moonbit-easings
A dependency-free MoonBit motion toolkit for media timelines, easing curves, cubic Bezier inversion, and scalar keyframes.
animation
easing
tween
bezier
keyframe
media
moon add Zlj6566/moonbit-easings@0.1.0
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0.1.0
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README#moonbit-easings
MoonBit 数字媒体补间动画与贝塞尔缓动函数库：为 UI 交互、游戏镜头、数字艺术和离线媒体提供可组合、无运行时依赖的运动学基础设施。
#项目定位
moonbit-easings 负责“时间、数值和运动轨迹如何变化”，不负责窗口渲染、资源解析或具体 UI 框架。它可以作为渲染器、游戏循环、音视频导出器和交互式编辑器的底层采样层，输出标量、向量、颜色、变换、路径和事件数据。
项目把 easing、Cubic-Bezier 时间轴求逆、Tween、关键帧轨道、时间线、路径和传输控制放在统一的数据模型中，同时保持核心包不依赖平台 I/O，适合 Wasm、Wasm-GC、JavaScript 和 Native 目标。
#核心能力
- 31 个内建 easing：Linear、Quad、Cubic、Quart、Quint、Sine、Expo、Circ、Back、Elastic、Bounce。
- Bezier::new(x1, y1, x2, y2)：缓存采样表、Newton 迭代和二分回退组成稳定的时间轴求逆器。
- Tween 与 ScalarTrack：支持 delay、repeat、Mirror、Continue、逐段曲线、速度和加速度。
- 多媒体类型：Point2、Point3、RGBA、Transform2D、颜色渐变、Hermite 和 Catmull-Rom。
- 轨迹编排：命名标记、MarkerCursor、ScalarTrackBundle、MotionStateMachine、MotionClip 和 ClipSequence。
- 几何与时间：Spline2D/Spline3D、复合 Path2D、距离采样、投影、边界框和 Piecewise RetimeMap。
- 离线分析：固定帧率与自适应采样、信号滤波、峰值、积分、单调性、曲线报告和可复现实验入口。
与只提供基础 easing 函数的包相比，本项目的重点是可直接接入数字媒体工作流的轨道、时间、路径和导出层；它不复制其他生态包的实现，也不绑定 Lottie、Canvas 或某个游戏引擎。
#快速开始
要求 MoonBit stable 0.10.7 或更新版本。
moon add Zlj6566/moonbit-easings在 moon.pkg 中导入：
///|
import {
"Zlj6566/moonbit-easings" @easings,
}最小 Tween 示例：
let curve = try! @easings.Bezier::new(0.25, 0.1, 0.25, 1.0)
let tween = try! @easings.Tween::new(
0.0,
320.0,
1.0,
curve=@easings.Curve::bezier(curve),
)
let sample = tween.sample_motion(0.5)
println(sample.value().to_string())
println(sample.velocity().to_string())#CLI
仓库提供两个可运行入口：
# 展示 Tween、关键帧、颜色渐变和序列组合
moon run cmd/demo
# 运行可复现的 Native 工作负载并打印校验和
moon run --target native --release cmd/benchcmd/bench 不把主机时钟写入库 API；它打印固定迭代次数、采样校验和和自适应采样结果，主机耗时由 BENCHMARKS.md 中的测量命令取得。
#架构
Easing / Bezier
│
├── Tween / Keyframe / ScalarTrack
│ │
│ ├── Timeline / Bundle / StateMachine
│ └── Clip / Sequence / Transport / Markers
│
├── Point / Color / Transform Tracks
├── Spline / Path / RetimeMap
└── Sampling / Signal / Diagnostics主要模块按职责拆分：easing_*.mbt 与 bezier*.mbt 提供曲线内核；keyframe_*.mbt、tween.mbt 和 timeline.mbt 提供时间数据模型；typed_tracks.mbt、path.mbt、spline.mbt 和 path_geometry.mbt 提供数字媒体值与几何；adaptive_sampling.mbt、signal_processing.mbt 和 curve_analysis.mbt 面向离线导出与质量检查；motion_clip.mbt、motion_transport.mbt、motion_markers.mbt 和 motion_state_machine.mbt 面向运行时编排。
核心采样函数只在调用者明确请求批量结果时分配输出数组；Bezier 单点采样使用缓存表、Newton 迭代和二分回退，不创建临时采样数组。
