NetFabric.Angle

Implements a structure representing an angle.

The angle is stored in memory in the angle measurement unit it was originally defined, with double precision, allowing fine control over conversions and reducing rounding errors. All operations are strongly-typed.

Includes angle operations like lerp, reduction, reference angle, comparison, classification and trigonometry.

Usage:

Adding to your project

NetFabric.Angle is available as a NuGet package and as a Unity package.

Creation of the angle:

Use the methods for the measurement units you are working with:

var right0 = Angle.FromRadian(Math.PI / 2.0);
var right1 = Angle.FromDegrees(90.0);
var right3 = Angle.FromGradian(100.0);

When using DMS format, arcminutes and arcseconds have to be values in the interval [0.0, 60.0[

var right3 = Angle.FromDegrees(90, 59.9); // degrees and arcminutes
var right4 = Angle.FromDegrees(-90, 59, 59.9); // degrees, arcminutes and arcseconds

You can use the predefined angles in any measuring unit:

var zero = AngleDegrees.Zero;          // 0 degrees
var right = AngleDegrees.Right;        // 90 degrees
var straight = AngleDegrees.Straight;  // 180 degrees
var full = AngleDegrees.Full;          // 360 degrees

var zero = AngleRadians.Zero;          // 0 radians
var right = AngleRadians.Right;        // PI/2 radians
var straight = AngleRadians.Straight;  // PI radians
var full = AngleRadians.Full;          // 2 * PI radians

Converting the angle:

Use the static methods to convert any angle:

var radians = Angle.ToRadians(angle);

Angles are strongly typed so it knows what measuring unit is converting from.

Note: If required, the results have to be explicitly reduced.

Reading the angle:

Use the property named after the measuring unit (to be explicit):

var radians = angleRadians.Radians;
var degrees = angleDegrees.Degrees;
var gradians = angleGradians.Gradians;

An angle in degrees can be deconstructed into DMS notation. This can be done using either out arguments:

int degrees0;
double minute0;
angleDegrees.Deconstruct(out degrees0, out minutes0);

int degrees1;
int minute1;
double seconds1;
angleDegrees.Deconstruct(out degrees1, out minutes1, out seconds1);

out arguments with C# 7 syntax:

angleDegrees.Deconstruct(out var degrees0, out var minutes0);
angleDegrees.Deconstruct(out var degrees1, out var minutes1, out var seconds1);

or using C# 7 deconstructors:

var (degrees0, minutes0) = angleDegrees;
var (degrees1, minutes1, seconds1) = angleDegrees;

Reduction and reference

The angle can be reduced to a coterminal angle in the range [0.0, 360.0[ degrees: ​

var angle = Angle.Reduce(AngleDegrees.Right + AngleDegrees.Full); // result is AngleDegrees.Right

Getting the reference angle (the smallest angle with the x-axis):

var angle = Angle.GetReference(AngleDegrees.Right + AngleDegrees.FromDegrees(45.0)); // result is an angle with 45 degrees

Math operations

Math operators are defined allowing calculations with angles. ​

var angle0 = -AngleDegrees.Right;
var angle1 = AngleDegrees.Straight + Angle.FromDegrees(45.0);
var angle2 = 2.0 * Angle.FromDegrees(30.0);
var angle3 = Angle.FromDegrees(30.0) / 2.0;

Note: If required, the results have to be explicitly reduced.

Equivalent methods are also defined so they can be used for languages that do not support operators.

var angle0 = Angle.Negate(AngleDegrees.Right);
var angle1 = Angle.Add(AngleDegrees.Straight, Angle.FromDegrees(45.0));
var angle2 = Angle.Multiply(2.0, Angle.FromDegrees(30.0));
var angle3 = Angle.Divide(Angle.FromDegrees(30.0), 2.0);

Comparison

Comparison operatores can be used to compare two angles: ​

if(angle0 > angle1 || angle0 == angle2) {
    ...
}

For languages that do not support operators use the static Compare() method: ​

if(Angle.Compare(angle0, angle1) <= 0) { // less or equal to
    ...
}

For performance reasons, the values compared are not reduced. If required, they have to be explicitly reduced: ​

if(Angle.Reduce(angle0) > Angle.Reduce(angle1)) {
    ...
}

or use the static CompareReduced() method:

if(Angle.CompareReduced(angle0, angle1) > 0) {
    ...
}

Trigonometry

The usual trigonometry operations (sin, cos, tan, asin, acos, atan, sinh and cosh) are available as static methods but only for angles in radians:

double value0 = Angle.Sin(angleRadians);
AngleRadians angle0 = Angle.Asin(value0);

Angles not in radians have to be converted:

double value1 = Angle.Sin(Angle.ToRadians(angleDegrees));
AngleDegrees angle1 = Angle.ToDegrees(Angle.Asin(value1));

Classification

You can get the quadrante of the angle

var quad0 = Angle.GetQuadrant(Angle.FromDegrees(45.0)); // Angle.Quadrant.First
var quad1 = Angle.GetQuadrant(Angle.FromDegrees(220.0)); // Angle.Quadrant.Third
var quad2 = Angle.GetQuadrant(Angle.FromDegrees(-45.0)); // Angle.Quadrant.Fourth

and can check if an angle is acute, right, obtuse, straight or reflex:

var isAcute = Angle.IsAcute(AngleDegrees.Right); // false
var isAcute = Angle.IsAcute(Angle.FromDegrees(45.0)); // true
var isRight = Angle.IsRight(AngleDegrees.Right); // true

Classification considers the reduced positive equivalent of the angle so:

var isAcute = Angle.IsAcute(Angle.FromDegrees(45.0)); // true
var isAcute = Angle.IsAcute(Angle.FromDegrees(-45.0)); // true
var isAcute = Angle.IsAcute(Angle.FromDegrees(315.0)); // false