joka.math
The math module provides mathematical data structures and functions.
var beige black blank blue brown cyan dpi dpi180 dpi2 dsqrt2 epsilon euler gray gray1 gray2 gray3 gray4 green ln10 ln2 log10e log2e magenta maroon orange pi pi180 pi2 pi4 pink red sqrt2 white yellow
alias Circ EasingFunc IRect IVec2 IVec3 IVec4 Line Rect Rounding64Func RoundingFunc SRect Tween Tween2 Vec2 Vec3 Vec4
fn acos acos64 applyRounding applyRounding64 asin asin64 atan atan2 atan264 atan64 ceil ceil64 cos cos64 easeInBack easeInBounce easeInCirc easeInCubic easeInElastic easeInExpo easeInOutBack easeInOutBounce easeInOutCirc easeInOutCubic easeInOutElastic easeInOutExpo easeInOutQuad easeInOutQuart easeInOutQuint easeInOutSine easeInQuad easeInQuart easeInQuint easeInSine easeLinear easeOutBack easeOutBounce easeOutCirc easeOutCubic easeOutElastic easeOutExpo easeOutQuad easeOutQuart easeOutQuint easeOutSine easing exp exp2 exp264 exp64 fequals fequals64 floor floor64 fmod fmod64 followState followState64 lerp lerp64 log log10 log1064 log2 log264 log64 moveTo moveTo64 moveToState moveToState64 moveToWithSlowdown moveToWithSlowdown64 pow pow64 remainder remainder64 round round64 rounding rounding64 roundNothing roundNothing64 sin sin64 smootherstep smootherstep64 smoothstep smoothstep64 snap sqrt sqrt64 tan tan64 toDegrees toDegrees64 toIRect toIVec toRadians toRadians64 toRect toRgb toRgba toVec wrap
Types 30
aliasRoundingFunc = float function(float x)
A function used for rounding.
aliasRounding64Func = double function(double x)
A function used for rounding.
aliasEasingFunc = float function(float x)
A function used for easing.
enumRounding : ubyte
A type representing rounding functions.
noneNo rounding.
floorRound down.
roundRound to nearest.
ceilRound up.
enumEasing : ubyte
A type representing easing functions.
linearConstant speed.
inSineSlow start.
outSineSlow end.
inOutSineSlow start and end.
inCubicCubic in.
outCubicCubic out.
inOutCubicCubic in-out.
inQuintQuintic in.
outQuintQuintic out.
inOutQuintQuintic in-out.
inCircCircular in.
outCircCircular out.
inOutCircCircular in-out.
inElasticElastic in.
outElasticElastic out.
inOutElasticElastic in-out.
inQuadQuadratic in.
outQuadQuadratic out.
inOutQuadQuadratic in-out.
inQuartQuartic in.
outQuartQuartic out.
inOutQuartQuartic in-out.
inExpoExponential in.
outExpoExponential out.
inOutExpoExponential in-out.
inBackBack in.
outBackBack out.
inOutBackBack in-out.
inBounceBounce in.
outBounceBounce out.
inOutBounceBounce in-out.
enumTweenMode : ubyte
A type that describes how a tween should update.
bombIt stops updating when it reaches the beginning or end of the animation.
loopIt returns to the beginning or end of the animation when it reaches the beginning or end of the animation.
yoyoIt reverses the given delta time when it reaches the beginning or end of the animation.
enumHook : ubyte
A type representing relative points.
topLeftThe top left point.
topThe top point.
topRightThe top right point.
leftThe left point.
centerThe center point.
rightThe right point.
bottomLeftThe bottom left point.
bottomThe bottom point.
bottomRightThe bottom right point.
structMargin
structRgba
A RGBA color using ubytes.
Fields
ubyte rubyte gubyte bubyte a formThe form of the color. zeroThe zero value of the color. oneThe one value of the color. lengthThe length of the color.Methods
structGVec2(T)
A generic 2D vector.
Fields
T xT y formThe form of the vector. zeroThe zero value of the vector. oneThe one value of the vector. lengthThe length of the vector.Methods
structGVec3(T)
A generic 3D vector.
Fields
T xT yT z formThe form of the vector. zeroThe zero value of the vector. oneThe one value of the vector. lengthThe length of the vector.Methods
structGVec4(T)
A generic 4D vector.
