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

Interfaces

Other Type aliases

Value type Type aliases

Variables

Functions

Other Type aliases

BaseValue

BaseValue: number | BaseValueNonScalar

BaseValueInFrame

BaseValueInFrame: Point | Orientation

BaseValueNonScalar

BaseValueNonScalar: Point | Vector | Orientation | Rotation | NonScalarValue

BaseValueRelative

BaseValueRelative: ScalarValue | Vector | Rotation

Type parameters

U: Unit

BaseValueRelativeNonScalar

BaseValueRelativeNonScalar: Vector | Rotation

Type parameters

U: Unit

Constructor3N

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

Type parameters

Constructor4N

Constructor4N<R>: Constructor<R, [Unit, 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 & IPDisplay

Type parameters

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

IPFunction

IPFunction<R, U, N, D, I>: N extends 1 | 0 ? 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

Type parameters

U: Unit

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

Variable

Variable: string

Value type Type aliases

Time

Time: Value<number, time>

Velocity

Velocity: Value<Vector<velocity>, 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<U, 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<U, R>(a: R, ...rest: R[]): R
add<R>(a: R, ...rest: Rotation<angle>[]): R
add<U, R>(a: IPCompiled<R>, ...rest: IPCompiled<R>[]): 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<U, R>(a: IPFunction<R>, ...rest: IPFunction<R>[]): 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
- U: Unit
- R: Vector | Rotation
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
- U: Unit
- R: Rotation
Parameters
- a: R
- Rest ...rest: R[]
Returns R
- Defined in src/arith.ts:44
Type parameters
- R: Orientation
Parameters
- a: R
- Rest ...rest: Rotation<angle>[]
Returns R
- Defined in src/arith.ts:45
Type parameters
- U: Unit
- R: Rotation
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<R>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:46
Type parameters
- R: Orientation
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<Rotation>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:47
Type parameters
- R: number
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<BaseValueRelative>[]
Returns IPFunction<R>
- Defined in src/arith.ts:48
Type parameters
- R: Point | Vector
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<Vector>[]
Returns IPFunction<R>
- Defined in src/arith.ts:49
Type parameters
- U: Unit
- R: Rotation
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<R>[]
Returns IPFunction<R>
- Defined in src/arith.ts:50
Type parameters
- R: Orientation
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]

Const checkUnits

checkUnits(a: Value, b: Value): true | never

- Defined in src/math-types.ts:219
Parameters
- a: Value
- b: Value
Returns true | never

constant

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

- Defined in src/scalar.ts:89
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>
 
 A value, a PFunction, or a Value.
- unit: U
 
 a Unit describing the type of constant.
Returns Value<T, U>
- Defined in src/scalar.ts:92
Type parameters
- T: BaseValueInFrame
- U: Unit
Parameters
- v: T | IPFunction<T, U> | Value<T, U>
- unit: U
Returns Value<T, U>

Const datatype

datatype(d: any): TYPE

- Defined in src/math-types.ts:38
Parameters
- d: any
Returns TYPE

equal

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

- Defined in src/arith.ts:392
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:668
Parameters
- v: any
Returns v is BaseValue

Const isIntrinsicValue

isIntrinsicValue(v: any): v is BaseValueInFrame

- Defined in src/math-types.ts:687
Parameters
- v: any
Returns v is BaseValueInFrame

Const isNonScalarValue

isNonScalarValue(v: any): v is NonScalarValue

- Defined in src/math-types.ts:691
Parameters
- v: any
Returns v is NonScalarValue

Const isOrientation

isOrientation(v: any): v is Orientation

- Defined in src/math-types.ts:684
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:229
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:230
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:221
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:222
Parameters
- a: any
Returns a is IPFunction

