geometry, a prism is a polyhedron made of two parallel copies of some polygonal base joined by faces that are rectangles or parallelograms.
It is said that an object is constructed from primitives by means of allowable operations, which are typically Boolean operations on sets: union, intersection and difference.
www.nationmaster.com /encyclopedia/Constructive-solid-geometry   (829 words)

 MSN Encarta - Search Results - Solid Geometry
Solid Geometry, branch of geometry that deals with the properties and measurement of geometric figures in three-dimensional space.
Two-dimensional Euclidean geometry is often called plane geometry; three-dimensional Euclidean geometry is frequently referred to as solid geometry....
Prism, in geometry, three-dimensional solid, of which the bases are two parallel planes.
encarta.msn.com /Solid_Geometry.html   (131 words)

 Combinatorial Solid Geometry, Boundary Representations, and Non-Manifold Geometry   (Site not responding. Last check: 2007-11-07)
Solid models differ from drafting-type systems in several important ways: objects are composed of combinations of primitive objects (some quite complex), each of which is complete, unambiguous, physically realizable, and modifiable.
For example, the geometry information associated with a planar face is the plane equation which includes the outward-pointing surface normal; the plane equation does not have to be re-derived from the vertices.
Therefore, the conclusion was that the existing combinatorial solid geometry database would remain unchanged, and that any application that required an explicit representation of the modeled shapes would obtain that explicit representation through some form of conversion of the underlying CSG database.
ftp.arl.mil /~mike/papers/90nmg/joined.html   (20066 words)

 Solid Geometry
Solid Geometry is comprised of a theoretical overview, and a variety of interactive educational tools helping students understand the essence of Solid Geometry.
Solid Geometry is ideal for high school, college, and university classrooms, as well as for independent studies.
Solid Geometry interface was developed through implementation of Java and JavaScript, as well as a variety of plug-ins and HTML technologies.
www.openteach.com /products/stereo.php   (242 words)

 Solid geometry -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07)
It was studied as a sequel to (The geometry of 2-dimensional figures) plane geometry.
(The geometry of properties that remain invariant under projection) descriptive geometry.
A major reason to study this subject is the application to (The pictorial representation and manipulation of data by a computer) computer graphics, meaning that (A precise rule (or set of rules) specifying how to solve some problem) algorithms become important.
www.absoluteastronomy.com /encyclopedia/s/so/solid_geometry.htm   (339 words)

 Geometry.Net - Math_Discover: Solid Geometry
Constructive solid geometry, or CSG for short, is yet another way of representing solids.
solid geometry is concerned with polyhedra, spheres, threedimensional solids, lines in three-space, planes, and so on.
Solid geometry also includes the study of points lines, shapes, and regions in relation to solids and surfaces Coordinates are not used.
www4.geometry.net /math_discover/solid_geometry.html   (2028 words)

 Generalized Method of Decomposing Solid Geometry into Hexahedron Finite Elements   (Site not responding. Last check: 2007-11-07)
Decomposing geometry in terms of a function of external features is novel in that it utilizes the relationship of the solid geometry outer surface connectivity with respect to the number of edges on a solid independant of an assessment of the solid's interior.
The majority of the remaining solid is easily meshed with the smooth transition boundary of the sub-volume.
Reducing external complex shape characteristics to a level compatible with generic geometry is interfaced with various shape recognition conditions for identifying local configurations such as: reentrant edges, multiple surface solid geometry in compacted transition regions, and various hybrid solids, such as the filletted trailing edge of a turbine blade.
www.andrew.cmu.edu /user/sowen/abstracts/Ho169.html   (684 words)

 [No title]   (Site not responding. Last check: 2007-11-07)
This work was called geometry and was seen as a re-establishment of the principle of order and law on earth....This activity of 'measuring the earth' became the basis for a science of natural law as it embodied in the archetypal forms of the circle, square, and triangle"[1]
"Geometry as a contemplative practice is personified by an elegant and refined woman, for geometry functions as an intuitive, synthesizing, creative, yet exact activity of mind associated with the feminine principle.
Geometry is a tool to 1)deep philosophical contemplation in its harmony and universality as well as to 2)practical studies such as its applicability to other disciplines including agriculture, astronomy and music.
www.perseus.tufts.edu /GreekScience/Students/Jordana/MATH.html   (1723 words)