Fields
T xT yT zT w formThe form of the vector. zeroThe zero value of the vector. oneThe one value of the vector. lengthThe length of the vector.Methods
structGRect(P, S = P) if (P.sizeof >= S.sizeof)
A generic 2D rectangle.
Methods
structGCirc(T)
A generic 2D Circle.
Methods
structGLine(T)
A generic 2D Line.
Methods
structGTween(T)
Handles the transition between two values over a specified duration.
Methods
bool isAtStart() @safe nothrow @nogcReturns true if time is at the start (0.0). Useful when using `TweenMode.bomb`.bool isAtEnd() @safe nothrow @nogcReturns true if time is at the end (duration). Useful when using `TweenMode.bomb`.T update(float delta) @safe nothrow @nogcAdvances the tween by the given delta time and returns the current value.void setProgress(float value) @safe nothrow @nogcSets the progress to a specific value (between 0.0 to 1.0).void setTime(float value) @safe nothrow @nogcSets the current time and applies the tween mode rules.structSmoothToggle
Handles the transition between two boolean states.
Fields
float progressbool stateMethods
bool isActive() @safe nothrow @nogcReturns true if progress is not at the start (0.0) or the end (1.0).float update(float delta) @safe nothrow @nogcAdvances the progress toward the current state. Returns the updated progress.bool toggleSnap() @safe nothrow @nogcToggles the state and instantly sets progress to match. Returns the new state.Constructors
this(bool state)Creates a new toggle.Functions 126
fn
T wrap(T)(T x, T a, T b) @trusted @safe nothrow @nogcReturns `x` wrapped to the range [`a`, `b`], wrapping around when out of bounds.fn
T snap(T)(T x, T step) @trusted @safe nothrow @nogcReturns `x` rounded to the nearest multiple of `step`.fn
float fmod(float x, float y) @trusted @safe nothrow @nogcReturns the floating-point remainder of `x / y`.fn
double fmod64(double x, double y) @trusted @safe nothrow @nogcReturns the floating-point remainder of `x / y`.fn
float remainder(float x, float y) @trusted @safe nothrow @nogcReturns the IEEE 754 floating-point remainder of `x / y`.fn
double remainder64(double x, double y) @trusted @safe nothrow @nogcReturns the IEEE 754 floating-point remainder of `x / y`.fn
float exp(float x) @trusted @safe nothrow @nogcReturns Euler's number `e` raised to the power of `x`.fn
double exp64(double x) @trusted @safe nothrow @nogcReturns Euler's number `e` raised to the power of `x`.fn
float pow(float base, float exponent) @trusted @safe nothrow @nogcReturns `base` raised to the power of `exponent`.fn
double pow64(double base, double exponent) @trusted @safe nothrow @nogcReturns `base` raised to the power of `exponent`.fn
float atan2(float y, float x) @trusted @safe nothrow @nogcReturns the angle between the positive x-axis and the point (`x`, `y`).fn
double atan264(double y, double x) @trusted @safe nothrow @nogcReturns the angle between the positive x-axis and the point (`x`, `y`).fn
float applyRounding(float x, Rounding type) @trusted @safe nothrow @nogcApplies the specified `type` of rounding to `x`.fn
double applyRounding64(double x, Rounding type) @trusted @safe nothrow @nogcApplies the specified `type` of rounding to `x`.fn
float lerp(float from, float to, float weight) @trusted @safe nothrow @nogcReturns the linear interpolation between `from` and `to` by `weight`. A weight of 0 returns `from`, a weight of 1 returns `to`.fn
double lerp64(double from, double to, double weight) @trusted @safe nothrow @nogcReturns the linear interpolation between `from` and `to` by `weight`. A weight of 0 returns `from`, a weight of 1 returns `to`.fn
float smoothstep(float from, float to, float weight) @trusted @safe nothrow @nogcReturns the smooth interpolation between `from` and `to` by `weight` using a cubic curve. Eases in and out, with zero first-order derivatives at both endpoints.fn