Const isPoint

isPoint(v: any): v is Point

- Defined in src/math-types.ts:681
Parameters
- v: any
Returns v is Point

Const isPositional

isPositional(v: any): v is Positional

- Defined in src/math-types.ts:680
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:731
Parameters
- v: IPFunction
Returns v is IPFunction<BaseValueRelative>
- Defined in src/math-types.ts:732
Parameters
- v: IPCompiled
Returns v is IPCompiled<BaseValueRelative>
- Defined in src/math-types.ts:733
Parameters
- v: number
Returns v is number
- Defined in src/math-types.ts:734
Parameters
- v: Positional
Returns v is Vector
- Defined in src/math-types.ts:735
Parameters
- v: Rotational
Returns v is Orientation
- Defined in src/math-types.ts:736
Parameters
- v: BaseValue
Returns v is BaseValueRelative

Const isRotation

isRotation(v: any): v is Rotation

- Defined in src/math-types.ts:685
Parameters
- v: any
Returns v is Rotation

Const isRotational

isRotational(v: any): v is Rotational

- Defined in src/math-types.ts:683
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:754
Parameters
- v: IPFunction
Returns v is IPFunction<number>
- Defined in src/math-types.ts:755
Parameters
- v: IPCompiled
Returns v is IPCompiled<number>
- Defined in src/math-types.ts:756
Parameters
- v: number
Returns v is number
- Defined in src/math-types.ts:757
Parameters
- v: Positional
Returns false
- Defined in src/math-types.ts:758
Parameters
- v: Rotational
Returns false
- Defined in src/math-types.ts:759
Parameters
- v: BaseValue
Returns v is number

Const isScalarValue

isScalarValue(v: any): v is ScalarValue<Unit>

- Defined in src/math-types.ts:689
Parameters
- v: any
Returns v is ScalarValue<Unit>

Const isVector

isVector(v: any): v is Vector

- Defined in src/math-types.ts:682
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:111
Type parameters
- U: Unit
Parameters
- f: IPCompiled<Rotation>
Returns (Anonymous function)

Const makeDerivativeV

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

- Defined in src/derivative.ts:78
Type parameters
- U: Unit
Parameters
- f: IPCompiled<Vector | Point>
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<{}>>> & IPDisplay))[]): IPCompiled<R>
mul<R>(a: IPFunction<R>, ...rest: (number | IPFunctionCalculus<number, Unit<{}>, 1, Unit<{}>, Unit<{}>>)[]): IPFunction<R>

- Defined in src/arith.ts:316
Type parameters
- R: BaseValueRelative
Parameters
- a: R
- Rest ...rest: number[]
Returns R
- Defined in src/arith.ts:317
Type parameters
- R: BaseValueRelative
Parameters
- a: IPCompiled<R>
- Rest ...rest: (number | (IPCompileResult1<number> & IPFunctionPtr<IPFunctionCalculus<number, Unit<{}>, 1, Unit<{}>, Unit<{}>>> & IPDisplay))[]
Returns IPCompiled<R>
- Defined in src/arith.ts:318
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:400
Type parameters
- T: BaseValue
Parameters
- a: T
- b: T
- Default value epsilon: number = glMatrix.EPSILON
Returns boolean

orientation

orientation<F>(frame: F): (x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number) => Orientation
orientation<F>(frame: F, x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number): Orientation

- Defined in src/math-types.ts:722
Type parameters
- F: InertialFrame
Parameters
- frame: F
Returns (x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number) => Orientation
- - (x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number): Orientation
  - Parameters
    - Optional x: undefined | number
    - Optional y: undefined | number
    - Optional z: undefined | number
    - Optional w: undefined | number
    Returns Orientation
- Defined in src/math-types.ts:723
Type parameters
- F: InertialFrame
Parameters
- frame: F
- Optional x: undefined | number
- Optional y: undefined | number
- Optional z: undefined | number
- Optional w: undefined | number
Returns Orientation

point

point<F>(frame: F): (x?: undefined | number, y?: undefined | number, z?: undefined | number) => Point
point<F>(frame: F, x?: undefined | number, y?: undefined | number, z?: undefined | number): Point

