Class MathEx

constructor

• new MathEx(): MathEx

  Returns MathEx

Static ReadonlyDeg2Rad

Static ReadonlyHalfPi

Static ReadonlyPi

Static ReadonlyRad2Deg

Static ReadonlyTwoPi

Staticacos

• acos(cosine: number): rsx.Radian

  Returns the angle whose cosine is the specified number.

  Parameters

  • cosine: number

    Cosine of an angle.

  Returns rsx.Radian

  Angle in radians.

Staticasin

• asin(sine: number): rsx.Radian

  Returns the angle whose sine is the specified number.

  Parameters

  • sine: number

    Sine value.

  Returns rsx.Radian

  Cosine in radians.

Staticatan

• atan(tangent: number): rsx.Radian

  Returns the angle whose tangent is the specified number.

  Parameters

  • tangent: number

    Tangent of an angle.

  Returns rsx.Radian

  Angle in radians.

Staticatan2

• atan2(y: number, x: number): rsx.Radian

  Returns an angle of the point x and y in radians.

  Parameters

  • y: number

    Y coordinate of the point.

  • x: number

    X coordinate of the point.

  Returns rsx.Radian

  Angle in radians in range [Pi, -Pi].

StaticcalculateBezierCurvePoint2

• calculateBezierCurvePoint2(
      start: Immutable<Vector2>,
      controlPoint1: Immutable<Vector2>,
      controlPoint2: Immutable<Vector2>,
      end: Immutable<Vector2>,
      t: number,
  ): Vector2

  Calculates the point at t of the Cubic Bezier curve in 2D-space.

  Parameters

  • start: Immutable<Vector2>

    The starting point of the Bezier curve.

  • controlPoint1: Immutable<Vector2>

    The first cubic Bezier control point.

  • controlPoint2: Immutable<Vector2>

    The second cubic Bezier control point.

  • end: Immutable<Vector2>

    The ending point of the Bezier curve.

  • t: number

    The point at which to calculate the curve derivative for. Must be in the range [0, 1].

  Returns Vector2

  The tangent vector to at the desired point.

StaticcalculateBezierCurvePoint3

• calculateBezierCurvePoint3(
      start: Immutable<Vector3>,
      controlPoint1: Immutable<Vector3>,
      controlPoint2: Immutable<Vector3>,
      end: Immutable<Vector3>,
      t: number,
  ): Vector3

  Calculates the point at t of the Cubic Bezier curve in 3D-space.

  Parameters

  • start: Immutable<Vector3>

    The starting point of the Bezier curve.

  • controlPoint1: Immutable<Vector3>

    The first cubic Bezier control point.

  • controlPoint2: Immutable<Vector3>

    The second cubic Bezier control point.

  • end: Immutable<Vector3>

    The ending point of the Bezier curve.

  • t: number

    The point at which to calculate the curve derivative for. Must be in the range [0, 1].

  Returns Vector3

  The tangent vector to at the desired point.

StaticcalculateBezierCurveTangent2

• calculateBezierCurveTangent2(
      start: Immutable<Vector2>,
      controlPoint1: Immutable<Vector2>,
      controlPoint2: Immutable<Vector2>,
      end: Immutable<Vector2>,
      t: number,
  ): Vector2

  Calculates the tangent at point t of the Cubic Bezier curve.

  Parameters

  • start: Immutable<Vector2>

    The starting point of the Bezier curve.

  • controlPoint1: Immutable<Vector2>

    The first cubic Bezier control point.

  • controlPoint2: Immutable<Vector2>

    The second cubic Bezier control point.

  • end: Immutable<Vector2>

    The ending point of the Bezier curve.

  • t: number

    The point at which to calculate the curve derivative for. Must be in the range [0, 1].

  Returns Vector2

  The tangent vector to at the desired point.

StaticcalculateBezierCurveTangent3

• calculateBezierCurveTangent3(
      start: Immutable<Vector3>,
      controlPoint1: Immutable<Vector3>,
      controlPoint2: Immutable<Vector3>,
      end: Immutable<Vector3>,
      t: number,
  ): Vector3

  Calculates the tangent at point t of the Cubic Bezier curve.

  Parameters

  • start: Immutable<Vector3>

    The starting point of the Bezier curve.

  • controlPoint1: Immutable<Vector3>

    The first cubic Bezier control point.

  • controlPoint2: Immutable<Vector3>

    The second cubic Bezier control point.

  • end: Immutable<Vector3>

    The ending point of the Bezier curve.

  • t: number

    The point at which to calculate the curve derivative for. Must be in the range [0, 1].

  Returns Vector3

  The tangent vector to at the desired point.

Staticcbrt

• cbrt(val: number): number

  Return a cubic root of the provided value.

  Parameters

  • val: number

    Value to take the cubic root of.

  Returns number

  Cubic root of the provided value.

Staticclamp

• clamp<T = Numeric>(value: T, min: T, max: T): T

  Clamps the value between min and max values.

