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Chapter 2
Published in Pearson Frederick, Map Projections:, 2018
The radius of curvature is the reciprocal of the curvature. Thus, Rc=[1+(dydx)2]3/2d2ydx2
Four-Point Perspective
Published in Craig Attebery, The Complete Guide To Perspective Drawing, 2018
The length of each wall is represented on the picture plane as an arc, a section of a circle. To find the length of each wall, the length of each arc must be calculated (Figure 33.19). This next step requires a little math. The formula to measure the length of an arc is 2πR(C/360) where:C is the central angle of the arc in degrees;R is the radius of the arc; andπ is 3.14.
Geometry
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
A chord of a circle is a line segment between two of its points (Figure 4.21). A diameter is a chord that goes through the center, or the length of such a chord (therefore the diameter is twice the radius). Given two points P1=(x1,y1) $ P_{1} = (x_{1} , y_{1} ) $ and P2=(x2,y2) $ P_{2} = (x_{2} , y_{2} ) $ , there is a unique circle whose diameter is P1P2; its equation is (x-x1)(x-x2)+(y-y1)(y-y2)=0. $$ (x - x_{1} )(x - x_{2} ) + (y - y_{1} )(y - y_{2} ) = 0. $$
A physical effort-based model for pedestrian movement in topographic urban environments
Published in Journal of Urban Design, 2020
Eliyahu Greenberg, Asya Natapov, Dafna Fisher-Gewirtzman
The abovementioned calculation describes global integration; global in the sense that this measure is calculated relative to the entire system in question. It is possible to calculate centrality measures, including integration, on a more local scale. The calculation itself is identical, the only difference is that the sum of the shortest paths incorporates paths only up to a certain distance. This distance is referred to as a radius. Some specific radii have been demonstrated to be more useful than others when describing certain things. There have also been suggestions for more complex methods, such as decay functions, for local indices calculation to describe complex phenomena (Conroy Dalton and Dalton 2007).
Underwater thrust vectoring based on inflated surface
Published in Journal of Marine Engineering & Technology, 2020
The effect of the curvature on the thrust vectoring is analysed in this section. The curvature of the surface is measured using the radius. The curvature is the reverse of the radius. So the larger is the radius, the smaller is the curvature. The length of the surface is l = 40 mm and keeps invariant. The depth in all cases is d = 0 mm.