 Exploring Solid Geometry-VHS   (Site not responding. Last check: 2007-11-07)
The journey started in World of Geometry concludes with a complete exploration of solid geometry.
Once again, real world examples showing solid geometry principles are demonstrated with computer animation, graphics and live action video.
All aspects of solid geometry are covered, including basic properties of solids, relationships among solids, the lateral area, and volume.
gpn.unl.edu /static_catalog/811.html   (69 words)

 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 2.17).
The leaves of the CSG tree are the primitives, and the nodes are marked either as a Boolean set operation or with a rigid motion.
First, the CSG primitives have to be converted to boundary models, and then these models have to be combined using the Boolean set operations, which, as already stated in section, turns out to be very complicated.
www.ipf.tuwien.ac.at /fr/buildings/diss/node38.html   (529 words)

 Math Forum - Mathematics Teacher Bibliography: Higher Dimensions   (Site not responding. Last check: 2007-11-07)
The Algebra and Geometry Of Polyhedra Joseph A. Troccolo Algebraic and geometric approaches to the building of polyhedra.
Models In Solid Geometry Miles C. Hartley Models and theorems which they can be used to illustrate.
Geometry Of Four Dimensions Henry P. Manning Results which are presented in more detail in the author's book which has the same title.
www.mathforum.com /mathed/mtbib/higher.dimensions.html   (2050 words)

 GVU: Geometry Group   (Site not responding. Last check: 2007-11-07)
The Geometry Group focuses on the rendering, modeling, simplification, and compression of geometric models.
One of our focuses in the Geometry Group is how to automatically generate models from point sets, polygonal data sets, and medical data sets.
Several projects in the Geometry Group are collaborations with the Vision and Animation research groups.
www.cc.gatech.edu /gvu/geometry   (152 words)

 3.4 Constructive Solid Geometry with the Stencil Buffer   (Site not responding. Last check: 2007-11-07)
The representation used in CSG for solid objects varies, but we will consider a solid to be a collection of polygons forming a closed volume.
The ``convexity'' of a solid is defined as the maximum number of pairs of front and back surfaces that can be drawn from the viewing direction.
Because a solid may vary in convexity when viewed from different directions, accurately representing the convexity of a primitive may be difficult and may also involve reevaluating the CSG tree at each new view.
opengl.org /resources/tutorials/advanced/advanced97/notes/node11.html   (1980 words)

 Solid geometry - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-11-07)
Geometry, Particles, and Fields (Graduate Texts in Contemporary Physics)
Schaum's Outline of Theory and Problems of Geometry: Includes Plane, Analytic, Transformational, and Solid Geometries (Schaum's Outline S.)
Geometry - Plane, Solid & Analytic Problem Solver (Problem Solvers)
encyclopedia.worldsearch.com /solid_geometry.htm   (286 words)

 Constructive Solid Geometry
Constructive solid geometry systems allow the definition of complex three dimensional objects using a combination of simpler objects.
A CSG system normally includes a set of solid shape primitives such as cubes, cylinders, cones, etc. which can be defined in a range of sizes and shapes.
Constructive solid geometry systems are more powerful than boundary representations in the same ways that boundary representations are more powerful than wireframes.
www.cl.cam.ac.uk /~afb21/publications/masters/node23.html   (287 words)

 Math Forum: Geometry Lesson Plans
A classroom activity (similar to Pentomino + 1 = Hexomino; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored...
Understanding factoring through geometry: students work cooperatively to display a numeral as the area of a rectangle, and make...
Students review the concepts of solid geometry, then try to determine all of the ways that they can join no more than four cubes at their faces in an...
mathforum.org /geometry/geom.units.html   (920 words)

 Pro/ENGINEER > Limiting Drawing View Size to Solid Geometry - the Design Knowledge Base   (Site not responding. Last check: 2007-11-07)
Even if this non-solid geometry (surfaces, copy geoms, etc.) isn't visible, it will cause the view size to be larger than the solid geometry.
Surface cuts directly in the model may be another way to reduce the size of the extra geometry that is affecting the size of the drawing view boundaries.
If the extra geometry is an IGES or STEP import, it may be possible to redefine the import feature to exclude surfaces to reduce the size of the view boundaries.
www.designkb.com /show_tip.php?tip=39   (275 words)

