Class MathHelper

Utility math functions and constants.

Inheritance

System.Object

MathHelper

Inherited Members

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

System.Object.ToString()

Namespace: netDxf

Assembly: CADability.dll

Syntax

public static class MathHelper

Fields

DegToGrad

Constant to transform an angle between degrees and gradians.

Declaration

public const double DegToGrad = 1.1111111111111112

Field Value

Type	Description
System.Double

DegToRad

Constant to transform an angle between degrees and radians.

Declaration

public const double DegToRad = 0.017453292519943295

Field Value

Type	Description
System.Double

GradToDeg

Constant to transform an angle between degrees and gradians.

Declaration

public const double GradToDeg = 0.9

Field Value

Type	Description
System.Double

HalfPI

PI/2 (90 degrees)

Declaration

public const double HalfPI = 1.5707963267948966

Field Value

Type	Description
System.Double

PI

PI (180 degrees)

Declaration

public const double PI = 3.1415926535897931

Field Value

Type	Description
System.Double

RadToDeg

Constant to transform an angle between degrees and radians.

Declaration

public const double RadToDeg = 57.295779513082323

Field Value

Type	Description
System.Double

ThreeHalfPI

3*PI/2 (270 degrees)

Declaration

public const double ThreeHalfPI = 4.71238898038469

Field Value

Type	Description
System.Double

TwoPI

2*PI (360 degrees)

Declaration

public const double TwoPI = 6.2831853071795862

Field Value

Type	Description
System.Double

Properties

Epsilon

Represents the smallest number used for comparison purposes.

Declaration

public static double Epsilon { get; set; }

Property Value

Type	Description
System.Double

Remarks

The epsilon value must be a positive number greater than zero.

Methods

ArbitraryAxis(Vector3)

Gets the rotation matrix from the normal vector (extrusion direction) of an entity.

Declaration

public static Matrix3 ArbitraryAxis(Vector3 zAxis)

Parameters

Type	Name	Description
Vector3	zAxis	Normal vector.

Returns

Type	Description
Matrix3	Rotation matrix.

FindIntersection(Vector2, Vector2, Vector2, Vector2)

Calculates the intersection point of two lines.

Declaration

public static Vector2 FindIntersection(Vector2 point0, Vector2 dir0, Vector2 point1, Vector2 dir1)

Parameters

Type	Name	Description
Vector2	point0	First line origin point.
Vector2	dir0	First line direction.
Vector2	point1	Second line origin point.
Vector2	dir1	Second line direction.

Returns

Type	Description
Vector2	The intersection point between the two lines.

Remarks

If the lines are parallel the method will return a NaN.

FindIntersection(Vector2, Vector2, Vector2, Vector2, Double)

Calculates the intersection point of two lines.

Declaration

public static Vector2 FindIntersection(Vector2 point0, Vector2 dir0, Vector2 point1, Vector2 dir1, double threshold)

Parameters

Type	Name	Description
Vector2	point0	First line origin point.
Vector2	dir0	First line direction.
Vector2	point1	Second line origin point.
Vector2	dir1	Second line direction.
System.Double	threshold	Tolerance.

Returns

Type	Description
Vector2	The intersection point between the two lines.

Remarks

If the lines are parallel the method will return a NaN.

IsEqual(Double, Double)

Checks if a number is equal to another.

Declaration

public static bool IsEqual(double a, double b)

Parameters

Type	Name	Description
System.Double	a	Double precision number.
System.Double	b	Double precision number.

Returns

Type	Description
System.Boolean	True if its close to one or false in any other case.

IsEqual(Double, Double, Double)

Checks if a number is equal to another.

Declaration

public static bool IsEqual(double a, double b, double threshold)

Parameters

Type	Name	Description
System.Double	a	Double precision number.
System.Double	b	Double precision number.
System.Double	threshold	Tolerance.

Returns

Type	Description
System.Boolean	True if its close to one or false in any other case.

IsOne(Double)

Checks if a number is close to one.

