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Measure-Based Functions

 

Introduction

A circle is a group or series of distinct points drawn at an exact same distance from another point referred to as the center. The distance from the center C to one of these equidistant points is called the radius, R. The line that connects all of the points that are equidistant to the center is called the circumference of the circle. The diameter is the distance between two points of the circumference to the center; in other words, a diameter is double the radius.

To manage the measurements and other related operations, the circumference is divided into 360 portions. Each of these portions is called a degree. The unit used to represent the degree is the degree, written as ˚. Therefore, a circle contains 360 degrees, that is 360˚. The measurement of two points A and D of the circumference could have 15 portions of the circumference. In this case, this measurement would be represents as 15˚.

The distance between two equidistant points A and B is a round shape geometrically defined as an arc. An angle, ө, is the ratio of the distance between two points A and B of the circumference divided by the radius R. This can be written as:

Therefore, an angle is the ratio of an arc over the radius. Because an angle is a ratio and not a “physical” measurement, which means an angle is not a dimension, it is independent of the size of a circle. Obviously this angle represents the number of portions included by the three points. A better unit used to measure an angle is the radian or rad.

A cycle is a measurement of the rotation around the circle. Since the rotation is not necessarily complete, depending on the scenario, a measure is made based on the angle that was covered during the rotation. A cycle could cover part of the circle in which case the rotation would not have been completed. A cycle could also cover the whole 360˚ of the circle and continue there after. A cycle is equivalent to the radian divided by 2 * Pi.

The VCL ships with functions used to perform conversions of values between different units. To use any of these functions, you must include the VCL math header file as:

#include <math.hpp>

 
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