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Radiometry and Photometry
Published in Vasudevan Lakshminarayanan, Hassen Ghalila, Ahmed Ammar, L. Srinivasa Varadharajan, Understanding Optics with Python, 2018
Vasudevan Lakshminarayanan, Hassen Ghalila, Ahmed Ammar, L. Srinivasa Varadharajan
We know that a circular arc of length s subtends an angle θ at the center of a circle, where θ is defined as the ratio of the arc length to the radius r of the circle. We could easily extend this two-dimensional idea to three-dimensions and define what is called a solid angle. The solid angle is defined as ) Ω=area of the surface projected onto the tangent of a sphere(radius of the sphere)2
The circle
Published in John Bird, Science and Mathematics for Engineering, 2019
(l) The angle at the centre of a circle, subtended by an arc, is double the angle at the circumference subtended by the same arc. With reference to Figure 13.3, Angle AOC=2×angle ABC
Electrical fundamentals
Published in Mike Tooley, Electronic Circuits, 2019
In electrical circuits, angles are measured in either degrees or radians (both of which are strictly dimensionless units). You will doubtless already be familiar with angular measure in degrees where one complete circular revolution is equivalent to an angular change of 360°. The alternative method of measuring angles, the radian, is defined somewhat differently. It is the angle subtended at the centre of a circle by an arc having length which is equal to the radius of the circle (see Fig. 1.2).
Design Guidelines for Schematizing and Rendering Haptically Perceivable Graphical Elements on Touchscreen Devices
Published in International Journal of Human–Computer Interaction, 2020
Hari P. Palani, Paul D. S. Fink, Nicholas A. Giudice
The cord length is a variable that depends on: (1) θ – angle subtended between the lines, (2) r – the radius of the traced circle, or (3) both 1 and 2. In theory, the 4 mm gap width identified in Exp-2 should be translated into a 4 mm cord length for accurate detection of distinct oriented lines. However, the cord length cannot be fixed at a constant value as it varies depending on the angle (θ) subtended between oriented vibrotactile lines and the radius (r) of the circle formed by the user while performing the “circling” exploratory procedure. For instance, at a circle radius of 1-inch and a 4 mm cord length, the user can (in theory) discriminate oriented lines separated by an angular magnitude of 5°, but by increasing their radius to 2-inches, they should be able to discriminate oriented lines separated by an angular magnitude as low as 2°. Acknowledging the dependency between these three variables, Experiment 3 was designed to identify the minimum cord length that supports detection and discrimination of oriented vibrotactile lines.