- Defined in src/math-types.ts:702
Type parameters
- F: InertialFrame
Parameters
- frame: F
Returns (x?: undefined | number, y?: undefined | number, z?: undefined | number) => Point
- - (x?: undefined | number, y?: undefined | number, z?: undefined | number): Point
  - Parameters
    - Optional x: undefined | number
    - Optional y: undefined | number
    - Optional z: undefined | number
    Returns Point
- Defined in src/math-types.ts:703
Type parameters
- F: InertialFrame
Parameters
- frame: F
- Optional x: undefined | number
- Optional y: undefined | number
- Optional z: undefined | number
Returns Point

rotation

rotation(unit: U): (x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number) => Rotation
rotation(unit: U, x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number): Rotation

- Defined in src/math-types.ts:712
Type parameters
- U: Unit
Parameters
- unit: U
Returns (x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number) => Rotation
- - (x?: undefined | number, y?: undefined | number, z?: undefined | number, w?: undefined | number): Rotation
 - Parameters
 - Optional x: undefined | number
 - Optional y: undefined | number
 - Optional z: undefined | number
 - Optional w: undefined | number
 Returns Rotation
- Defined in src/math-types.ts:713
Type parameters
- U: Unit
Parameters
- unit: U
- Optional x: undefined | number
- Optional y: undefined | number
- Optional z: undefined | number
- Optional w: undefined | number
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:212
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:213
Type parameters
- R: BaseValueInFrame
Parameters
- a: R
- b: R
Returns RelativeOf<R>
- Defined in src/arith.ts:214
Type parameters
- R: BaseValueRelative
Parameters
- a: R
- Rest ...b: R[]
Returns R
- Defined in src/arith.ts:216
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPCompiled<R>
- Rest ...rest: IPCompiled<RelativeOf<R>>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:217
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPCompiled<R>
- b: IPCompiled<R>
Returns IPCompiled<RelativeOf<R>>
- Defined in src/arith.ts:218
Type parameters
- R: BaseValueRelative
Parameters
- a: IPCompiled<R>
- Rest ...b: IPCompiled<R>[]
Returns IPCompiled<R>
- Defined in src/arith.ts:220
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPFunction<R>
- Rest ...rest: IPFunction<RelativeOf<R>>[]
Returns IPFunction<R>
- Defined in src/arith.ts:221
Type parameters
- R: BaseValueInFrame
Parameters
- a: IPFunction<R>
- b: IPFunction<R>
Returns IPFunction<RelativeOf<R>>
- Defined in src/arith.ts:222
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:669
Parameters
- v: any
Returns TYPE

vector

vector(unit: U): (x?: undefined | number, y?: undefined | number, z?: undefined | number) => Vector
vector(unit: U, x?: undefined | number, y?: undefined | number, z?: undefined | number): Vector

- Defined in src/math-types.ts:693
Type parameters
- U: Unit
Parameters
- unit: U
Returns (x?: undefined | number, y?: undefined | number, z?: undefined | number) => Vector
- - (x?: undefined | number, y?: undefined | number, z?: undefined | number): Vector
 - Parameters
 - Optional x: undefined | number
 - Optional y: undefined | number
 - Optional z: undefined | number
 Returns Vector
- Defined in src/math-types.ts:694
Type parameters
- U: Unit
Parameters
- unit: U
- Optional x: undefined | number
- Optional y: undefined | number
- Optional z: undefined | number
Returns Vector

Index

Enumerations

Classes

Interfaces

Other Type aliases

Value type Type aliases

Variables

Functions

Other Type aliases

BaseValue

BaseValueInFrame

BaseValueNonScalar

BaseValueRelative

Type parameters

U: Unit

BaseValueRelativeNonScalar

Type parameters

U: Unit

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

Type parameters

U: Unit

TexFormatter

Type declaration

Parameters

tex: string

Returns Element

Variable

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>[]