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Topic: Scaling geometry

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	scaling - Search Results - MSN Encarta
		Scale (music) (Italian scala, “ladder”), the arrangement, by rising or falling pitch sequence, of the tones used in a musical system.
		Scaling may refer to: * Scaling (geometry), a linear transformation that enlarges or diminishes objects * Scaling (computer network), a network's ability to function as the number of people on the...
		In Euclidean geometry, uniform scaling is a linear transformation that enlarges or diminishes objects; the scale factor is the same in all directions; it is also called a homothety.
	encarta.msn.com /scaling.html (366 words)

	Isner
		With scaling the behavior is a bit different than a simple delta that starts at zero and becomes your values at the end of the stick.
		You are scaling back to the inverse of the scaling only, and that results in a non-uniformly scaled (but not sheared) starting grid on the inverse.
		Basically if you have scaling on the origin grid (which is what introduces shearing) then we need to add two add two new steps to the visual instructions to also invert that origin scale.
	www.isner.com /Transform/IsnerTransformManip_04.htm (2450 words)

	ProfilesMagazine.com
		The two basic rules when creating your geometry are that the UDF (1) needs to prompt for all references used, and (2) recognizes if a parent is used multiple times.
		When scaling geometry is an option, model the geometry so that there is a primary dimension with a value of 1.
		Geometry is created quickly and accurately by new as well as experienced users.
	www.profilesmagazine.com /p30/grabau.html (2138 words)

	X(7) manual page
		Although many window managers will honor geometry specifications as given, others may choose to ignore them (requiring the user to explicitly draw the window's region on the screen with the pointer, for example).
		Scaling from outline fonts usually produces significantly better results than scaling from bitmap fonts.
		Note that h indicates the value scaled in 4 bits, hh the value scaled in 8 bits, hhh the value scaled in 12 bits, and hhhh the value scaled in 16 bits, respectively.
	www.xfree86.org /current/X.7.html (6112 words)

	Scale Tool
		Scale operations within a component's context (such as scaling a Line entity within a component) affects the component definition and, therefore, all instances of the component will be scaled to match (all instances of the same Line entity in all component instances).
		The default behavior is a uniform scale such that the proportions remain intact and a single scale factor or dimension is displayed in the VCB.
		The VCB at the bottom right corner of the SketchUp window displays the axis dimensions that are being scaled, and the value of the scale itself, in the default units (as specified under the Units panel of the Model Info dialog box) during a scaling operation.
	download.sketchup.com /OnlineDoc/gsu_mac/D-Modification_Tools/ModTool-Scale.htm (1104 words)

	Gamasutra - Features - "Building Scalable 3D Games for the PC" [11.24.99]
		Scaling the content itself is not so much defined by any one particular algorithm, but rather the concept of adding or modifying characters, objects and scenery dynamically.
		Scaling the geometry content involves adding or removing polygons to the scene to maintain a sufficient frame rate or level of visual quality.
		Scaling the geometry content in each scene definitely helps scale the application across a wide range of systems, but other approaches to managing scalability also exist.
	www.gamasutra.com /features/19991124/pallistermacri_02.htm (1616 words)

	CONSTRUCT TRANSFRM SCALE [tnam] pnam1 pnam2 fact1 [fact2]
		The scaling is performed relative to a plane containing the point `pnam1' and with a normal direction (the axis of scaling) from `pnam1' to point `pnam2'.
		Scaling is done in the normal direction with the specified axis scale factor.
		Similarly, if the plane scale factor is less than 1.0, then points will move towards the axis; and if the plane scale factor is greater than 1.0, then points will move away from the axis.
	www.princeton.edu /~dynaflow/femgv/manuals/userman/node108.htm (228 words)

	Research
		This property is known as scaling invariance and is closely related to the notions of fractals and chaos.
		Scaling invariance is a useful property for hydrologists because it relates the statistical properties of small features to those of large features.
		They are quantitatively characterizing the scaling invariance, understanding its dynamic origin (as well as the origin of deviations from scaling), and exploring the interconnections between the scaling of topography and soil moisture.
	www.engr.colostate.edu /~jniemann/research.htm (423 words)

