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Topic: Intrinsic coordinates

	Pellionisz "Dusseldorf-1" 1987
		Given the existence of such intrinsic coordinates, the axiom of generalized coordinates appears inevitable if identification of the internal mathematical language, actually used by neuronal networks, is intended, especially since the mathematical fundamentals of transforming such covariant- contravariant and mixed tensorial expressions in non-orthogonal general frames are well established (30).
		Transformation from coordinates intrinsic to a sensory system to an intrinsic motor frame (where the latter may be of higher dimensions) can be accomplished by a three-step tensorial scheme (53).
		Schematic illustration of (joint-angle) coordinates intrinsic to the structure of a motor apparatus (A) and the required metric tensor transformation from a unique set of projection-type (covariant, B) to overcomplete parallelogram-type (contravariant, C) vectorial expression.
	www.usa-siliconvalley.com /inst/pellionisz/dussel1dorf/dussel1dorf.html (4571 words)

	Coordinate system - Wikipedia, the free encyclopedia
		Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
		Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates.
		Intrinsic coordinates describe a point upon a curve by the length of the curve to that point and the angle the tangent to that point makes with the x-axis.
	en.wikipedia.org /wiki/Coordinates (743 words)

	Coordinate system Summary
		However, in a two-dimensional coordinate system, it is impossible to describe the location of an object that is off the plane of the floor, such as the location of a crystal on a chandelier that is hanging from the ceiling.
		In a three-dimensional coordinate system, it is possible to refer to the location of a chandelier crystal with reference to the two walls of the room and also the floor.
		Intrinsic coordinates describe a point upon a curve by the length of the curve to that point and the angle the tangent to that point makes with the x-axis.
	www.bookrags.com /Coordinate_system (2007 words)

	Coordinates (Site not responding. Last check: 2007-10-21)
		The center of each Cartesian coordinate system, hereafter referred to as a node, is where the optical element resides.
		The axes of each Cartesian coordinate system are defined according to the following convention: (1) the z-axis always points in the nominal neutron beam direction, (2) right-hand coordinate system, and (3) x-z lies in the nominal scattering plane.
		These variables are then transformed into an intrinsic coordinate system of optical element n, in which the simulation of the interaction is performed.
	www.sns.gov /ideas/coordinates.htm (408 words)

	Multiscale Procedural Shape Synthesis
		where p is a point given either in local intrinsic surface coordinates (u,v) or in global extrinsic coordinates (x,y,z); and detail is a displacement relative to the surface at level l.
		Some of our models are based on intrinsic coordinates and some on extrinsic coordinates.
		The spatial coordinates of the reference surface are used as a seed of a noise function generator.
	w3.impa.br /~lvelho/spd (1641 words)

	Intrinsic reaction coordinates
		A tool that have proved valuable in the study of molecular dynamics is the use of steepest descent based algorithms for following a molecular reaction from a transition state towards a minimum.
		The IRC is calculated by taking small steps along the negative gradient in a mass-weighted coordinate system.
		As the IRC is defined with respect to mass-weighted coordinates, care has to be taken in order to specify the correct isotopic substitution of the molecule through the keyword
	www.kjemi.uio.no /software/dalton/manual/node42.html (565 words)

	Schemes
		A procedure to change the print names of the coordinate functions of the ambient space A. It leaves A unchanged except that the visible names of the first #N coordinate functions are replaced by the strings of N and the rest return to their default.
		At this stage it is not closely tied to the coordinate ring and its homogeneous field of fractions except in the affine case.
		This intrinsic returns a sequence of maps from affine spaces to the projective space P whose images are these affine pieces of a decomposition.
	www.umich.edu /~gpcc/scs/magma/text1019.htm (7582 words)

