Functionals | Physics Math

Functions that know their type and units, and can display themselves meaningfully.

Each PFFunction object has a corresponding function object and vice versa.

Index

Enumerations

TYPE

Other Type aliases

Value type Type aliases

Variables

Other Type aliases

BaseValue

BaseValue: BaseValueRelative | BaseValueInFrame

BaseValueInFrame

BaseValueInFrame: Point | Orientation

BaseValueNonScalar

BaseValueNonScalar: Point | Vector | Orientation | Rotation

BaseValueRelative

BaseValueRelative: ScalarValue | Vector | Rotation

BaseValueRelativeNonScalar

BaseValueRelativeNonScalar: Vector | Rotation

Constructor3N

Constructor3N<R>: Constructor<R, [number, number, number]>

Type parameters

Constructor4N

Constructor4N<R>: Constructor<R, [number, number, number, number]>

Type parameters

DataTypeOf

DataTypeOf<D>: D extends number ? SCALAR : D extends DataType<infer T> ? T : never

Type parameters

IPCompileResult

IPCompileResult<R, N>:

The result of compilation is a function of N arguments, annotated with originating PFunction and convenience methods.

Type parameters

R: BaseValue
N: ArgCount

IPCompiled

IPCompiled<R, U, N, P>: IPFunctionPtr<P> & IPCompiledDisplay

Type parameters

R: BaseValue
U: Unit
N: ArgCount
P: IPFunction<R, U, N>

IPFunction

IPFunction<R, U, N, D, I>: N extends 1 ? R extends number ? IPFunctionCalculus<number, U, N, D, I> : R extends Rotation ? IPFunctionCalculus<Rotation, U, N, D, I> : R extends Vector ? IPFunctionCalculus<Vector, U, N, D, I> : R extends Point ? IPFunctionBase<Point, U, N> : R extends Orientation ? IPFunctionBase<Orientation, U, N> : never : IPFunctionBase<R, U, N>

Type parameters

R: BaseValue
U: Unit
N: ArgCount
D: Unit
I: Unit

InFrameOf

InFrameOf<T>: T extends Vector ? Point : T extends Rotation ? Orientation : T

Type parameters

Positional

Positional: Point | Vector

RelativeOf

RelativeOf<T>: T extends Point ? Vector : T extends Orientation ? Rotation : T

Type parameters

Rotational

Rotational: Orientation | Rotation

ScalarValue

ScalarValue: number

Our primitive datatypes

TVPairs

TVPairs<R, C, D, I>: [number, IPCalculus<R, C, D, I>, Object]

Type parameters

TexFormatter

TexFormatter: (tex: string) => Element

Hook to provide a compatible LaTeX parser, such as an existing KaTeX implementation, such as provided by ObservableHQ.

Type declaration

- (tex: string): Element
- Parameters
  - tex: string
  Returns Element

Value type Type aliases

Time

Time: Value<number, time>

Velocity

Velocity: Value<Vector, velocity>

Variables

Const PFunctionDefaults

PFunctionDefaults: [Omit<PFunctionOpts<Unit, 0>, "unit">, Omit<PFunctionOpts<Unit>, "unit">, Omit<PFunctionOpts<Unit, 2>, "unit">, Omit<PFunctionOpts<Unit, 3>, "unit">, Omit<PFunctionOpts<Unit, 4>, "unit">, Omit<PFunctionOpts<Unit, 5>, "unit">, Omit<PFunctionOpts<Unit, 6>, "unit">] = [{vars: [], nargs: 0},{vars: ['t'], nargs: 1},{vars: ['t0', 't'], nargs: 2},{vars: ['t1', 't0', 't'], nargs: 3},{vars: ['t2', 't1', 't0', 't'], nargs: 4},{vars: ['t3', 't2', 't1', 't0', 't'], nargs: 5},{vars: ['t4', 't3', 't2', 't1', 't0', 't'], nargs: 6}]

Let TIMESTEP

TIMESTEP: number = 0.001

Default integration timestep. This can be adjusted per-function.