	Building Scalable 3D Games for the PC
		The topic of scalability can be divided into two areas: techniques for scaling content (for example, a method for varying the polygon count of an object on the fly), and approaches to scaling the content (deciding what polygon count should be used for that object, given the current system performance).
		While increasing the amount of geometry in game applications provides more realistic looking objects, as well as allowing for more objects within in scenes, there is more to creating a realistic looking environment than just the models in it.
		You can scale down a particle system by altering the granularity of the effect (reducing the number of particles), but increasing the particle size so that the effect has the same density, but a grainier appearance).
	www.gamasutra.com /features/19991124/pallistermacri_pfv.htm (4569 words)

	Scaling Graph Paper (Site not responding. Last check: 2007-10-26)
		In this case the x and y axes are scaled identically.
		One unit of physical distance along the x-axis is equal in length to one unit of physical distance along the y-axis.
		For example, 1 centimeter might separate the coordinates x = 0 and x = 1 along the x-axis, while 2 centimeters might separate the the coordinates y = 0 and y = 1 along the y-axis.
	id.mind.net /~zona/mmts/graphPaper/scalingGraphPaper/scalingGraphPaper.html (165 words)

	Scaling
		scale the graph of y = f(x) parallel to the x-axis by scale factor 1/a.
		--> Scale parallel to the x-axis by factor 1/2.
		scale y = f(x) parallel to the y-axis with scale factor a.
	library.thinkquest.org /C0110248/geometry/transscale.htm (97 words)

	Scaling of Geometry> what do you do? - AutoCAD Forums (Site not responding. Last check: 2007-10-26)
		One of us is scaling the titleblock to match the geometry and the other is scaling the geometry to fit the titleblock.
		I have always been told to scale the titleblock not the geometry.
		I scale the dimensions accordingly using scale factor.
	www.cadtutor.net /forum/showthread.php?t=3533 (526 words)

	Scaling Research (Site not responding. Last check: 2007-10-26)
		They have exploited fractal geometry so that critical linear dimensions and surface areas scale as the 1/4 and 3/4 powers of body mass, respectively, rather than the 1/3 and 2/3 powers expected from conventional Euclidean geometry.
		It closely predicts many empirical scaling relationships and measured fractal dimensions of roots and shoots in the botanical and forestry literature.
		We proved that the 4 in the denominator of allometric scaling exponents is due to the fact that organisms effectively function in four spatial dimensions.
	biology.unm.edu /jhbrown/Research/Scaling/Scaling.htm (924 words)

	Geometry
		Attempts to sew the s geometry to the current shape geometry if the a and b parameters are both nonzero.
		Attempts to sew the s geometry to the current shape geometry if the a and b parameters are both nonzero according to transformation matrix m.
		The geometry may still be rendered on both sides if the material is set to be doublesided.
	artport.whitney.org /gatepages/artists/perlin/packing/render/doc/render/Geometry.html (3151 words)

	ImageMagick: Command-line Options
		By adding a exclamation character flag to the geometry argument, the cropped images virtual canvas page size and offset will be set as if the geometry argument was a viewport or window.
		The displacement is scaled to determine the pixel shift.
		Offsets, if present in the geometry specification, are handled in the same manner as the -geometry option, using X11 style to handle negative offsets.
	imagemagick.org /script/command-line-options.php (10866 words)

	Transformation (mathematics) Summary
		Uniform scaling is a linear transformation that enlarges or diminishes objects; the scale factor is the same in all directions; it is also called a homothety.
		The result of uniform scaling is similar (in the geometric sense) to the original.
		More general is scaling with a separate scale factor for each axis direction; a special case is directional scaling (in one direction).
	www.bookrags.com /Transformation_(mathematics) (1734 words)

