Trigonometric

Full name Microsoft.VisualBasic.Math.Trigonometric Assembly Microsoft.VisualBasic.Runtime Members 34

三角函数拓展模块

01 Syntax

Microsoft.VisualBasic.Math.Trigonometric

02 Methods

Name	Overloads	Summary
Atn	1	Taylor Atan
ToCartesianPoint	1	Polar to cartesian coordinate system point.(将极坐标转换为笛卡尔坐标系直角坐标系)
GetAngleVector	1
Angle	1	计算结果为角度
Distance	2	Calculate the Euclidean distance between two points.
GetAngle	2	计算两个点之间的线段的夹角
MovePoint	1	以当前的点为圆心，向angle方向移动给定的距离
ToRadians	1	Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
ToDegrees	1	Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
Sec	1	Secant（正割） Sec(X) = 1 / Cos(X)
Cosec	1	Cosecant（余割） Cosec(X) = 1 / Sin(X)
Cotan	1	Cotangent（余切） Cotan(X) = 1 / Tan(X)
Arcsin	1	Inverse Sine（反正弦） Arcsin(X) = Atn(X / Sqr(-X * X + 1))
Arccos	1	Inverse Cosine（反余弦） Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)
Arcsec	1	Inverse Secant（反正割） Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) - 1) * (2 * Atn(1))
Arccosec	1	Inverse Cosecant（反余割） Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))
Arccotan	1	Inverse Cotangent（反余切） Arccotan(X) = Atn(X) + 2 * Atn(1)
HSin	1	Hyperbolic Sine（双曲正弦） HSin(X) = (Exp(X) - Exp(-X)) / 2
HCos	1	Hyperbolic Cosine（双曲余弦） HCos(X) = (Exp(X) + Exp(-X)) / 2
HTan	1	Hyperbolic Tangent（双曲正切） HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
HSec	1	Hyperbolic Secant（双曲正割） HSec(X) = 2 / (Exp(X) + Exp(-X))
HCosec	1	Hyperbolic Cosecant（双曲余割） HCosec(X) = 2 / (Exp(X) - Exp(-X))
HCotan	1	Hyperbolic Cotangent（双曲余切） HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
HArcsin	1	Inverse Hyperbolic Sine（反双曲正弦） HArcsin(X) = Log(X + Sqr(X * X + 1))
HArccos	1	Inverse Hyperbolic Cosine（反双曲余弦） HArccos(X) = Log(X + Sqr(X * X - 1))
Harctan	1	Inverse Hyperbolic Tangent（反双曲正切） HArctan(X) = Log((1 + X) / (1 - X)) / 2
HArcsec	1	Inverse Hyperbolic Secant（反双曲正割） HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
HArccosec	1	Inverse Hyperbolic Cosecant（反双曲余割） HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)
HArccotan	1	Inverse Hyperbolic Cotangent（反双曲余切） HArccotan(X) = Log((X + 1) / (X - 1)) / 2
NearestPoint	1

03 Fields

Name	Overloads	Summary
AtanPrecise	2	通过这个参数来控制计算精度，这个参数值越大，计算精度越高

04 Members

method Atn #

Atn(Double)

Taylor Atan

Remarks

Atan测试没有问题

Parameters

Name	Type	Description
`x`	`Double`	-

method ToCartesianPoint #

ToCartesianPoint(ValueTuple(Of Double, Single), Boolean, Double, Double)

Polar to cartesian coordinate system point.(将极坐标转换为笛卡尔坐标系直角坐标系)

Parameters

Name	Type	Description
`polar`	`ValueTuple(Of Double, Single)`	(半径, 角度)
`fromDegree`	`Boolean`	alpha角度参数是否是度为单位，默认是真，即函数会在这里自动转换为弧度

method GetAngleVector #

GetAngleVector(Single, Double)

Parameters

Name	Type	Description
`radian`	`Single`	`0 -> 2*[Math.PI](cref:F:System.Math.PI)`

method Angle #

Angle(PointF)

计算结果为角度

Parameters

Name	Type	Description
`p`	`PointF`	-

method Distance #

Distance(Point, Point)

Calculate the Euclidean distance between two points.

Parameters

Name	Type	Description
`a`	`Point`	-
`b`	`Point`	-

method Distance overload 2 #

Distance(PointF, PointF)

Calculate the Euclidean distance between two points.

Parameters

Name	Type	Description
`a`	`PointF`	-
`b`	`PointF`	-

method GetAngle #

GetAngle(Point, Point)

计算两个点之间的线段的夹角

Parameters

Name	Type	Description
`p1`	`Point`	-
`p2`	`Point`	-

method MovePoint #

MovePoint(PointF, Double, Int32)

以当前的点为圆心，向angle方向移动给定的距离

Parameters

Name	Type	Description
`distance#`	`PointF`	-
`angle#`	`Double`	-

method ToRadians #

ToRadians(Double)

Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.

