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Topic: Parallelepiped

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	Parallelepiped - Wikipedia, the free encyclopedia
		The parallelepipeds are the results of linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations).
		A cuboid is a parallelepiped of which all faces are rectangular.
		A rhombohedron is a parallelepiped with all rhombic faces.
	en.wikipedia.org /wiki/Parallelepiped (528 words)

	Lord Kelvin \| On Homogeneous Division of Space
		Now, suppose any one pair of the tetrahedrons to be taken away from their positions in the primitive parallelepiped, and, by purely transitional motion, to be brought into position with their edges of length QD coincident, and the same to be done for each of the other two pairs.
		Similarly two other parallelepipeds may be made by putting together the pairs that have edges of lengths equal to QB and QC respectively with those edges coincident, and finishing in each case with the remaining pair of tetrahedrons.
		The three parallelepipeds thus found are essentially different from one another, and from the four of §10; and thus we have the seven parallelepipeds fulfilling the statement of §9.
	zapatopi.net /kelvin/papers/on_homogeneous_division_of_space.html (3396 words)

	CGH at LSU: Dealing with VRML Objects
		A wireframe model is constructed by first specifying the coordinates of various strategically placed points (vertices) that lie on the surface of the object, then specifying how subsets of these points are to be connected in sequence in order to form various polygons that coincide with individual (flat) segments of the surface.
		One of the simplest examples is the wireframe model of a rectangular parallelepiped of width 2w, height 2h, and depth 2d, as depicted here in Figure III.4.
		The entire surface of the rectangular parallelepiped shown in Figure III.4 can be completely specified by eight vertices (numbered 0 through 7 in the figure; but note that the vertex numbered zero is hidden from view) and six four-sided (rectangular) polygons.
	www.phys.lsu.edu /faculty/tohline/phys4412/howto/VRML.coordinates.shtml (757 words)

	Finding the Volume of a Parallelpiped in Space: Application of Determinants
		A parallelepiped is a 3-dimensional figure in which opposite faces are congruent parallelograms.
		Note: The volume of a parallelepiped can also be found by taking the determinant of the 3 by 3 matrix formed using each vector as a row in the matrix.
		Since the determinant of the above matrix is 2, the volume of the parallelepiped formed from the vectors <1,2,1>, <-1,0,1>, and <0,1,2> is 2.
	students.uww.edu /muellerbt15/VPar.htm (955 words)

	All Elementary Mathematics - Study Guide - Geometry - Polyhedrons. Prism, parallelepiped, pyramid...
		Parallelepiped is a prism, bases of which are parallelograms.
		A parallelepiped has four diagonals; they all intersect in the one point and they are divided in it into two.
		A right-angled parallelepiped, all faces of which are squares, is called a cube.
	www.bymath.com /studyguide/geo/sec/geo15.htm (579 words)

	Parallelepiped walk (Site not responding. Last check: 2007-09-06)
		) are placed on the surface of parallelepiped P = {(x, y, z): 0 <= x <= L, 0 <= y <= W, 0 <= z <= H} with LWH dimensions (see figure).
		These two points can be linked with various curves lying on the surface of P.
		Parallelepiped dimensions L, W, H and coordinates of the points are integers, 0 <= L,W,H <= 1000.
	acm.uva.es /p/v5/503.html (146 words)

	Camera for shooting movie and still pictures - Patent 4829384
		A video camera includes a casing having a generally rectangular parallelepiped shape, a first imaging optical system for shooting a still image and a second imaging optical system for shooting a video picture.
		A video camera in accordance with claim 1 wherein said predetermined longitudinal direction is a direction in which a cutaway portion of said leader portion of said film is directed to a direction of depth of said first opening.
		Basically, the camera includes a casing 10 having generally the shape of a substantially rectangular parallelepiped, and the casing 10 contains a unit having a function of a video camera and a unit having a function of a still camera.
	www.freepatentsonline.com /4829384.html (6172 words)