Functions

add

add<R>(a: R, ...rest: R[]): R
add<R>(a: R, ...rest: RelativeOf<R>[]): R
add<R>(a: IPCompiled<R>, ...rest: IPCompiled<R>[]): IPCompiled<R>
add<R>(a: IPCompiled<R>, ...rest: IPCompiled<RelativeOf<R>>[]): IPCompiled<R>
add<R>(a: IPCompiled<R>, ...rest: IPCompiled<Vector>[]): IPCompiled<R>
add<R>(a: IPCompiled<R>, ...rest: IPCompiled<Rotation>[]): IPCompiled<R>
add<R>(a: IPFunction<R>, ...rest: IPFunction<BaseValueRelative>[]): IPFunction<R>
add<R>(a: IPFunction<R>, ...rest: IPFunction<Vector>[]): IPFunction<R>
add<R>(a: IPFunction<R>, ...rest: IPFunction<Rotation>[]): IPFunction<R>

- Defined in src/arith.ts:38
Add two BaseValue quantities or BaseValue-valued functions together.

Type parameters
- R: BaseValueRelative
Parameters
- a: R
- Rest ...rest: R[]
Returns R
- Defined in src/arith.ts:39
Type parameters
- R: BaseValueInFrame
Parameters
- a: R
- Rest ...rest: RelativeOf<R>[]
Returns R
- Defined in src/arith.ts:40
Type parameters
- R: BaseValueRelative
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<R>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:41
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<RelativeOf<R>>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:42
Type parameters
- R: Point | Vector
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<Vector>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:43
Type parameters
- R: Orientation | Rotation
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<Rotation>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:44
Type parameters
- R: number
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<BaseValueRelative>[]
Returns IPFunction<R>
- Defined in src/arith.ts:45
Type parameters
- R: Point | Vector
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<Vector>[]
Returns IPFunction<R>
- Defined in src/arith.ts:46
Type parameters
- R: Orientation | Rotation
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<Rotation>[]
Returns IPFunction<R>

Const bounds

bounds<R>(f: IPCompiled<R>, t: number): [R, R, number]

- Defined in src/derivative.ts:22
Type parameters
- R: BaseValue
Parameters
- f: IPCompiled<R>
- t: number
Returns [R, R, number]

constant

constant<T, U>(v: T | IPFunction<T, U> | Value<T, U> | IConstant<T, U>, unit: U): IConstant<T, U>
constant<T, U>(v: T | IPFunction<T, U> | Value<T, U> | IConstantInFrame<T, U>, unit: U): IConstantInFrame<T, U>

- Defined in src/scalar.ts:110
Get an IConstant from a value or a function at T=0;

Type parameters
- T: BaseValueRelative
- U: Unit
Parameters
- v: T | IPFunction<T, U> | Value<T, U> | IConstant<T, U>
  
  A value, a PFunction, or a Value.
- unit: U
  
  a Unit describing the type of constant.
Returns IConstant<T, U>
- Defined in src/scalar.ts:113
Type parameters
- T: BaseValueInFrame
- U: Unit
Parameters
- v: T | IPFunction<T, U> | Value<T, U> | IConstantInFrame<T, U>
- unit: U
Returns IConstantInFrame<T, U>

Const datatype

datatype(d: any): TYPE

- Defined in src/math-types.ts:36
Parameters
- d: any
Returns TYPE

equal

equal<T>(a: T, b: T): boolean

- Defined in src/arith.ts:386
Type parameters
- T: BaseValue
Parameters
- a: T
- b: T
Returns boolean

Const integrate

integrate(f: IPCompiled<number>): (Anonymous function)

- Defined in src/integral.ts:174
Parameters
- f: IPCompiled<number>
Returns (Anonymous function)

Const isBaseValue

isBaseValue(v: any): v is BaseValue

- Defined in src/math-types.ts:508
Parameters
- v: any
Returns v is BaseValue

isIntrinsic

isIntrinsic(v: IPFunction): v is IPFunction<BaseValueInFrame>
isIntrinsic(v: IPCompiled): v is IPCompiled<BaseValueInFrame>
isIntrinsic(v: number): false
isIntrinsic(v: Positional): v is Point
isIntrinsic(v: Rotational): v is Orientation
isIntrinsic(v: BaseValue): v is BaseValueInFrame

- Defined in src/math-types.ts:571
Parameters
- v: IPFunction
Returns v is IPFunction<BaseValueInFrame>
- Defined in src/math-types.ts:572
Parameters
- v: IPCompiled
Returns v is IPCompiled<BaseValueInFrame>
- Defined in src/math-types.ts:573
Parameters
- v: number
Returns false
- Defined in src/math-types.ts:574
Parameters
- v: Positional
Returns v is Point
- Defined in src/math-types.ts:575
Parameters
- v: Rotational
Returns v is Orientation
- Defined in src/math-types.ts:576
Parameters
- v: BaseValue
Returns v is BaseValueInFrame

