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Stratifications
Published in Christopher Beorkrem, Material Strategies in Digital Fabrication, 2017
To create the variation of block heights, create copies of each type or row, even or odd. In each sequence of the blocks scale the heights of the appropriate number of each size of block. As the program proceeds through its repetitious task of stacking layer upon layer, it is scanning to verify or define the appropriate height for each block. As the wall gets higher, the blocks will be at increasingly large variables. As this proceeds, the height is not defined by a set of absolute geometry, or by an adaptive script, but by the scan, which the robot performs, before setting the block down in its position. This project was a successful demonstration of techniques for adapting a machine to changing scenarios for particular components within a script.
Optical Metrology in Manufacturing Technology
Published in Toru Yoshizawa, Handbook of Optical Metrology, 2015
It is a common experience that images generated by curved mirrors show characteristic deformations that carry information about the geometry of the reflective surface. This property is used since long time to check the homogeneity of polished surfaces by looking at the mirror images of line grids. In modern test setups, the grid pattern often is displayed by a flat screen monitor, so that the pattern can be adapted quickly and easily to different testing tasks. This so-called deflectometric technique can be modified to measure the absolute geometry of reflecting and transmitting surfaces. In [5], a correspondence of different deflectometric approaches to the basic principles of active and passive triangulation is outlined.
From Kepler problem to skyrmions
Published in Maricel Agop, Ioan Merches, Operational Procedures Describing Physical Systems, 2018
Indeed, even superficially it can be seen at once that the mentioned freedom of the parameters defining the types of orbits, allows us to construct a Cayley-Klein (or Absolute) geometry [2,3] characterizing the variation of those orbits. We know that an Absolute geometry is related to some conservation laws, at least as long as some realizations of SL(2, R) group structure are involved. And indeed, the absolute metric for the interior of the circle (15) ds2=(1-v2)(dμ)2+2μv(dμ)(dv)+(1-μ2)(dv)2(1-μ2-v2)2 $$ \left( {ds} \right)^{2} = ~\frac{{(1 - v^{2} )(d\mu )^{2} + 2\mu v(d\mu )(dv) + (1 - \mu ^{2} )(dv)^{2} }}{{(1 - \mu ^{2} - v^{2} )^{2} }} $$
Nearness as context-dependent expression: an integrative review of modeling, measurement and contextual properties
Published in Spatial Cognition & Computation, 2020
Marc Novel, Rolf Grütter, Harold Boley, Abraham Bernstein
Crangle and Suppes (1994) and Suppes (1991) discusses which geometry is appropriate for different prepositions. To model “near” they use absolute geometry, which is a weakened Euclidean geometry with the axiom of parallels removed. Since only congruence is required (for instance qualitative equidistance or ordering of qualitative distance, as investigated by Suppes, Krantz, Luce and Tversky (1989)), such a geometry allows for strict-positiveness and non-symmetry (including weak symmetry). Unfortunately, this approach does not solve the problem of the triangle inequality, which still holds true in absolute geometry.