	PlanetMath: triple scalar product
		Thus, the magnitude of the triple scalar product is equivalent to the volume of the parallelepiped formed by the three vectors.
		(A parallelepiped is a three-dimensional object where opposing faces are parallel.
		An example is a brick or sheared brick.)It follows that the triple scalar product of three coplanar or collinear vectors is then 0.
	planetmath.org /encyclopedia/TripleScalarProduct.html (239 words)

	figure 7 parallelepiped (Site not responding. Last check: 2007-09-06)
		Figure 7: Parallelepiped classified TM sub-scene performed with 4 classes.
		However, parallelepiped classification was a useful discovery technique.
		Small discrete clusters of red pixels can be seen in the center of the image, lower center, as well as the upper right corner.
	titicaca.ucsb.edu /~craig/research/tm_paper/figure7.htm (206 words)

	Programming Assignment 3 - CS535 (Site not responding. Last check: 2007-09-06)
		If the second button is clicked, your program should shade the faces of the parallelepiped so that adjacent faces are always shaded with different colors.
		The bouncing of the parallelepiped should be performed using a pre-defined velocity and rotation speed about the main axis of the parallelepiped.
		This means that your program needs to clip the parallelepiped against the walls of the room periodically before the centroid reaches a wall.
	www.cs.engr.uky.edu /~cheng/cs535/Prog3-02-fal.html (519 words)

	[No title] (Site not responding. Last check: 2007-09-06)
		The parallelepiped classifier uses the class limits (LOLIM) and (UPLIM) stored in each class signature to determine if a given pixel falls within the class or not.
		The class limits specify the dimensions (in standard deviation units) of each side of a parallelepiped surrounding the mean of the class in feature space.
		The parallelepiped classifier is typically used when speed is required.
	www.pcigeomatics.com /cgi-bin/pcihlp/MLC\|DETAILS\|PARALLELEPIPED (134 words)

	[No title]
		There are three types of multi-class classifiers available: the PARAllelepiped classifier (MAXL="PARA"); the FULL maximum likelihood classifier (MAXL="FULL"); and the TIES classifier which is a parallelepiped classifier which uses full maximum likelihood classification in the event of class ties.
		The basic concept is to use parallelepiped classification unless we have a tie (overlap) in which case the tie is resolved by using full maximum likelihood classification.
		This type of classification is an attempt to gain the speed of the parallelepiped classifier while eliminating the large number of pixels classed as ties (overlap).
	www.pcigeomatics.com /cgi-bin/pcihlp/MLC\|DETAILS (860 words)

	A simple GNOME example (Site not responding. Last check: 2007-09-06)
		This is the same thing for the rectangular parallelepiped representing the car at the rawer level.
		The quantification of the geometrical attribute-objects is made by associating to the rectangular parallelepiped, cylinders, triangular prisms, and tori an application which specifies their dimensions.
		For example, for a rectangular parallelepiped, the application is the constant one and simplifies to (w,h,l), a point in R
	users.aber.ac.uk /ffl/gnome/these/exemple_simple.html (288 words)

	[No title]
		Draw a rectangular parallelepiped that has the line AB as its diagonal.
		Four materials are ready from same rectangular parallelepiped, as a rectangular parallelepiped has four diagonals.
		These actions help her making clear the direction of rectangular parallelepiped and the position of diagonal in rectangular parallelepiped.
	psych.hanover.edu /vygotsky/takaha.html (682 words)