double smoothstep64(double from, double to, double weight) @trusted @safe nothrow @nogcReturns the smooth interpolation between `from` and `to` by `weight` using a cubic curve. Eases in and out, with zero first-order derivatives at both endpoints.fn
float smootherstep(float from, float to, float weight) @trusted @safe nothrow @nogcReturns the smoother interpolation between `from` and `to` by `weight` using a quintic curve. Eases in and out, with zero first and second-order derivatives at both endpoints.fn
double smootherstep64(double from, double to, double weight) @trusted @safe nothrow @nogcReturns the smoother interpolation between `from` and `to` by `weight` using a quintic curve. Eases in and out, with zero first and second-order derivatives at both endpoints.fn
float easeLinear(float x) @trusted @safe nothrow @nogcEasing function with no acceleration. Returns `x` unchanged.fn
float easeInSine(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates using a sine curve.fn
float easeOutSine(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates using a sine curve.fn
float easeInOutSine(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates using a sine curve.fn
float easeInCubic(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates using a cubic curve.fn
float easeOutCubic(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates using a cubic curve.fn
float easeInOutCubic(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates using a cubic curve.fn
float easeInQuint(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates using a quintic curve.fn
float easeOutQuint(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates using a quintic curve.fn
float easeInOutQuint(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates using a quintic curve.fn
float easeInCirc(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates along a circular arc.fn
float easeOutCirc(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates along a circular arc.fn
float easeInOutCirc(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates along a circular arc.fn
float easeInElastic(float x) @trusted @safe nothrow @nogcEasing function that overshoots the start with an elastic spring effect.fn
float easeOutElastic(float x) @trusted @safe nothrow @nogcEasing function that overshoots the end with an elastic spring effect.fn
float easeInOutElastic(float x) @trusted @safe nothrow @nogcEasing function that overshoots both ends with an elastic spring effect.fn
float easeInQuad(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates using a quadratic curve.fn
float easeOutQuad(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates using a quadratic curve.fn
float easeInOutQuad(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates using a quadratic curve.fn
float easeInQuart(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates using a quartic curve.fn
float easeOutQuart(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates using a quartic curve.fn
float easeInOutQuart(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates using a quartic curve.fn
float easeInExpo(float x) @trusted @safe nothrow @nogcEasing function that starts slow and accelerates exponentially.fn
float easeOutExpo(float x) @trusted @safe nothrow @nogcEasing function that starts fast and decelerates exponentially.fn
float easeInOutExpo(float x) @trusted @safe nothrow @nogcEasing function that accelerates then decelerates exponentially.fn
float easeInBack(float x) @trusted @safe nothrow @nogcEasing function that pulls back slightly before accelerating forward.fn
float easeOutBack(float x) @trusted @safe nothrow @nogcEasing function that overshoots the target before settling.fn
float easeInOutBack(float x) @trusted @safe nothrow @nogcEasing function that pulls back at the start and overshoots at the end.fn
float easeInBounce(float x) @trusted @safe nothrow @nogcEasing function that starts with a bouncing effect before reaching the target.fn
float easeOutBounce(float x) @trusted @safe nothrow @nogcEasing function that ends with a bouncing effect after reaching the target.fn