	Pellionisz "Torino" 1987
		This latter utilizations became possible as the axiom that the CNS operates with natural coordinates that are intrinsic to the sensorimotor apparatus led to tensor geometry, the formalism of general coordinates, as a unifying mathematical language describing both neuronal network transformations and coordination of man- made (robotic) sys-tems.
		Tensor Network Model of the Cerebellum: Coordination by Coordinates As it is impossible to consider the role of the cerebellar olivary system without a treatment of the cerebellum as a whole, the fundamental task is to establish its broadest general functional features.
		This class of frames intrinsic to CNS function (and not to the anatomical structure) are, of course, much more difficult to experimentally establish than skeleto-muscular intrinsic coordinates, nevertheless this type of experimental research will undoubtedly flourish in the future.
	www.usa-siliconvalley.com /inst/pellionisz/torino87/torino87.html (8414 words)

	Curved Coordinates and Acceleration
		We will tend to view things with respect to a coordinate system co-moving with the elevator, and as a result we notice that the natural paths of things are different than they would normally be, as if those objects were being influenced by an additional force field.
		If the intrinsic curvature is zero, then non-vanishing Christoffel symbols simply represent the necessary compensation for non-linear coordinates, so, at most (the argument goes) they represent "pseudo-gravity" in such circumstances.
		In contrast, the importance and conceptual significance of the curvature (as opposed to the connection) is mainly due to the fact that it defines the mode of coupling of the coordinates with the "source" side of the equation.
	www.mathpages.com /rr/s5-06/5-06.htm (1826 words)

	General relativity mathematics : physically acceptable ?
		Note here that the curvature in GR is intrinsic (not like a cylinder which has only an extrinsic curvature, but which is in fact equivalent to a flat space).
		In this case, the intrinsic curvatures are equivalent to the principal curvatures.
		This transformation of coordinates is what Einstein calls "local coordinate transformation", in the sense that at every point, the transformation of coordinate is different.
	www.physicsforums.com /showthread.php?t=72879 (2655 words)

	Editing Intrinsic Fields in Tables (Site not responding. Last check: 2007-10-21)
		This capability is less frequently used than moving points by specifying their location via intrinsic fields; however, changing the values of intrinsic fields can be a very handy way of "nudging" areas or lines horizontally or vertically into a desired location.
		Projected coordinates are native coordinates adjusted with the local scale and local offset parameters of the coordinate system (projection) in use.
		In many cases, projected coordinates are the same as native coordinates (because of the local scale and offset values) but sometimes they are different.
	www.manifold.net /doc/7x/editing_intrinsic_fields_in_tables.htm (973 words)

	Double Integrals in Polar Coordinates
		Recall that a system of coordinates on the eucliean plane is only an artifact that allows us to assign a numeric label to all the points on the plane.
		When computing integrals, a change in the coordinate system of the space can be thought as a change in the way we partition the domain of integration.
		Cartesian) coordinates a rectangle is a rectangle as usual but in other coordinate systems it would be something of a different shape (see figure).
	omega.albany.edu:8008 /calc3/double-integrals-dir/polar-coord-m2h.html (551 words)

	4 INTRINSIC FUNCTIONS
		Some intrinsic functions are generic meaning that they return the same type as their input argument.
		It is possible to nest intrinsic functions, that is, to use the function of one intrinsic function as the argument for another function (composition of functions).
		The values for the x and y coordinates for point A and point B are assigned.
	www.krellinst.org /AiS/textbook/unit7/fortran7.5.html (1070 words)

	Intrinsic coordinates - Wikipedia, the free encyclopedia
		Intrinsic coordinates is a coordinate system which defines points upon a curve partly by the nature of the tangents to the curve at that point.
		This coordinate system has limited use, it may break down entirely when straight lines are considered, but inspection reveals three properties regarding the rate of change of its variables, namely:
		This allows the radius of curvature of a line to be found from only Cartesian coordinates.
	en.wikipedia.org /wiki/Intrinsic_coordinates (219 words)