	Slit Lamp Biomicroscopy Part One
		Use a parallelepiped approximately 2 mm wide and 4 mm high Focus on the iris then the pulled back the focus into the anterior chamber.
		A parallelepiped is essentially an optic section, except the slit width is greater (2.0 - 4.0 mm) and the height may vary, providing a more three dimensional view of the cornea or crystalline lens.
		The eye lid is only about 1 mm thick, therefore, when you instructed the patient to open their eyes you should almost be in focus on the tear film of the cornea.
	www.opt.indiana.edu /riley/HomePage/newslitlamp/1_part_one_slitlamp.html (3573 words)

	tetrahedra (Site not responding. Last check: 2007-09-06)
		The edges of the tetrahedron are six of the twelve diagonals of the parallelepiped's faces.
		Generalizing is easy: the four pyramids have the same volume (same height, that of the parallelepiped, and bases with same area, half of that of the parallelepiped's base).
		Generalization of Pythagoras theorem: in a right-angled tetrahedron (three right angles around one vertex) the square of the area of the non right-angled face is equal to the sum of the squares of the areas of the three other faces.
	www.ac-noumea.nc /maths/amc/polyhedr/tetra_.htm (1767 words)

	Volume of a a parallelepiped (Site not responding. Last check: 2007-09-06)
		These three vectors form three edges of a parallelepiped.
		The volume of this parallelepiped (is the product of area of the base and altitude) is equal to the scalar triple product
		It can be shown that the volume of the parallelepiped is the absolute value of the determinant of the following matrix:
	www.math.ucdavis.edu /~daddel/linear_algebra_appl/Applications/Determinant/Determinant/node11.html (64 words)

	Parallelepiped A parallelepiped is a solid (Site not responding. Last check: 2007-09-06)
		A parallelepiped is a solid (3-dimensional) figure in which all faces are parallelograms.
		A special kind of parallelepiped is a rectangular box,
		It is a solid figure and has a volume.
	home.satx.rr.com /bowiemathconn/GlsParallelepiped.htm (31 words)

	Minimal enclosing parallelepiped in 3D (Site not responding. Last check: 2007-09-06)
		We investigated the problem of finding a minimal volume parallelepiped enclosing a given set of n three-dimensional points.
		Using two mathematical properties of these parallelepipeds, we derived algorithms of theoretical complexity O(n^6).
		The parallelepiped library is the implementation of our quickest algorithm, which is available under the
	graal.ens-lyon.fr /~fvivien/parallelepiped.html (70 words)

	A parallelepiped (Site not responding. Last check: 2007-09-06)
		I'm taking a university math course (Geometry and Discrete math) The question is: " If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,-2), B is (3,6,1), and C is (4,0,-1), find the coordinates of the other vertices of the parallelepiped.)" (Crippin, page 173).
		Look at a cardboard box and imagine that one of the corners is O and the ends of the three edges that start at that corner are A, B and C. This is a rectangular parallelepiped but it is an approximate model of what you have.
		I see the three edges of the parallelepiped OA, OB and OC as vectors from O to the other three points.
	mathcentral.uregina.ca /QQ/database/QQ.09.04/aman1.html (264 words)

	hpux pus008.3g (Site not responding. Last check: 2007-09-06)
		The following is a description of each of the test methods: TEST EXTENT 3: The data record contains a rectangular parallelepiped, a relation, and a threshold.
		The parallelepiped is transformed to DC space and the diagonal of the transformed DC rectangle is then compared Hewlett-Packard Company - 6 - HP-PHIGS Release 3.0: April 1994 PUS008(3G) CONDITIONAL EXECUTE STRUCTURE GSE PUS008(3G) pgse_u8 pgse_u8 against the threshold using the relation specified.
		The parallelepiped is then used to determine if the object is clipped or not.
	www.informatik.uni-frankfurt.de /doc/man/hpux/pus008.3g.html (1007 words)

	Solids II - Parallelepiped - Analytical Geometry with POV-Ray
		Solids II - Parallelepiped - Analytical Geometry with POV-Ray
		A parallelepiped with the corners P,Q,R and S we get with a macro from "analytical_g.inc" :
		A parallelepiped with the starting point at P and the edge vectors V
	www.f-lohmueller.de /pov_tut/a_geo/a_geo62e.htm (159 words)