  Type Parameters

  • T = Numeric

  Parameters

  • value: T

    Value to clamp.

  • min: T

    Minimum value of the range to clamp. Must be lower than max

  • max: T

    Maximum value of the range to clamp. Must be higher than min

  Returns T

  Returns unchanged value if it is in valid range, otherwise returns value clamped to the range extremes.

Staticclamp01

• clamp01<T = Numeric>(value: T): T

  Clamps a value between zero and one.

  Type Parameters

  • T = Numeric

  Parameters

  • value: T

    Value to clamp.

  Returns T

  Returns unchanged value if it is in [0, 1] range, otherwise returns value clamped to the range.

Staticcos

• cos(angle: rsx.Radian): number

  Returns the cosine of the specified angle in radians.

  Parameters

  • angle: rsx.Radian

    Angle in radians.

  Returns number

  Cosine in radians.

Staticcubic

• cubic(val1: number, val2: number, val3: number, val4: number, f: number): number

  Performs cubic interpolation between two values bound between two other values where f is the alpha value in range [0, 1]. If it is 0 the method returns val2. If it is 1 the method returns val3.

  Parameters

  • val1: number

    First value.

  • val2: number

    Second value.

  • val3: number

    Third value.

  • val4: number

    Fourth value.

  • f: number

    Value in range [0, 1].

  Returns number

  Value resulting from cubic interpolation.

Staticdegrees2Radians

• degrees2Radians(value: number): number

  Converts the value in degrees to radians.

  Parameters

  • value: number

  Returns number

StaticdivideAndRoundUp

• divideAndRoundUp(n: number, d: number): number

  Divides an integer value by another value and returns the result, rounded up.

  Parameters

  • n: number

    Numerator.

  • d: number

    Denominator.

  Returns number

  Divided and rounded value.

  Note

  Only works if both values are positive.

Staticeval

• eval<T extends Vector2 | Vector3 | Quaternion | Vector4>(
      resultType: ClassOf<T>,
      fnExpression: () => number,
  ): ValueTypeOf<T>

  Evaluates the specified math expression and returns the result.

  Type Parameters

  • T extends Vector2 | Vector3 | Quaternion | Vector4

  Parameters

  • resultType: ClassOf<T>

    The return type of the expression. Only numbers and vectors of this type may be referenced in the expression.

  • fnExpression: () => number

    The lambda expression to evaluate.

  Returns ValueTypeOf<T>

  A vector type containing the result of the expression.

  Note

  This is a helper to make writing math expressions in Javascript easier. There is a slight overhead compared to doing math expressions manually as the expression must be evaluted N-times for each component of the vector type. However, the cost amortizes well as no temporary objects must be constructed that hold the result. The expression is evaluated using only numbers, and then assigned to the respective component of the vector result.

  The fastest possible way of doing math is still using the do math type APIs such as doAdd as these APIs will avoid the construction of a temporary object, but will instead, apply the expression on the calling object and return a reference to the same object. This allows to quickly chain a math expression together.

  Evaluatable Variables

  To make a variable evaluatable it must either be casted to the Evaluatable<T> type where T is an evaluatable type such as Vector3. Alternatively, the variable can be prefixed with the unary plus to allow the compiler to use the variable in the expression.

  The following example shows basic usage:

  		// This vector is marked as `Evaluatable` and can be directly referenced in the expression.
  		const myVector = new Vector3(10, 20, 30) as Evaluatable<Vector3>;
  		// This vector is not evaluatable, it must be prefixed with the `unary plus`.
  		const myVector2 = new Vector3(-10, -20, 20);
  
  		const result:Vector3 = MathEx.eval(Vector3, () => (myVector + +myVector2) * 2)
  Copy

  The result in the above example will be [0, 0, 100].

  Bad Practice: Function invocations

  It's important to note that performing function invocations can dramatic overhead as the function must be invoked once for each component of the resultType.

  The following example shows a bad practice and should be avoided.

  		const result:Vector3 = MathEx.eval(Vector3, () => myVector.normalized() * myVector2)
  
  Copy

  The normalized function will be slowing down the execution as it must be invoked once for each component of the resultType. In the case of the Vector3 it results in calling the expensive function three times.

  While calling eval recursively, it results in evaluating the sub expression once for each component. So calling eval inside of a Vector3 evaluation for a Vector3 type results in 3 * 3 invocations.

Staticfract

• fract(value: number): number

  Returns the fractional part of the provided value.

  Parameters

  • value: number

    Parameter to take fractional value from.

  Returns number

  Fractional value of value.

StaticinverseSquareRoot

• inverseSquareRoot(f: number): number

  Returns an inverse square root (1/sqrt(x)) of the provided value.

  Parameters

  • f: number

    Value to take the inverse square root of. Must not be negative or zero.

  Returns number

  Inverse square root of the provided value.