float easeInOutBounce(float x) @trusted @safe nothrow @nogcEasing function that bounces at both the start and end.fn
bool fequals(float a, float b, float localEpsilon = epsilon) @trusted @safe nothrow @nogcReturns true if `a` and `b` are within `localEpsilon` of each other.fn
bool fequals64(double a, double b, double localEpsilon = epsilon) @trusted @safe nothrow @nogcReturns true if `a` and `b` are within `localEpsilon` of each other.fn
bool fequals(Vec2 a, Vec2 b, float localEpsilon = epsilon) @trusted @safe nothrow @nogcReturns true if all components of `a` and `b` are within `localEpsilon` of each other.fn
bool fequals(Vec3 a, Vec3 b, float localEpsilon = epsilon) @trusted @safe nothrow @nogcReturns true if all components of `a` and `b` are within `localEpsilon` of each other.fn
bool fequals(Vec4 a, Vec4 b, float localEpsilon = epsilon) @trusted @safe nothrow @nogcReturns true if all components of `a` and `b` are within `localEpsilon` of each other.fn
IVec2 toIVec(Vec2 vec) @trusted @safe nothrow @nogcConverts a `Vec2` to an `IVec2` by truncating each component to an integer.fn
IVec3 toIVec(Vec3 vec) @trusted @safe nothrow @nogcConverts a `Vec3` to an `IVec3` by truncating each component to an integer.fn
IVec4 toIVec(Vec4 vec) @trusted @safe nothrow @nogcConverts a `Vec4` to an `IVec4` by truncating each component to an integer.fn
Vec4 toVec(Rgba color) @trusted @safe nothrow @nogcConverts an `Rgba` color to a `Vec4` with components in the order `(r, g, b, a)`.fn
IRect toIRect(Rect rect) @trusted @safe nothrow @nogcConverts a `Rect` to an `IRect` by truncating position and size components to integers.fn
Rgba toRgb(uint rgb) @trusted @safe nothrow @nogcConverts a packed 24-bit RGB integer to an `Rgba` color with full opacity.fn
Rgba toRgba(uint rgba) @trusted @safe nothrow @nogcConverts a packed 32-bit RGBA integer to an `Rgba` color.fn
Rgba toRgba(Vec3 vec) @trusted @safe nothrow @nogcConverts a `Vec3` to an `Rgba` color, clamping each component to the range [0, 255] with full opacity.fn
Rgba toRgba(Vec4 vec) @trusted @safe nothrow @nogcConverts a `Vec4` to an `Rgba` color, clamping each component to the range [0, 255].fn
Rgba toRgba(IStr str) @trusted @safe nothrow @nogcConverts a hex color string (e.g. `"#RGB"`, `"RRGGBB"`, `"RRGGBBAA"`) to an `Rgba` color. Returns `blank` if the string is invalid.fn
Vec2 lerp(Vec2 from, Vec2 to, float weight) @trusted @safe nothrow @nogcReturns the linear interpolation between `from` and `to` by `weight`, applied per component.fn
Vec3 lerp(Vec3 from, Vec3 to, float weight) @trusted @safe nothrow @nogcReturns the linear interpolation between `from` and `to` by `weight`, applied per component.fn
Vec4 lerp(Vec4 from, Vec4 to, float weight) @trusted @safe nothrow @nogcReturns the linear interpolation between `from` and `to` by `weight`, applied per component.fn
RoundingFunc rounding(Rounding type) @trusted @safe nothrow @nogcReturns the rounding function corresponding to the given `Rounding` type.fn
Rounding64Func rounding64(Rounding type) @trusted @safe nothrow @nogcReturns the 64-bit rounding function corresponding to the given `Rounding` type.fn
EasingFunc easing(Easing type) @trusted @safe nothrow @nogcReturns the easing function corresponding to the given `Easing` type.fn
float moveToState(float from, bool to, float delta) @trusted @safe nothrow @nogcMoves `from` toward 1 by `delta` if `to` is true, or toward 0 if false. Result is clamped to [0, 1].fn
float moveToState64(double from, bool to, double delta) @trusted @safe nothrow @nogcMoves `from` toward 1 by `delta` if `to` is true, or toward 0 if false. Result is clamped to [0, 1].fn
float followState(ref float weight, bool target, float speed) @trusted @safe nothrow @nogcMoves `weight` by ref toward the `target` state by `speed` and returns the updated value.fn