Parameters

Name	Type	Description
`angdeg`	`Double`	an angle, in degrees

Returns

the measurement of the angle {@code angdeg} in radians. @since 1.2

method ToDegrees #

ToDegrees(Double)

Converts an angle measured in radians to an approximately equivalent angle measured in degrees. The conversion from radians to degrees is generally inexact; users should not expect {@code cos(toRadians(90.0))} to exactly equal {@code 0.0}.

Parameters

Name	Type	Description
`angrad`	`Double`	an angle, in radians

Returns

the measurement of the angle {@code angrad} in degrees. @since 1.2

method Sec #

Sec(Double)

Secant（正割） Sec(X) = 1 / Cos(X)

Parameters

Name	Type	Description
`x`	`Double`	-

method Cosec #

Cosec(Double)

Cosecant（余割） Cosec(X) = 1 / Sin(X)

Parameters

Name	Type	Description
`x`	`Double`	-

method Cotan #

Cotan(Double)

Cotangent（余切） Cotan(X) = 1 / Tan(X)

Parameters

Name	Type	Description
`x`	`Double`	-

method Arcsin #

Arcsin(Double)

Inverse Sine（反正弦） Arcsin(X) = Atn(X / Sqr(-X * X + 1))

Parameters

Name	Type	Description
`x`	`Double`	-

method Arccos #

Arccos(Double)

Inverse Cosine（反余弦） Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)

Parameters

Name	Type	Description
`x`	`Double`	-

method Arcsec #

Arcsec(Double)

Inverse Secant（反正割） Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) - 1) * (2 * Atn(1))

Parameters

Name	Type	Description
`x`	`Double`	-

method Arccosec #

Arccosec(Double)

Inverse Cosecant（反余割） Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))

Parameters

Name	Type	Description
`x`	`Double`	-

method Arccotan #

Arccotan(Double)

Inverse Cotangent（反余切） Arccotan(X) = Atn(X) + 2 * Atn(1)

Parameters

Name	Type	Description
`x`	`Double`	-

method HSin #

HSin(Double)

Hyperbolic Sine（双曲正弦） HSin(X) = (Exp(X) - Exp(-X)) / 2

Parameters

Name	Type	Description
`x`	`Double`	-

method HCos #

HCos(Double)

Hyperbolic Cosine（双曲余弦） HCos(X) = (Exp(X) + Exp(-X)) / 2

Parameters

Name	Type	Description
`x`	`Double`	-

method HTan #

HTan(Double)

Hyperbolic Tangent（双曲正切） HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))

Parameters

Name	Type	Description
`x`	`Double`	-

method HSec #

HSec(Double)

Hyperbolic Secant（双曲正割） HSec(X) = 2 / (Exp(X) + Exp(-X))

Parameters

Name	Type	Description
`x`	`Double`	-

method HCosec #

HCosec(Double)

Hyperbolic Cosecant（双曲余割） HCosec(X) = 2 / (Exp(X) - Exp(-X))

Parameters

Name	Type	Description
`x`	`Double`	-

method HCotan #

HCotan(Double)

Hyperbolic Cotangent（双曲余切） HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))

Parameters

Name	Type	Description
`x`	`Double`	-

method HArcsin #

HArcsin(Double)

Inverse Hyperbolic Sine（反双曲正弦） HArcsin(X) = Log(X + Sqr(X * X + 1))

Parameters

Name	Type	Description
`x`	`Double`	-

method HArccos #

HArccos(Double)

Inverse Hyperbolic Cosine（反双曲余弦） HArccos(X) = Log(X + Sqr(X * X - 1))

Parameters

Name	Type	Description
`x`	`Double`	-

method Harctan #

Harctan(Double)

Inverse Hyperbolic Tangent（反双曲正切） HArctan(X) = Log((1 + X) / (1 - X)) / 2

Parameters

Name	Type	Description
`x`	`Double`	-

method HArcsec #

HArcsec(Double)

Inverse Hyperbolic Secant（反双曲正割） HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)

Parameters

Name	Type	Description
`x`	`Double`	-

method HArccosec #

HArccosec(Double)

Inverse Hyperbolic Cosecant（反双曲余割） HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)

Parameters

Name	Type	Description
`x`	`Double`	-

method HArccotan #

HArccotan(Double)

Inverse Hyperbolic Cotangent（反双曲余切） HArccotan(X) = Log((X + 1) / (X - 1)) / 2

Parameters

Name	Type	Description
`x`	`Double`	-

field AtanPrecise #

AtanPrecise

通过这个参数来控制计算精度，这个参数值越大，计算精度越高

field AtanPrecise overload 2 #

AtanPrecise

method GetAngle overload 2 #

GetAngle(Single, Single, Single, Single)

method NearestPoint #

NearestPoint(IEnumerable(Of Point), Int32, Int32, Double)