Const isIntrinsicValue

isIntrinsicValue(v: any): v is BaseValueInFrame

- Defined in src/math-types.ts:529
Parameters
- v: any
Returns v is BaseValueInFrame

Const isNonScalarValue

isNonScalarValue(v: any): v is NonScalarValue

- Defined in src/math-types.ts:533
Parameters
- v: any
Returns v is NonScalarValue

Const isOrientation

isOrientation(v: any): v is Orientation

- Defined in src/math-types.ts:526
Parameters
- v: any
Returns v is Orientation

isPCompiled

isPCompiled<U, N>(a: any, u: U, n: N): a is IPCompiled<BaseValue, U, N>
isPCompiled(a: any): a is IPCompiled<BaseValue, Unit, ArgCount>

- Defined in src/pfunction.ts:226
Type parameters
- U: Unit
- N: ArgCount
Parameters
- a: any
- u: U
- n: N
Returns a is IPCompiled<BaseValue, U, N>
- Defined in src/pfunction.ts:227
Parameters
- a: any
Returns a is IPCompiled<BaseValue, Unit, ArgCount>

isPFunction

isPFunction<U, N>(a: any, u: U, n: N): a is IPFunction<BaseValue, U, N>
isPFunction(a: any): a is IPFunction

- Defined in src/pfunction.ts:218
Type parameters
- U: Unit
- N: ArgCount
Parameters
- a: any
- u: U
- n: N
Returns a is IPFunction<BaseValue, U, N>
- Defined in src/pfunction.ts:219
Parameters
- a: any
Returns a is IPFunction

Const isPoint

isPoint(v: any): v is Point

- Defined in src/math-types.ts:523
Parameters
- v: any
Returns v is Point

Const isPositional

isPositional(v: any): v is Positional

- Defined in src/math-types.ts:522
Parameters
- v: any
Returns v is Positional

isRelative

isRelative(v: IPFunction): v is IPFunction<BaseValueRelative>
isRelative(v: IPCompiled): v is IPCompiled<BaseValueRelative>
isRelative(v: number): v is number
isRelative(v: Positional): v is Vector
isRelative(v: Rotational): v is Orientation
isRelative(v: BaseValue): v is BaseValueRelative

- Defined in src/math-types.ts:548
Parameters
- v: IPFunction
Returns v is IPFunction<BaseValueRelative>
- Defined in src/math-types.ts:549
Parameters
- v: IPCompiled
Returns v is IPCompiled<BaseValueRelative>
- Defined in src/math-types.ts:550
Parameters
- v: number
Returns v is number
- Defined in src/math-types.ts:551
Parameters
- v: Positional
Returns v is Vector
- Defined in src/math-types.ts:552
Parameters
- v: Rotational
Returns v is Orientation
- Defined in src/math-types.ts:553
Parameters
- v: BaseValue
Returns v is BaseValueRelative

Const isRotation

isRotation(v: any): v is Rotation

- Defined in src/math-types.ts:527
Parameters
- v: any
Returns v is Rotation

Const isRotational

isRotational(v: any): v is Rotational

- Defined in src/math-types.ts:525
Parameters
- v: any
Returns v is Rotational

isScalar

isScalar(v: IPFunction): v is IPFunction<number>
isScalar(v: IPCompiled): v is IPCompiled<number>
isScalar(v: number): v is number
isScalar(v: Positional): false
isScalar(v: Rotational): false
isScalar(v: BaseValue): v is number

- Defined in src/math-types.ts:594
Parameters
- v: IPFunction
Returns v is IPFunction<number>
- Defined in src/math-types.ts:595
Parameters
- v: IPCompiled
Returns v is IPCompiled<number>
- Defined in src/math-types.ts:596
Parameters
- v: number
Returns v is number
- Defined in src/math-types.ts:597
Parameters
- v: Positional
Returns false
- Defined in src/math-types.ts:598
Parameters
- v: Rotational
Returns false
- Defined in src/math-types.ts:599
Parameters
- v: BaseValue
Returns v is number

Const isScalarValue

isScalarValue(v: any): v is ScalarValue

- Defined in src/math-types.ts:531
Parameters
- v: any
Returns v is ScalarValue

Const isVector

isVector(v: any): v is Vector

- Defined in src/math-types.ts:524
Parameters
- v: any
Returns v is Vector

Const makeDerivative

makeDerivative(f: IPCompiled<number>): (Anonymous function)

- Defined in src/derivative.ts:35
Calculate the derivative of a function numerically, by examining nearby values on either side of the point. Points that are technically no-differentiable (such as where piecewise-define segments meet) are computed as an average.