#基准
基准说明、工具链版本、机器环境、完整输出和重复测量方式见 BENCHMARKS.md。本地执行：
moon build --target native --release cmd/bench
moon run --target native --release cmd/bench校验和用于确认不同构建目标实际执行了同一工作负载；墙钟数据不被当作跨机器的绝对性能承诺。
#测试
提交前执行完整检查：
moon fmt --check
moon info --target all
git diff --exit-code
moon check --fmt --deny-warn --target all
moon build --target all
moon test --deny-warn --target all测试覆盖 easing 边界、Bezier 参数求逆、重复和镜像时间、关键帧排序、向量/颜色/变换插值、路径端点、空输入、非法参数、标记方向、轨迹投影、自适应采样、重映射、信号边界和 Native/JS/Wasm 全目标行为。
#CI
.github/workflows/test.yml 在 Ubuntu、macOS 和 Windows 上安装官方 MoonBit stable 工具链，执行格式化、moon info 生成物差异检查、全目标检查、全目标构建和全目标测试，并开启 --deny-warn。
.github/workflows/publish.yml 只在手动触发时验证同一检查链，并使用仓库 Secret 中的 MOONCAKES_TOKEN 发布包；日常 CI 不执行发布。基准程序不进入普通测试矩阵，可按文档在 Native Release 模式单独运行。
#许可证
本项目采用 MIT License，见 LICENSE。实现来源和第三方生态边界见 SOURCES.md。
#MotionError
pub(all) suberror MotionError {
InvalidBezierX(Double, Double)
InvalidSampleCount(Int)
InvalidTime(Double)
InvalidDuration(Double)
InvalidDelay(Double)
InvalidRepeatCount(Int)
EmptyTrack
NonIncreasingKeyframe(Double, Double)
InvalidFrameRate(Double)
InvalidPointCount(Int)
InvalidTension(Double)
InvalidSegmentCount(Int)
InvalidThreshold(Double)
InvalidMarkerName
InvalidChannelName
InvalidRetimeSegment
InvalidStateName
}Errors raised while constructing or validating motion primitives.
#AdaptiveSamplePoint
A scalar sample with a subdivision depth for diagnostics and renderers.
#AdaptiveSamplePoint::value
#AdaptiveSampleResult
pub(all) struct AdaptiveSampleResult {
points : Array[AdaptiveSamplePoint]
accepted_segments : Int
rejected_segments : Int
maximum_error : Double
} derive(Debug)Result metadata for an adaptive sample pass.
#AdaptiveSampleResult::accepted_segments
#AdaptiveSampleResult::maximum_error
#AdaptiveSampleResult::points
#AdaptiveSampleResult::rejected_segments
#AdaptiveSamplingConfig
pub struct AdaptiveSamplingConfig {
tolerance : Double
max_depth : Int
max_samples : Int
} derive(Debug)Controls recursive subdivision of a scalar motion signal.
#AdaptiveSamplingConfig::max_depth
#AdaptiveSamplingConfig::max_samples
#AdaptiveSamplingConfig::new
fn AdaptiveSamplingConfig::new(tolerance : Double, max_depth? : Int, max_samples? : Int) -> AdaptiveSamplingConfig raise MotionError#AdaptiveSamplingConfig::tolerance
#Bezier
A cached cubic Bézier timing curve.
The x controls must lie in [0, 1], while y controls may overshoot for
spring-like or expressive motion. Construction builds a small lookup table;
evaluation only reads the table and performs scalar arithmetic.
