Equal-area projection

Figure 1.8 (left). IPF for a PTFE sample strained 1 in. (35%) at 25°C. presented in a polar equal-area projection. ( rystallographic directions are given by poles to the indicated planes. Contours represent the tendency for crystallographic directions to be aligned with the tensile axis."... 

Example of two projections. Panel A shows a Mercator projection Panel B shows an interrupted flat polar quartic equal-area projection. 

Fig. 1.12 In (a) a pole, corresponding to the direction perpendicular to a diffraction plan, is projected on to the equatorial plane resulting in a pole plot (b) of diffraction intensities as function of the azimuthal rotation <[) and the tilt tp. (c) and (e) show side view of (a), in a plane normal to the equatorial plane, (d) and (f) are top views of (a), parallel to the equatorial plane. In the Wulff (stereographic or equal-angle) projection the end of the pole is projected to the lower end of the plane perpendicular to the equatorial plane (c) and the point W in the pole plot is defined by the intersection with of this projection with the equatorial plane (d). The Schmidt (equal area) projection (e, f) the pole is projected to the horizontal (equatorial) plane with the intersection point S...

Earthquake Mechanisms and Stress Field, Fig. 9 The fault instability is shown for all possible fault normals it is colour-scaled and ranges between 0 (the most stable plane) and 1 (the most unstable plane). The lower-hemisphere equal-area projection is used. Directions of the (Tj, (72 and (73 axes are (azimuth/plunge) 146748°, 327°/42° and 237°/l°. The shape ratio/f is 0.80 and the fault Motion n is 0.5 (Modified after Vavrycuk et al. (2013))... 

Numbers to the right of each plot give values of k and e (Eqs. 18 and 19), for each mechanism. Focal hemispheres (either upper or lower, because of symmetry) are shown in equal-area projection... 

Fig. 12 Long Valley caldera, California, and vicinity, showing the best located earthquakes in 1980 and mechanisms for the — largest earthquakes of 1978 and 1980 as lower-hemisphere, equal-area projections, with fields of compressional-wave polarity in black...

Several diameter definitions are used in particle image measurements (Fig. 7). Martin diameter, the chord length which divides the projected particle into two equal areas with respect to a fixed dkection (29) Feret diameter, the projected length with respect to a reference dkection (30) and the diameter of equivalent surface area, the diameter of a ckcle the area of which is equivalent to the projected area of the particle in question (3). 

Ferefs diameter (Fig. 20-5) is the perpendicular projection, in a fixed direction, of the tangents to the extremities of the particle profile. Martin s diameter is a hne, parallel to a fixed direction, which divides the particle profile into two equal areas. Since the magnitude of these statistical diameters varies with particle orientation, these diameters have meaning only when a sufficient number of measurements are averaged. 

Base from US Geological Survey digital data, 1 2 000 000, 1994 Albers Equal-Area Conic projection... 

Since there are no flat surfaces in the foam borders and vertexes, the entire incident light changes its initial direction, similarly to the case of a spherical bubble. Thus, the optical cross section of borders and vertexes will equal the projection area of these structural elements on a plane perpendicular to the light beam direction (shadow area). 

R Because the plant is spherical, the total solar radiation absorbed equals its projected area (jrr2) times the solar flux density perpendicular to the solar beam (1000 W m-2) times the absorbance (0.30). To obtain the average solar radiation absorbed over the plant surface, we divide by the plant s surface area (47rr2). Thus... 

Martin s Diameter The length of a line which divides the projected outline of the particle into two equal areas and is paiallel to a given direction (nomially the hoiizomal cross-hait in a microscope field of view)... 

The three basic types of cylindrical projection are the simple cylindrical, the equal-area, and Mercator s projections. A modified equal-area form of cylindrical projection was invented in 1973 by the German historian Arno Peters - and is known as the Peters projection, it draws attention to Third World countries, which are prominently placed in the centre of the map. Landforms close to the equator are elongated, while those in high lattitudes are compressed. 

At the right-hand side of Fig. 11.33, the orientations (small dots) of connecting lines between event pairs are plotted in an equal-area, lower hemisphere projection. Most orientations in Fig. 11.33 are near the periphery of the hemisphere, thus indicating nearly horizontal inclination of the plane. The big filled dots indicate the orientation of the three coordinate axes. The normal vector of the plane is in the center of the hemisphere, i.e. nearly in z direction. 

Fig. 11.33. Correlation integral and fractal dimension (left-hand side) of Cluster No. 1 and the orientations of connecting lines between event pairs (small dots) in an equal-area, lower hemisphere projection (right-hand side).

If most of the sensors have compressional or dilatational first motions, the events were classified in Type T and Type C, respectively. Otherwise, the events were of Type S. According to this nomenclature, a source with a uniform compressional polarity pattern was interpreted as a tensile type, and one with compressional as well as dilatational first motions as a shear type. From all events emitted before and during fincturing of the specimen, 70% were of Type S, 20% of Type T and 10% of Type C. In Fig. 11.39 single fault-plane solutions of the six strongest Type S events are plotted in projection on the x-z-plane. The polarities of the eight sensors are shown at the right-hand site of Fig. 11.39 in an equal-area, lower hemisphere projec-... 

Figure 1 - Distribution of sources observed at 4.2 ym on an Aitoff equal area all sky projection. Heavy lines are the survey limits, dashed line is the galactic equator.

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