Parameters
- f: IPCompiled<number>
Returns (Anonymous function)

Const makeDerivativeQ

makeDerivativeQ(f: IPCompiled<Rotation>): (Anonymous function)

- Defined in src/derivative.ts:115
Parameters
- f: IPCompiled<Rotation>
Returns (Anonymous function)

Const makeDerivativeV

makeDerivativeV(f: IPCompiled<Point | Vector>): (Anonymous function)

- Defined in src/derivative.ts:81
Parameters
- f: IPCompiled<Point | Vector>
Returns (Anonymous function)

Const makePoly

makePoly(...coeffs: number[]): (Anonymous function)

- Defined in src/poly.ts:138
Parameters
- Rest ...coeffs: number[]
Returns (Anonymous function)

mul

mul<R>(a: R, ...rest: number[]): R
mul<R>(a: IPCompiled<R>, ...rest: (number | (IPCompileResult1<number> & IPFunctionPtr<IPFunctionCalculus<number, Unit<{}>, 1, Unit<{}>, Unit<{}>>> & IPCompiledDisplay))[]): IPCompiled<R>
mul<R>(a: IPFunction<R>, ...rest: (number | IPFunctionCalculus<number, Unit<{}>, 1, Unit<{}>, Unit<{}>>)[]): IPFunction<R>

- Defined in src/arith.ts:311
Type parameters
- R: BaseValueRelative
Parameters
- a: R
- Rest ...rest: number[]
Returns R
- Defined in src/arith.ts:312
Type parameters
- R: BaseValueRelative
Parameters
- a: IPCompiled<R>
- Rest ...rest: (number | (IPCompileResult1<number> & IPFunctionPtr<IPFunctionCalculus<number, Unit<{}>, 1, Unit<{}>, Unit<{}>>> & IPCompiledDisplay))[]
Returns IPCompiled<R>
- Defined in src/arith.ts:313
Type parameters
- R: BaseValueRelative
Parameters
- a: IPFunction<R>
- Rest ...rest: (number | IPFunctionCalculus<number, Unit<{}>, 1, Unit<{}>, Unit<{}>>)[]
Returns IPFunction<R>

near

near<T>(a: T, b: T, epsilon?: number): boolean

- Defined in src/arith.ts:394
Type parameters
- T: BaseValue
Parameters
- a: T
- b: T
- Default value epsilon: number = glMatrix.EPSILON
Returns boolean

Const orientation

orientation(frame: InertialFrame, i?: number, j?: number, k?: number, w?: number): Orientation

- Defined in src/math-types.ts:544
Parameters
- frame: InertialFrame
- Default value i: number = 0
- Default value j: number = 0
- Default value k: number = 0
- Default value w: number = 1
Returns Orientation

Const point

point(frame: InertialFrame, x?: number, y?: number, z?: number): Point

- Defined in src/math-types.ts:537
Parameters
- frame: InertialFrame
- Default value x: number = 0
- Default value y: number = 0
- Default value z: number = 0
Returns Point

Const rotation

rotation(i?: number, j?: number, k?: number, w?: number): Rotation

- Defined in src/math-types.ts:541
Parameters
- Default value i: number = 0
- Default value j: number = 0
- Default value k: number = 0
- Default value w: number = 1
Returns Rotation

Const setFormatter

setFormatter(inline: TexFormatter, block?: TexFormatter): { block: (tex: string) => Element; inline: (tex: string) => Element }

- Defined in src/base.ts:50
Set the converter to convert LaTeX to HTML. This csn be ObservableHQ's tex... string interpolator—the argument will be set up properly.