Declaration

public static bool IsOne(double number)

Parameters

Type	Name	Description
System.Double	number	Double precision number.

Returns

Type	Description
System.Boolean	True if its close to one or false in any other case.

IsOne(Double, Double)

Checks if a number is close to one.

Declaration

public static bool IsOne(double number, double threshold)

Parameters

Type	Name	Description
System.Double	number	Double precision number.
System.Double	threshold	Tolerance.

Returns

Type	Description
System.Boolean	True if its close to one or false in any other case.

IsZero(Double)

Checks if a number is close to zero.

Declaration

public static bool IsZero(double number)

Parameters

Type	Name	Description
System.Double	number	Double precision number.

Returns

Type	Description
System.Boolean	True if its close to one or false in any other case.

IsZero(Double, Double)

Checks if a number is close to zero.

Declaration

public static bool IsZero(double number, double threshold)

Parameters

Type	Name	Description
System.Double	number	Double precision number.
System.Double	threshold	Tolerance.

Returns

Type	Description
System.Boolean	True if its close to one or false in any other case.

NormalizeAngle(Double)

Normalizes the value of an angle in degrees between [0, 360[.

Declaration

public static double NormalizeAngle(double angle)

Parameters

Type	Name	Description
System.Double	angle	Angle in degrees.

Returns

Type	Description
System.Double	The equivalent angle in the range [0, 360[.

Remarks

Negative angles will be converted to its positive equivalent.

PointInSegment(Vector2, Vector2, Vector2)

Checks if a point is inside a line segment.

Declaration

public static int PointInSegment(Vector2 p, Vector2 start, Vector2 end)

Parameters

Type	Name	Description
Vector2	p	A point.
Vector2	start	Segment start point.
Vector2	end	Segment end point.

Returns

Type	Description
System.Int32	Zero if the point is inside the segment, 1 if the point is after the end point, and -1 if the point is before the start point.

Remarks

For testing purposes a point is considered inside a segment, if it falls inside the area from start to end of the segment that extends infinitely perpendicularly to its direction. Later, if needed, you can use the PointLineDistance method, if the distance is zero the point is along the line defined by the start and end points.

PointInSegment(Vector3, Vector3, Vector3)

Checks if a point is inside a line segment.

Declaration

public static int PointInSegment(Vector3 p, Vector3 start, Vector3 end)

Parameters

Type	Name	Description
Vector3	p	A point.
Vector3	start	Segment start point.
Vector3	end	Segment end point.

Returns

Type	Description
System.Int32	Zero if the point is inside the segment, 1 if the point is after the end point, and -1 if the point is before the start point.

Remarks

For testing purposes a point is considered inside a segment, if it falls inside the volume from start to end of the segment that extends infinitely perpendicularly to its direction. Later, if needed, you can use the PointLineDistance method, if the distance is zero the point is along the line defined by the start and end points.

PointLineDistance(Vector2, Vector2, Vector2)

Calculates the minimum distance between a point and a line.

Declaration

public static double PointLineDistance(Vector2 p, Vector2 origin, Vector2 dir)

Parameters

Type	Name	Description
Vector2	p	A point.
Vector2	origin	Line origin point.
Vector2	dir	Line direction.

Returns

Type	Description
System.Double	The minimum distance between the point and the line.

PointLineDistance(Vector3, Vector3, Vector3)

Calculates the minimum distance between a point and a line.

Declaration

public static double PointLineDistance(Vector3 p, Vector3 origin, Vector3 dir)

Parameters

Type	Name	Description
Vector3	p	A point.
Vector3	origin	Line origin point.
Vector3	dir	Line direction.

Returns

Type	Description
System.Double	The minimum distance between the point and the line.

RotateAboutAxis(Vector3, Vector3, Double)

Rotate given vector of angle in radians about a specified axis.

Declaration

public static Vector3 RotateAboutAxis(Vector3 v, Vector3 axis, double angle)

Parameters

Type	Name	Description
Vector3	v	Vector to rotate.
Vector3	axis	Rotation axis. This vector should be normalized.
System.Double	angle	Rotation angle in radians.