	PoAutoCubeAxis class Reference (Site not responding. Last check: 2007-09-06)
		Class to build a set of axes on a parallelepiped relating to the view.
		This class builds a set of 3D axes displayed on some of the 12 edges of a parallelepiped.
		The two points (start and end fields) define the diagonal of the parallelepiped and only the edges which are intersecting a visible face and an invisible face will be graduated.
	www.tgs.com /support/java_api_doc/api_cpp/html/classPoAutoCubeAxis.html (740 words)

	Mech Homework 2
		At time = 0, of this parallelepiped is viewed in a Cartesian co-ordinate system that has its origin at one of the corners of the parallelapiped and the axes parallel the sides.
		a) Find the numerical values for the elements of the inertia tensor for this parallelepiped at time t = 0.
		c) Determine the angular momentum of this parallelepiped at time t = 0.
	www.guilford.edu /physics/Mechanics/Mech_Homework_2.html (161 words)

	Mu Alpha Theta Andree Award (Site not responding. Last check: 2007-09-06)
		It is well known that there is a rectangular parallelepiped where three dimensions and plane diagonals are integers.
		It's clear there is a rectangular parallelepiped where its dimensions and space diagonal are integers.
		We aimed at exploring a rectanglar parallelepiped where dimensions, plane diagonals and space diagonal are integers.
	www.mualphatheta.org /Science_Fair/science_fair_winners.htm (1005 words)

	Quarky Volume Formula for Parallelepiped (Site not responding. Last check: 2007-09-06)
		{ A[(AxB).C] - C[(AxB).A] } Since the quantity (AxB).C equals the volume of the parallelepiped with the vectors A,B,C forming adjacent edges, it's clear that (AxB).A = 0, because two of the three edges are identical.
		Both factors equal the volume of a parallelepiped with edges A,B,C, so the product equals [A.(BxC)]^2.
		This is based on the volume formula V=ABC for rectangular solids, and the same degree of obviousness could be achieved in the general case if we had a suitable formula for the volume of a general parallelpiped.
	www.mathpages.com /home/kmath418.htm (273 words)

	INEQUALITIES IN MATRIX THEORY (Site not responding. Last check: 2007-09-06)
		are concurrent sides of a rectangular parallelepiped of the same volume as that of the original parallelepiped.
		are the concurrent side vectors of a parallelepiped in any inner product space (real or complex) and V is the volume of this k-dimensional parallelepiped and where the dimension of the space need not be k or even finite, is a generalized version of the above formula.
		and the last expression is the product of squares of sides of a rectangular parallelepiped of the same volume as the original parallelepiped.
	home.iitk.ac.in /~rksr/html/10INQ.htm (1125 words)

	RISC-Linz - Numerical Solving of Constraints of Multivariate Polynomial Strict Inequalities (Site not responding. Last check: 2007-09-06)
		The idea of bisecting of a parallelepiped is to halve all faces of (n-dimensional) parallelepiped and obtain
		-truth value of a constraint (which was undefined on the initial parallelepiped) will become true or false on new parallelepipeds.
		These ideas are implemented by extracting additional information from the sufficient condition for non-existence of roots of a polynomial in a parallelepiped.
	www.risc.uni-linz.ac.at /projects/basic/SFB/reals/themes/int-bisect/node4.html (147 words)

	Uniform Sampling of Steady-State Flux Spaces: Means to Design Experiments and to Interpret Enzymopathies -- Price et ...
		The smallest of these parallelepipeds is chosen and uniform random points within the parallelepiped are generated (D) based on uniform weightings on the basis vectors defining the parallelepiped (shown as fl arrows).
		The fraction of the points generated inside the parallelepiped that fall within the solution space is called the "hit fraction." The hit fraction multiplied by the volume of the parallelepiped yields the volume of the solution space.
		planes, the number of such parallelepipeds that could be used enclose the space is
	www.biophysj.org /cgi/content/full/87/4/2172 (6169 words)

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