	[No title]
		Our proposed theoretical framework for scaling in biology is based on the assumption that biological rates and times are ultimately limited by the rates at which limited energy and materials can be supplied to cells through a hierarchical branching network.
		The model predicts: i) a fractal-like branching network with scaling laws governing the sizes of the branches; ii) whole-organism metabolic rate scales as the body mass raised to the 3/4 power; and iii) many other anatomical and physiological characteristics of mammalian cardiovascular and respiratory systems (West et al.
		Excitingly, we are using our scaling framework to mechanistically link physiological variation within and between plants to the flux of energy and CO2 from diverse ecological systems.
	eeb37.biosci.arizona.edu /~brian/scaling.html (500 words)

	GAMBIT MODELING GUIDE: 2. CREATING THE GEOMETRY
		If you specify very large scaling factors, the scaled geometry may contain gaps between entities that are coincident with tolerance in the unscaled geometry.
		For example, in the scaling operation illustrated in Figure 2-6, one corner vertex of the rectangular brick volume to be scaled is exactly coincident with the reference point.
		specifies that all geometry connected to the vertex is to be aligned according to the specifications on the form.
	www.ent.ohiou.edu /~juwt/HTMLS/fluent/gambit2/html/modeling_guide/mg0201.htm (4934 words)

	Geometry Optimization
		If you choose steepest descent for both, geometry variables and the wavefunction, a combined method is used.
		For unusual geometries this may fail and the Hessian becomes singular.
		To achieve linear scaling with the system size, the L-BFGS optimizer starts from a unit Hessian and applies the BFGS update on the fly using the history of the optimization.
	www.cpmd.org /manual/node67.html (365 words)

	Anti-Grain Geometry -
		Suppose we have 4 transformations: // * rotate by 30 degrees, // * scale X to 2.0, // * scale Y to 1.5, // * move to (100, 100).
		x, y - scale coefficients by X and Y respectively class trans_affine_scaling : public trans_affine { public: trans_affine_scaling(double x, double y) : trans_affine(x, 0.
		0) {} }; //===============================================trans_affine_line_segment // Rotate, Scale and Translate, associating 0...dist with line segment // x1,y1,x2,y2 class trans_affine_line_segment : public trans_affine { public: trans_affine_line_segment(double x1, double y1, double x2, double y2, double dist) { double dx = x2 - x1; double dy = y2 - y1; if(dist > 0.
	www.antigrain.com /__code/include/agg_trans_affine.h.html (1089 words)

	Sophisticated Mathematics Behind African Village Designs / Fractal patterns use repetition on large, small scale
		Since then, Eglash has documented the use of fractal geometry -- the geometry of similar shapes repeated on ever-shrinking scales -- in everything from hairstyles and architecture to artwork and religious practices in African culture.
		Others have observed fractal patterns in the irregular features of rocky coastlines, the ever-diminishing scaling of ferns, and even the human respiratory and circulatory systems with their myriad divisions into smaller and smaller branches.
		A few years ago, Hastings and a team of medical researchers found that the clustering of pancreatic cells in the human body follows the same fractal rules that meteorologists have used to describe cloud formation and the shapes of snowflakes.
	www.sfgate.com /cgi-bin/article.cgi?file=/chronicle/archive/2000/02/23/MN36684.DTL&type=printable (1507 words)

	SGI - Products: Remarketed: SGI Onyx 3000 Series with InfiniteReality4 Graphics: Technical Info
		This tightly coupled architecture with inherent scaling of system and graphics bandwidth is central to the series' breakthrough visual performance.
		Geometry Engine--Four high-performance Geometry Engine processors perform lighting calculations and geometric transformations such as translation, rotation, and scaling.
		Geometry Engine processors also execute image-processing functions such as convolution and histogram equalization--a more effective approach than that of CPUs.
	www.sgi.com /products/remarketed/onyx3000/tech_info.html (786 words)

