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Distance-Shape-Texture Signature Trio for Facial Expression Recognition
Published in Sourav De, Paramartha Dutta, Computational Intelligence for Human Action Recognition, 2020
Asit Barman, Sankhayan Choudhury, Paramartha Dutta
Each triangle hold the following basic properties: The sum of the angles in a triangle is 180 degrees. This is called the angle-sum property.The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.The side opposite to the largest angle is the longest side of the triangle and the side opposite to the smallest angle is the shortest side of the triangle.
Terminology of Safety
Published in Chris Hobbs, Embedded Software Development for Safety-Critical Systems, 2017
The language of mathematics allows us to express ideas about universals. Mathematics doesn’t understand what a triangle actually is, but it can prove that the angles in any triangle add up to 180 degrees. The principle of duality in geometry emphasizes the abstraction from real objects by saying that, with a few constraints, we can exchange the terms “point” and “line” and all the geometric theorems remain true. For example, two points/lines define a line/point.
Perimeters, areas and volumes
Published in James Kidd, Ian Bell, Maths for the Building Trades, 2014
Before we look at the mathematics involved in finding the areas of circles, we need first to look at some of the names given to the various parts of the circle. On a sheet of paper, draw a circle and write the names of the parts as I describe them. You may need the help of your teacher with some of them. I have drawn them at the end of this chapter (in the summary, see Figure 7.8), but you will learn better if you do them yourself. Centre The centre point is the middle of the circle. The point of your compass was positioned at this centre point and the line forming your circle was drawn at a constant distance from it.Circumference The line that is drawn around the centre point is called the circumference. The circumference of a circle is a linear measurement. If we were to stretch a piece of string around the perimeter of a car tyre the string would represent the circumference of the tyre and could be measured.Radius The distance between any point on the circumference and the centre point is called the radius.Diameter The measurement from one side of the circle to the other side, passing on its way through the centre point, is called the diameter and should be thought of as the width of a circle. The line forms two semi-circles, one each side of the diameter. The diameter is always twice the length of the radius.Degree The amount that it was necessary to turn your compass in order to draw the circumference is one revolution. This is split up into 360 equal divisions, known as degrees. The sign for degree is °. A degree can be split into smaller units called minutes and seconds. There are 60 minutes in a degree and 60 seconds in a minute.Sector A sector is an area of part of a circle, formed by two lines radiating from the centre point out to the circumference, and the portion of the circumference between the two lines.Arc An arc is that part of the circumference that acts as a boundary to the sector. The arc is a linear distance.Chord A chord is a straight line joining two points on the circumference but not passing through the centre point. The smaller area of the circle cut off by the chord is called a minor segment, while the remainder of the circle is called a major segment.
Evaluation of maximum thigh angular acceleration during the swing phase of steady-speed running
Published in Sports Biomechanics, 2023
Kenneth P. Clark, Laurence J. Ryan, Christopher R. Meng, David J. Stearne
All angles in the model equations are measured in radians referenced to a vertical axis perpendicular to the ground. Experimentally measured angles in degrees can be expressed in radians by the standard conversion factor (2π rad/360 deg). The thigh segment moves from a positive maximum angle at peak flexion to zero at the downward vertical position to a negative maximum angle at peak extension. The total thigh range of motion (θtotal) is determined from peak extension to peak flexion of the thigh segment. The phase value (θphase) allows the experimental data acquisition of the thigh segment to occur at any time during the rotation cycle and determines the temporal position of the model equations on θ(t) vs. t, ω(t) vs. t and α(t) vs. t graphs. The offset angle (θshift) determines the central angular position of the sine wave model equation on the θ(t) vs. t graph. Conceptually, the θshift value represents a single metric to quantify the extent to which the mean thigh angular motion, averaged over the entire stride cycle, occurs in front or behind the vertical axis. From a practical standpoint, this θshift value is related to how ‘front-side’ thigh mechanics are shifted (Haugen et al., 2018; Kratky et al., 2016; R. V. Mann & Murphy, 2018).