 Constructive solid geometry   (Site not responding. Last check: 2007-11-07)
Constructive solid geometry (CSG) is a branch of solid modelling that deals with representations of a object as a combination of simpler solid It is a procedural modelling technique used 3D computer graphics and CAD.
The simplest solid objects used for the are called primitives.
Constructive solid geometry has a number of uses.
www.freeglossary.com /Constructive_solid_geometry   (542 words)

 Solid Geometry Encyclopedia Article, Definition, History, Biography   (Site not responding. Last check: 2007-11-07)
Looking For solid geometry - Find solid geometry and more at Lycos Search.
Find solid geometry - Your relevant result is a click away!
Look for solid geometry - Find solid geometry at one of the best sites the Internet has to offer!
www.artquilt.com /search/encyclopedia/Solid_geometry   (390 words)

 Constructive Solid Geometry
From left to right, the four solids are the union and intersection of A and B, A - B and B - A.
Therefore, a solid can be considered as the result of applying Boolean operators to a set of instantiated and transformed CSG primitives.
In fact, every solid constructed using the CSG technique has a corresponding CSG expression which in turn has an associated CSG tree.
www.cs.mtu.edu /~shene/COURSES/cs3621/NOTES/model/csg.html   (628 words)

 Geometry.Net - Math_Discover: Solid Geometry
More Phi and 3-dimensional geometry The five regular solids (where "regular" means all sides are equal and all angles are the same and all the faces are identical) are called the five Platonic solids after the Greek philosopher and mathematician, Plato.
solid geometry From Two Dimensions to Three Create your own three dimensionalshapes such as regular polyhedra, prisms and pyramids.
solid geometry, solid geometry is concerned with polyhedra, spheres, threedimensionalsolids, lines in three-space, planes, and so on.
www.geometry.net /math_discover/solid_geometry.html   (1856 words)

 Henry F Baker -Solid Geometry Quadrics Cubic Curves in Space Cubic Surfaces Principles of Geometry Vol 3 - Bob ...   (Site not responding. Last check: 2007-11-07)
Solid Geometry Quadrics Cubic Curves in Space Cubic Surfaces Principles of Geometry Vol 3
1: Solid Geometry Quadrics Cubic Curves in Space Cubic Surfaces Principles of Geometry Vol 3.
Solid Interstellar Matter The Iso Revolution Les Houches Workshop February 2 - 6 1998.
www.reviewofbooks.net /327476solid_geometry_quadrics_cubic_curves_space_cubic_surfaces_principles_geometry_3.html   (77 words)

 Citations: Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry - Duff ...   (Site not responding. Last check: 2007-11-07)
Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry.
The interactive texture placement methods of Pedersen should be directly applicable to variational implicit surfaces [20, 21] Finally, many marvelous animations have been produced using blobby implicit surfaces [3, 31] We anticipate that the interpolating properties of variational implicit....
The algorithm works only for agents represented by the Constructive Solid Geometry (CSG) modeling paradigm, though, and the authors are vague about how to handle agents whose motion is not linear.
citeseer.ist.psu.edu /context/3044/0   (2548 words)

 Resource: Learning Math: Geometry
Use dynamic geometry software to construct figures with given characteristics, such as segments that are perpendicular, parallel, or of equal length, and to examine the properties of parallel lines and circles.
Examine platonic solids and why there are a finite number of them.
Investigate nets and cross-sections for solids as a way of establishing the relationships between two–dimensional and three–dimensional geometry.
www.learner.org /resources/series167.html   (667 words)

 Constructive Solid Geometry   (Site not responding. Last check: 2007-11-07)
Be sure to tell your unzipping program to maintain the directory structure used in the zip file.
In this case we can easily turn the static geometry into dynamic objects.
Get some better geometry to boolean the world with, the current convex boxish thing is kinda lame.
www.melax.com /csg   (939 words)

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