	A method for Camera Calibration
		We assumed that by knowing the world coordinated of many points, and their corresponding image coordinates, we would be able to get enough constraints to estimate the intrinsic and the extrinsic parameters of the cameras.
		The 12 dimensions are our 12 unknowns (6 extrinsic parameters, 5 intrinsic ones, and the radial distortion term), and the 13-dimension is the value of the average error over all the points that we have between the real image coordinates and the estimated ones.
		This process could correct some errors while acquiring the coordinates of the led points (the led was a sphere of radius equal to about 0.5 – 1 pixel, and we always used its center – this might not be necessarily true).
	www.cs.umd.edu /~adeli/Calib.html (1695 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The purpose for finding this transformation is to correct for mechanical instabilities that cause changes in intrinsic properties, such as the focal length of the system.
		From the characterization of the fiducials the transformation matrix between the two coordinate systems is calculated.
		Step 3: Calculating the transformation matrix The P matrix is a compilation of three different factors: the pixel scaling, the projection, and the rigid transformation between the camera coordinate system and the object coordinate system.
	jhunix.hcf.jhu.edu /~djf1/cal.doc (850 words)

	[CPMD-list] Force on constraint.
		Fixed coordinates are easy to handle by just ignoring the forces acting on them.
		With other words the constraint force is just the actual force on the coordinate.
		Intrinsic constraints, like a bond length constraint are more difficult and need a SHAKE/RATTLE algorithm to calculate the constraint force.
	www.cpmd.org /pipermail/cpmd-list/2003-July/001108.html (360 words)

	[No title]
		Consider a verged stereo system where the baseline is a distance d along the x axis and the angle of vergence for the right camera is a known angle theta.
		The horopter is defined as the point of zero disparity (or equivalently, their coordinates in the left and right image are the same).
		Problem2.m Create two stereo camera systems: a) one that has a baseline translation of 100mm along the x axis and no rotation, and b) one that the same as a, but the right camera is also turned 5 degrees toward the left camera.
	www.ugrad.cs.jhu.edu /~cs461/Assignments/hw4.txt (600 words)

	[No title]
		deformation is done in extrinsic coordinates and not in intrinsic shape coordinates
		as intrinsic properties are to be compared, can align start points and their tangents
		As we are interested in averaging intrinsic properties of AB and A'B' we align the start points and their tangents
	www.lems.brown.edu /vision/Presentations/Kimia/MMBIA2000-II/talk.html (887 words)

	Springer Online Reference Works
		Bonnet gave new proofs of the facts known at that time on the theory of minimal surfaces and found other properties of minimal surfaces (the uniqueness of the catenoid as a minimal surface of revolution, the conformality of spherical Gauss mappings of minimal surfaces (cf.
		For the metrics of multi-dimensional minimal surfaces a necessary and sufficient condition is known only in the case of hypersurfaces [16].
		Another circle of problems in the intrinsic geometry of minimal surfaces is formed by isoperimetric inequalities (cf.
	eom.springer.de /M/m063920.htm (2815 words)

	P5 intrinsic coordinates - MathsNet Forums
		With my cluelessness in mind I wonder if somebody can help me in trying to understand intrinsic coordinates.
		The problem is to find an expression for the curvature of the curve as a function of arc length from the origin.
		It is called "intrinsic" because it does not depend on an external set of axis.
	www.mathsnet.net /forums/index.php?showtopic=739 (406 words)

	Dynamic and Intrinsic Reaction Coordinates (Site not responding. Last check: 2007-10-21)
		The Intrinsic Reaction Coordinate method pioneered and developed by Mark Gordon, North Dakota State University, has been incorporated into MOPAC in a modified form.
		As this facility is quite complicated all the keywords associated with the IRC have been grouped together in this section (these can be seen later on in this section).
		The Dynamic Reaction Coordinate is the path followed by all the atoms in a system assuming conservation of energy; i.e., as the potential energy changes the kinetic energy of the system changes in exactly the opposite way so that the total energy (kinetic plus potential) is a constant.
	www.cachesoftware.com /mopac/Mopac2002manual/node609.html (242 words)