double followState64(ref double weight, bool target, double speed) @trusted @safe nothrow @nogcMoves `weight` by ref toward the `target` state by `speed` and returns the updated value.fn
float moveTo(float from, float to, float delta) @trusted @safe nothrow @nogcMoves `from` toward `to` by at most `delta`, stopping exactly at `to`.fn
float moveTo64(double from, double to, double delta) @trusted @safe nothrow @nogcMoves `from` toward `to` by at most `delta`, stopping exactly at `to`.fn
Vec2 moveTo(Vec2 from, Vec2 to, Vec2 delta) @trusted @safe nothrow @nogcMoves `from` toward `to` per component by at most `delta`, stopping exactly at `to`.fn
Vec3 moveTo(Vec3 from, Vec3 to, Vec3 delta) @trusted @safe nothrow @nogcMoves `from` toward `to` per component by at most `delta`, stopping exactly at `to`.fn
Vec4 moveTo(Vec4 from, Vec4 to, Vec4 delta) @trusted @safe nothrow @nogcMoves `from` toward `to` per component by at most `delta`, stopping exactly at `to`.fn
float moveToWithSlowdown(float from, float to, float delta, float slowdown) @trusted @safe nothrow @nogcMoves `from` toward `to` by `delta` each step, decelerating as it approaches using `slowdown`. A `slowdown` value around 0.1 gives a natural deceleration feel.fn
float moveToWithSlowdown64(double from, double to, double delta, double slowdown) @trusted @safe nothrow @nogcMoves `from` toward `to` by `delta` each step, decelerating as it approaches using `slowdown`. A `slowdown` value around 0.1 gives a natural deceleration feel.fn
Vec2 moveToWithSlowdown(Vec2 from, Vec2 to, Vec2 delta, float slowdown) @trusted @safe nothrow @nogcMoves `from` toward `to` per component by `delta`, decelerating as it approaches using `slowdown`. A `slowdown` value around 0.1 gives a natural deceleration feel.fn
Vec3 moveToWithSlowdown(Vec3 from, Vec3 to, Vec3 delta, float slowdown) @trusted @safe nothrow @nogcMoves `from` toward `to` per component by `delta`, decelerating as it approaches using `slowdown`. A `slowdown` value around 0.1 gives a natural deceleration feel.fn
Vec4 moveToWithSlowdown(Vec4 from, Vec4 to, Vec4 delta, float slowdown) @trusted @safe nothrow @nogcMoves `from` toward `to` per component by `delta`, decelerating as it approaches using `slowdown`. A `slowdown` value around 0.1 gives a natural deceleration feel.Variables 34
enumvar
epsilon = 0.0001The value of epsilon.
enumvar
euler = 2.71828182845904523536028747135266249The value of Euler's number.
enumvar
log2e = 1.44269504088896340735992468100189214The value of log2(e).
enumvar
log10e = 0.43429448190325182765112891891660508The value of log10(e).
enumvar
ln2 = 0.69314718055994530941723212145817656The value of ln(2).
enumvar
ln10 = 2.30258509299404568401799145468436421The value of ln(10).
enumvar
pi = 3.14159265358979323846264338327950288The value of PI.
enumvar
pi2 = pi / 2.0The value of PI / 2.
enumvar
pi4 = pi / 4.0The value of PI / 4.
enumvar
pi180 = pi / 180.0The value of PI / 180.
enumvar
dpi = 1.0 / piThe value of 1 / PI.
enumvar
dpi2 = 2.0 / piThe value of 2 / PI.
enumvar
dpi180 = 180.0 / piThe value of 180 / PI.
enumvar
sqrt2 = 1.41421356237309504880168872420969808The value of sqrt(2).
enumvar
dsqrt2 = 0.70710678118654752440084436210484903The value of 1 / sqrt(2).
enumvar
blank = Rgba()#00000000
enumvar
black = Rgba(0)#000000FF
enumvar
white = Rgba(255)#FFFFFFFF
enumvar
red = Rgba(255, 0, 0)#FF0000FF
enumvar
green = Rgba(0, 255, 0)#00FF00FF
enumvar
blue = Rgba(0, 0, 255)#0000FFFF
enumvar
yellow = Rgba(255, 255, 0)#FFFF00FF
enumvar
magenta = Rgba(255, 0, 255)#FF00FFFF
enumvar
cyan = Rgba(0, 255, 255)#00FFFFFF
enumvar
pink = Rgba(255, 192, 204)#FFC0CCFF
enumvar
orange = Rgba(255, 165, 0)#FFA500FF
enumvar
beige = Rgba(240, 235, 210)#F0EBD2FF
enumvar
brown = Rgba(165, 72, 42)#A5482AFF
enumvar
maroon = Rgba(128, 0, 0)#800000FF
enumvar
gray1 = Rgba(32, 32, 32)#202020FF
enumvar
gray2 = Rgba(96, 96, 96)#606060FF
enumvar
gray3 = Rgba(159, 159, 159)#9F9F9FFF
enumvar
gray4 = Rgba(223, 223, 223)#DFDFDFFF
enumvar
gray = gray2#606060FF