#Bezier::approximate_length
A coarse arc-length estimate in parameter space, useful for diagnostics.
#Bezier::as_easing
Return the curve as a first-class easing function.
#Bezier::control_points
#Bezier::derivative
Derivative dy/dx at a normalized time. A zero x slope returns zero.
#Bezier::max_error
Return the maximum absolute difference between this curve and a reference.
#Bezier::new
fn Bezier::new(x1 : Double, y1 : Double, x2 : Double, y2 : Double, sample_count? : Int) -> Bezier raise MotionErrorConstruct a cubic timing curve with a cached lookup table.
#Bezier::reversed
Reverse the direction of a cubic timing curve.
#Bezier::sample
Evaluate the y coordinate at normalized time x.
#Bezier::sample_many
#Bounds2D
#BundleSample
The combined result at one timestamp. weighted_value is the normalized
blend of enabled channels; individual values remain available for output.
#BundleSample::value_named
#ClipLoopMode
Playback policy for a reusable motion clip.
#ClipSequence
A sequence compositor that averages overlapping clip contributions.
#ClipSequence::markers_between
fn ClipSequence::markers_between(self : ClipSequence, start : Double, end : Double) -> Array[MarkerHit]#ClipSequence::new
#ClipSequence::sample_many
fn ClipSequence::sample_many(self : ClipSequence, count : Int) -> Array[SamplePoint] raise MotionError#ClipSequenceBuilder
#ClipSequenceBuilder::add
fn ClipSequenceBuilder::add(self : ClipSequenceBuilder, item : ClipSequenceItem) -> ClipSequenceBuilder#ClipSequenceBuilder::add_at
fn ClipSequenceBuilder::add_at(self : ClipSequenceBuilder, clip : MotionClip, start : Double, weight? : Double) -> ClipSequenceBuilder raise MotionError#ClipSequenceBuilder::build
#ClipSequenceItem
A clip placed at a start offset in a larger composition.
#ColorGradient
A validated one-dimensional color gradient for UI and media rendering.
#ColorGradient::new
fn ColorGradient::new(stops : Array[GradientStop], premultiplied? : Bool) -> ColorGradient raise MotionError#ColorGradient::reversed
Return a gradient with the stop order and transition directions reversed.
#ColorGradient::sample
Sample the gradient. Values outside its declared range are clamped.
#ColorGradient::sample_many
#CubicPath2D
A cubic geometric Bézier path. This is separate from Bezier timing curves.
#CubicPath2D::polyline
#CubicPath2D::sample_by_distance
fn CubicPath2D::sample_by_distance(self : CubicPath2D, distance : Double, segments? : Int) -> Point2#Curve
A curve selector stored on a keyframe transition.
#CurveAnalysisPoint
pub(all) struct CurveAnalysisPoint {
time : Double
value : Double
velocity : Double
acceleration : Double
normalized_value : Double
} derive(Debug)A sample enriched with first and second derivative estimates.
#CurveAnalysisPoint::acceleration
#CurveAnalysisPoint::normalized_value
#CurveAnalysisPoint::velocity
#CurveChain
A piecewise curve used to choreograph a multi-stage motion.
#CurveChain::new
#CurveChain::sample_many
#CurveMonotonicity
#CurveReport
pub(all) struct CurveReport {
samples : Int
minimum : Double
maximum : Double
endpoint_error : Double
monotonic : Bool
peak_velocity : Double
peak_acceleration : Double
} derive(Debug)Summary metrics for comparing or previewing a motion curve.
#CurveReport::peak_acceleration
#EasingId
pub(all) enum EasingId {
Linear
QuadIn
QuadOut
QuadInOut
CubicIn
CubicOut
CubicInOut
QuartIn
QuartOut
QuartInOut
QuintIn
QuintOut
QuintInOut
SineIn
SineOut
SineInOut
ExpoIn
ExpoOut
ExpoInOut
CircIn
CircOut
CircInOut
BackIn
BackOut
BackInOut
ElasticIn
ElasticOut
ElasticInOut
BounceIn
BounceOut
BounceInOut
} derive(Eq, Debug)Families of easing curves used by a motion timeline.