	Foundations of Geometry
		The relationships between transformations, scaling, matrices and equations is studied in concert with computer-graphics applications.
		Attention is given to uses in areas such as science (trans-formations, scaling), art (Echer-type tessellations, projections), architecture (three-dimensional figures) and computer science (fractals, computer-aided design).
		The overall purpose of this course is to introduce students to modern geometries such as projective geometry, which has Euclidean geometry as a special case, and examples of non-Euclidean geometries.
	www.nu.edu /Academics/Schools/COLS/MthNSci/Courses/MTH417Syllabus.html (1287 words)

	GEOMETRIC Traditions / African cultures show sophisticated patterns noticed only recently in the West.
		Since then, Eglash has documented the use of fractal geometry-the geometry of similar shapes repeated on ever-shrinking scales-in everything from hairstyles and architecture to artwork and religious practices in African culture.
		"Basically I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on-why they had made it that way," he said.
		The concept is similar to the shapes that American geometry students produce using only a compass and a straight edge, he said.
	www.rpi.edu /~eglash/eglash.dir/nynd_rev.htm (2310 words)

	Manipulation (Site not responding. Last check: 2007-10-26)
		Move/Copy/Scale allows you to transform geometry by scaling it, moving it, rotating it, and mirroring it.
		Easy Scale resizes the entities you select in relation to a scaling position and a scale value you specify.
		Resize scales all the entities in your part in a single operation, based on the resize scale factor you enter.
	www.mcsaz.com /lite/manipulation.htm (287 words)

	Exercise-induced maximal metabolic rate scales with muscle aerobic capacity -- Weibel and Hoppeler 208 (9): 1635 -- ...
		that MMR scales in parallel with the mitochondrial and capillary
		of the scaling exponents observed for MMR as elicited by exercise?
		Scaling maximum aerobic capacity to body mass: wild and domestic mammals.
	jeb.biologists.org /cgi/content/full/208/9/1635 (5427 words)

	Eglash's African Fractals
		Fractal geometry has emerged as one of the most exciting frontiers in the fusion between mathematics and information technology.
		While fractal geometry can take us into the far reaches of high tech science, its patterns are surprisingly common in traditional African designs, and some of its basic concepts are fundamental to African knowledge systems.
		African Fractals introduces readers to fractal geometry and explores the ways it is expressed in African cultures.
	www.math.buffalo.edu /mad/special/eglash.african.fractals.html (2414 words)

	Geek.com Geek News - EUV lithography issues threaten Moore's Law
		While this may not mean the end of IC geometry scaling, it may mean the end of more price-efficient scaling since the alternatives to this standard methodology are more expensive.
		There will be a major break through on the scale of vacuum tubes to transistors or transistors to IC's or IC's to modern CPU technology, and count on it being fast, perhaps far exceeding Moores law.
		Yet these techniques are adding noise of their own to the surface geometry, a kind of noise that isn't going to be resolved - it being essentially quantum statistical in nature.
	www.geek.com /news/geeknews/2007Mar/wbc20070305003223.htm (1585 words)

	Extensional Tectonics at Rutgers
		Geometry and Scaling Relationships of Populations of Normal Faults and Associated Fractures>>
		Our work thus far has focused on (1) the displacement geometry, (2) length-displacement scaling relation, (3) the size distribution of the fault population, (4) the spatial distribution of the faults, and (5) fracture partitioning (different failure modes in interbedded lithologies).
		To get around this problem, we are using scaled physical models to study the temporal evolution of fault systems for distributed and basement-involved extension, shortening, and oblique deformation.
	www-rci.rutgers.edu /~schlisch (4915 words)

	Fractals, scaling and growth far from equilibrium (Site not responding. Last check: 2007-10-26)
		The application of fractal geometry and scaling concepts to the quantitative description and understanding of structure formed under non-equilibrium conditions is described.
		Self-similar fractals, multi-fractals and scaling methods are discussed, with examples, to facilitate applications in the physical sciences.
		The techniques and topics will be relevant to graduate students and researchers in physics, chemistry, materials science, engineering and the earth sciences, interested in applying the ideas of fractals and scaling.
	www.cs.ioc.ee /~bibi/kyber/Contents/meakin.html (164 words)

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