	Body
		intrinsically and geometrically, every point has a neighborhood that is isometric to a neighborhood of any other point).
		This is the usual upper half plane model of the hyperbolic plane thought of as a map of the hyperbolic plane in the same way that we use planar maps of the spherical surface of the earth.
		Along this coordinate curve (a radial geodesic) the speed is not constant; but, since the second coordinate of x measures arc length, the arc length from z(a,y) = x(a, r ln(y/r)) to z(a,b) = x(a, r ln(b/r)) is
	www.math.cornell.edu /~dwh/papers/crochet/crochet.html (3801 words)

	Curvature, Intrinsic and Extrinsic
		If u and v were projections of orthogonal coordinates (as were x and y in our prior discussion), the determinant of the surface metric at the origin would be 1, and the curvature would simply be 4ac-b
		. Substituting the expressions for dX and dY in terms of du and dv, the metric at the origin in terms of the u,v coordinates is
		The quantity inside the parentheses is a planar function, so the surface is a parabolic "valley", which has no intrinsic curvature (like the walls of a cylinder).
	www.mathpages.com /rr/s5-03/5-03.htm (2403 words)

	Navon, David (2001) The Puzzle of Mirror Reversal: a View from Clockland, Psycoloquy: 12,#17 Mirror Reversal (1) (Site not responding. Last check: 2007-10-21)
		Thus, mirror reversal is defined with respect to intrinsic coordinates (namely, object-centred in the case of mirrored objects, egocentric in the case of the observer's reflection).
		As stated in T1 and explained in paragraph 17, once labels are assigned to the intrinsic sides of the fronts of two dorsiventral objects in any consistent manner, arbitrary or non-arbitrary as the case may be, some cross-lateral inversion is entailed.
		It seems that the source of the confusion is that when focusing on the appearance of a certain facet, we tend to assign to it coordinates of its own that are not necessarily compatible with the overall object-centred coordinates.
	psycprints.ecs.soton.ac.uk /archive/00000146 (9840 words)

	Geometry optimization: *WALK
		Set the geometry walk to be an Intrinsic Reaction Coordinate (IRC) as described in Ref.
		This is the default for dynamic walks , gradient extremal walks and in calculations of Intrinsic Reaction Coordinates (IRCs) .
		In dynamic walks the trust radius is by default put to 0.005, and in walks along an Intrinsic Reaction Coordinate (IRC) the default trust radius is 0.020.
	www.lle.rochester.edu /pub/support/dalton/node87.html (1084 words)

	Quantitative Examinations of Internal Representations for Arm Trajectory Planning: Minimum Commanded Torque Change ...
		The initial and final positions were randomly selected, and the distance of the movement was constant at 45% of arm length.
		Shaded area shows ability of coordinated rotation of joints to model the actual whole deviation.
		in the extrinsic coordinates are not the same between these planes.
	jn.physiology.org /cgi/content/full/81/5/2140 (7003 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The purpose of this and the next section is to describe how the perspective projection matrix changes when we change the external and intrinsic coordinate systems.
		We will describe what happens to the coordinate system and the perspective projection matrix of a camera system when we make some or all of these changes to the camera system.
		this standard external coordinate system is `widely used in motion and stereo applications because it allows us to ignore the specific characteristics of the cameras and to think in terms of ideal systems.' (Faugeras however goes a little furter than we do, and normalises his coordinates to take the focal length f = 1.)
	www.maths.uwa.edu.au /~csaba/2GA2/cameracoord.html (594 words)

	IRC (Site not responding. Last check: 2007-10-21)
		An Intrinsic Reaction Coordinate calculation is to be run.
		To print reaction coordinate steps that are separated by constant distance, use
		In reactions involving more than one step, that is, a reaction in which there is a stable intermediate, the various individual .csf files can be joined together using a utility called "join_maps.exe".
	www.cachesoftware.com /mopac/Mopac2002manual/node198.html (115 words)

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