StaticisAlmostEqual

• isAlmostEqual(a: number, b: number, epsilon?: number): boolean

  Compares two numbers with an error margin.

  Parameters

  • a: number

    First number to compare.

  • b: number

    Second number to compare.

  • Optionalepsilon: number

    Error margin within which the numbers should be considered equal.

  Returns boolean

  True if equal, false otherwise.

Staticlerp

• lerp<T = Numeric>(a: T, b: T, t: number, tmin?: number, tmax?: number): T

  Linearly interpolates between two values.

  Type Parameters

  • T = Numeric

  Parameters

  • a: T

    Starting value to interpolate from.

  • b: T

    Ending value to interpolate towards.

  • t: number

    Interpolation factor in specified range.

  • Optionaltmin: number

    Minimum value for the range of t

  • Optionaltmax: number

    Maximum value for the range of t

  Returns T

  Interpolated value.

Staticlog10

• log10(f: number): number

  Returns the logarithm of a number in base 10.

  Parameters

  • f: number

    Value to get the logarithm of.

  Returns number

  Logarithm of a number in base 10.

StaticlogBase

• logBase(value: number, base: number): number

  Returns the logarithm of a number in a specified base.

  Parameters

  • value: number

    Value to get the logarithm of.

  • base: number

    Base of the logarithm

  Returns number

  Logarithm of a number in the specified base.

Staticmax

• max<T = Numeric>(a: T, b: T): T

  Returns the maximum value of the two provided.

  Type Parameters

  • T = Numeric

  Parameters

  • a: T

    First value to compare.

  • b: T

    Second value to compare.

  Returns T

  Maximum of the two values.

Staticmin

• min<T = Numeric>(a: T, b: T): T

  Returns the minimum value of the two provided.

  Type Parameters

  • T = Numeric

  Parameters

  • a: T

    First value to compare.

  • b: T

    Second value to compare.

  Returns T

  Minimum of the two values.

Staticmodulo

• modulo(dividend: number, divisor: number): number

  Returns dividend % divisor (floating point modulo).

  Parameters

  • dividend: number

    Value to repeat.

  • divisor: number

    Length after which to repeat the value.

  Returns number

  Result of f % length.

StaticnormalizeValue

• normalizeValue(value: number, minimum: number, maximum: number): number

  Normalize the value between based on the range. Returns 0 if f is less or equal that minimum, 1 if f is equal or greater than maximum, and value in range (0, 1) otherwise.

  Parameters

  • value: number

    Value to take inverse lerp of.

  • minimum: number

    Minimum value of the range.

  • maximum: number

    Maximum value of the range.

  Returns number

  The normalized value.

StaticpingPong

• pingPong(value: number, length: number): number

  Wraps the value in range [0, length] and reverses the direction every length increment. This results in f incrementing until length, then decrementing back to 0, and so on.

  Parameters

  • value: number

    Value to ping-pong.

  • length: number

    Length after which to reverse the direction.

  Returns number

  Result of the ping-pong operation.

Staticquintic

• quintic(value: number): number

  Performs quintic interpolation where value is the value to map onto a quintic S-curve.

  Parameters

  • value: number

    Value in range [0, 1].

  Returns number

  Value resulting from quintic interpolation.

Staticradians2Degrees

• radians2Degrees(value: number): number

  Converts the value in radians to degrees.

  Parameters

  • value: number

  Returns number

StaticroundToMultiple

• roundToMultiple(value: number, multiple: number): number

  Rounds to the nearest multiple.

  Parameters

  • value: number

    Value to round.

  • multiple: number

    Multiple to round to.

  Returns number

  Value rounded to the nearest multiple.

Staticsign

• sign(value: number): number

  Returns the sign of the provided value (positive or negative).

  Parameters

  • value: number

    Value to get the sign of.

  Returns number

  -1.0f if negative or 1.0f if positive.

Staticsin

• sin(angle: rsx.Radian): number

  Returns the sine of the specified angle in radians.

  Parameters

  • angle: rsx.Radian

    Angle in radians.

  Returns number

  Sine in radians.

StaticsmoothStep

• smoothStep(val1: number, val2: number, t: number): number

  Performs smooth Hermite interpolation between values.

  Parameters

  • val1: number

    First value.

  • val2: number

    Second Value.

  • t: number

    Value in range [0, 1] that determines how much to interpolate.

  Returns number

  Hermite interpolated value at position t.

Statictan

• tan(angle: rsx.Radian): number

  Returns the tangent of the specified angle in radians.

  Parameters

  • angle: rsx.Radian

    angle in radians.

  Returns number

  Tangent.

StaticwrapAngle

• wrapAngle(angle: rsx.Degree): rsx.Degree

  Wraps an angle in [0, 360) range. Values lower than zero, or higher or equal to 360 will get wrapped around back into [0, 360) range.

  Parameters

  • angle: rsx.Degree

    Angle to wrap.

  Returns rsx.Degree

  Angle in [0, 360) range.