Returns

Type	Description
Vector3	A copy of the vector, rotated.

Remarks

Method provided by: Idelana. Original Author: Paul Bourke ( http://paulbourke.net/geometry/rotate/ )

RoundToNearest(Double, Double)

Round off a numeric value to the nearest of another value.

Declaration

public static double RoundToNearest(double number, double roundTo)

Parameters

Type	Name	Description
System.Double	number	Number to round off.
System.Double	roundTo	The number will be rounded to the nearest of this value.

Returns

Type	Description
System.Double	The number rounded to the nearest value.

Sign(Double)

Returns a value indicating the sign of a double-precision floating-point number.

Declaration

public static int Sign(double number)

Parameters

Type	Name	Description
System.Double	number	Double precision number.

Returns

Type	Description
System.Int32	A number that indicates the sign of value. Return value Meaning -1 value is less than zero. 0 value is equal to zero. 1 value is greater than zero.

Remarks

This method will test for values of numbers very close to zero.

Sign(Double, Double)

Returns a value indicating the sign of a double-precision floating-point number.

Declaration

public static int Sign(double number, double threshold)

Parameters

Type	Name	Description
System.Double	number	Double precision number. Tolerance.
System.Double	threshold

Returns

Type	Description
System.Int32	A number that indicates the sign of value. Return value Meaning -1 value is less than zero. 0 value is equal to zero. 1 value is greater than zero.

Remarks

This method will test for values of numbers very close to zero.

Swap<T>(ref T, ref T)

Swaps two variables.

Declaration

public static void Swap<T>(ref T obj1, ref T obj2)

Parameters

Type	Name	Description
T	obj1	An object of type T.
T	obj2	An object of type T.

Type Parameters

Name	Description
T	Variable type.

Transform(Vector2, Double, CoordinateSystem, CoordinateSystem)

Transforms a point between coordinate systems.

Declaration

public static Vector2 Transform(Vector2 point, double rotation, CoordinateSystem from, CoordinateSystem to)

Parameters

Type	Name	Description
Vector2	point	Point to transform.
System.Double	rotation	Rotation angle in radians.
CoordinateSystem	from	Point coordinate system.
CoordinateSystem	to	Coordinate system of the transformed point.

Returns

Type	Description
Vector2	Transformed point.

Transform(Vector3, Vector3, CoordinateSystem, CoordinateSystem)

Transforms a point between coordinate systems.

Declaration

public static Vector3 Transform(Vector3 point, Vector3 zAxis, CoordinateSystem from, CoordinateSystem to)

Parameters

Type	Name	Description
Vector3	point	Point to transform.
Vector3	zAxis	Object normal vector.
CoordinateSystem	from	Point coordinate system.
CoordinateSystem	to	Coordinate system of the transformed point.

Returns

Type	Description
Vector3	Transformed point.

Transform(IEnumerable<Vector2>, Double, CoordinateSystem, CoordinateSystem)

Transforms a point list between coordinate systems.

Declaration

public static List<Vector2> Transform(IEnumerable<Vector2> points, double rotation, CoordinateSystem from, CoordinateSystem to)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<Vector2>	points	Point list to transform.
System.Double	rotation	Rotation angle in radians.
CoordinateSystem	from	Point coordinate system.
CoordinateSystem	to	Coordinate system of the transformed point.

Returns

Type	Description
System.Collections.Generic.List<Vector2>	Transformed point list.

Transform(IEnumerable<Vector3>, Vector3, CoordinateSystem, CoordinateSystem)

Transforms a point list between coordinate systems.

Declaration

public static List<Vector3> Transform(IEnumerable<Vector3> points, Vector3 zAxis, CoordinateSystem from, CoordinateSystem to)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<Vector3>	points	Points to transform.
Vector3	zAxis	Object normal vector.
CoordinateSystem	from	Points coordinate system.
CoordinateSystem	to	Coordinate system of the transformed points.

Returns

Type	Description
System.Collections.Generic.List<Vector3>	Transformed point list.