Parameters
- inline: TexFormatter
- Default value block: TexFormatter = (inline as any).block || inline
Returns { block: (tex: string) => Element; inline: (tex: string) => Element }
- block: (tex: string) => Element
  - - (tex: string): Element
    - Parameters
      - tex: string
      Returns Element
- inline: (tex: string) => Element
  - - (tex: string): Element
    - Parameters
      - tex: string
      Returns Element

sub

sub<R>(a: R, ...rest: RelativeOf<R>[]): R
sub<R>(a: R, b: R): RelativeOf<R>
sub<R>(a: R, ...b: R[]): R
sub<R>(a: IPCompiled<R>, ...rest: IPCompiled<RelativeOf<R>>[]): IPCompiled<R>
sub<R>(a: IPCompiled<R>, b: IPCompiled<R>): IPCompiled<RelativeOf<R>>
sub<R>(a: IPCompiled<R>, ...b: IPCompiled<R>[]): IPCompiled<R>
sub<R>(a: IPFunction<R>, ...rest: IPFunction<RelativeOf<R>>[]): IPFunction<R>
sub<R>(a: IPFunction<R>, b: IPFunction<R>): IPFunction<RelativeOf<R>>
sub<R>(a: IPFunction<R>, ...b: IPFunction<R>[]): IPFunction<R>

- Defined in src/arith.ts:207
Multiply a number, Vector, or Rotation by 0 or more scalar values. Works on individual values, or PFFunction or IPFunction's. (You cannot mix levels, however).

Returns the same type as the first argument.

Type parameters
- R: BaseValueInFrame
Parameters
- a: R
- Rest ...rest: RelativeOf<R>[]
Returns R
- Defined in src/arith.ts:208
Type parameters
- R: BaseValueInFrame
Parameters
- a: R
- b: R
Returns RelativeOf<R>
- Defined in src/arith.ts:209
Type parameters
- R: BaseValueRelative
Parameters
- a: R
- Rest ...b: R[]
Returns R
- Defined in src/arith.ts:211
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<RelativeOf<R>>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:212
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPCompiled<R>
- b: IPCompiled<R>
Returns IPCompiled<RelativeOf<R>>
- Defined in src/arith.ts:213
Type parameters
- R: BaseValueRelative
Parameters
- a: IPCompiled<R>
- Rest ...b: IPCompiled<R>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:215
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<RelativeOf<R>>[]
Returns IPFunction<R>
- Defined in src/arith.ts:216
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPFunction<R>
- b: IPFunction<R>
Returns IPFunction<RelativeOf<R>>
- Defined in src/arith.ts:217
Type parameters
- R: BaseValueRelative
Parameters
- a: IPFunction<R>
- Rest ...b: IPFunction<R>[]
Returns IPFunction<R>

Const valueType

valueType(v: any): TYPE

- Defined in src/math-types.ts:509
Parameters
- v: any
Returns TYPE

Const vector

vector(x?: number, y?: number, z?: number): Vector

- Defined in src/math-types.ts:535
Parameters
- Default value x: number = 0
- Default value y: number = 0
- Default value z: number = 0
Returns Vector

Index

Enumerations

Classes

Interfaces

Other Type aliases

Value type Type aliases

Variables

Functions

Other Type aliases

BaseValue

BaseValueInFrame

BaseValueNonScalar

BaseValueRelative

BaseValueRelativeNonScalar

Constructor3N

Type parameters

R

Constructor4N

Type parameters

R

DataTypeOf

Type parameters

D

IPCompileResult

Type parameters

R: BaseValue

N: ArgCount

IPCompiled

Type parameters

R: BaseValue

U: Unit

N: ArgCount

P: IPFunction<R, U, N>

IPFunction

Type parameters

R: BaseValue

U: Unit

N: ArgCount

D: Unit

I: Unit

InFrameOf

Type parameters

T

Positional

RelativeOf

Type parameters

T

Rotational

ScalarValue

TVPairs

Type parameters

R: BaseValueRelative

C: Unit

D: Unit

I: Unit

TexFormatter

Type declaration

Parameters

tex: string

Returns Element

Value type Type aliases

Time

Velocity

Variables

Const PFunctionDefaults

Let TIMESTEP

Functions

add

Type parameters

R: BaseValueRelative

Parameters

a: R

Rest ...rest: R[]

Returns R

Type parameters

R: BaseValueInFrame

Parameters

a: R

Rest ...rest: RelativeOf<R>[]

Returns R