#EasingId::apply
Evaluate a built-in easing curve.
#Extrapolation
Extrapolation policy for a keyframe track or a tween.
#FrameClock
Frame clock for deterministic media time conversion.
#FrameClock::frame_times
#FrameClock::frame_to_seconds
#FrameClock::new
#FrameClock::seconds_to_frame
#GradientBuilder
A builder for gradients assembled by an editor or an importer.
#GradientBuilder::add
#GradientBuilder::build
#GradientBuilder::remove_at
#GradientStop
A color stop whose curve controls the transition to the next stop.
#Hsv
Hue, saturation, value and alpha representation.
#Keyframe
#MarkerCursor
A cursor for deterministic marker dispatch in a transport loop.
#MarkerCursor::advance
#MarkerDirection
Direction of playback when a marker window is traversed.
#MarkerHit
A marker together with the direction in which it was crossed.
#MarkerTimeline
A sorted marker index for transport controls, editors, and event dispatch.
#MarkerTimeline::add
#MarkerTimeline::at
fn MarkerTimeline::at(self : MarkerTimeline, time : Double, tolerance? : Double) -> Array[MotionMarker]#MarkerTimeline::between
Return markers crossed while moving from start to end.
The start boundary is excluded and the end boundary is included.
#MarkerTimeline::find
#MarkerTimeline::markers
#MarkerTimeline::next_after
#MarkerTimeline::previous_before
#MarkerTimeline::remove_at
#MarkerTimeline::window
#MotionBounds
Bounds used to keep generated motion within a safe output range.
#MotionBounds::new
#MotionClip
pub struct MotionClip {
name : String
track : ScalarTrack
markers : MarkerTimeline
loop_mode : ClipLoopMode
} derive(Debug)A named, timestamped scalar motion clip with optional marker events.
#MotionClip::markers_between
#MotionClip::sample_many
#MotionClip::sample_motion
#MotionClip::scale_time
#MotionClip::shift
#MotionClip::with_loop_mode
#MotionClip::with_markers
#MotionClipLibrary
A small library for resolving named clips at runtime.
#MotionClipLibrary::add
#MotionClipLibrary::clips
#MotionClipLibrary::find
#MotionClipLibrary::remove
#MotionClipLibrary::total_duration
#MotionMarker
A named event attached to a motion timeline.
#MotionSample
pub(all) struct MotionSample {
time : Double
value : Double
velocity : Double
acceleration : Double
} derive(Debug)A compact sample of a scalar motion function.
#MotionSignal
A lightweight signal buffer for post-processing sampled motion data.
#MotionSignal::clamp
#MotionSignal::map
#MotionSignal::new
fn MotionSignal::new(values : Array[Double], start : Double, step : Double) -> MotionSignal raise MotionError#MotionSignal::offset
#MotionSignal::sample_many
fn MotionSignal::sample_many(self : MotionSignal, count : Int) -> Array[SamplePoint] raise MotionError#MotionSignal::scale
#MotionSignal::zip_map
fn MotionSignal::zip_map(self : MotionSignal, other : MotionSignal, func : (Double, Double) -> Double) -> MotionSignal#MotionStateMachine
pub struct MotionStateMachine {
states : Array[MotionStateNode]
transitions : Array[MotionStateTransition]
current : String
transition_from : String
transition_to : String
transition_start : Double
transition_duration : Double
transition_curve : Curve
has_transition : Bool
} derive(Debug)A transition engine with explicit transport time. State changes are
deterministic and do not allocate per sample.
#MotionStateMachine::add_state
fn MotionStateMachine::add_state(self : MotionStateMachine, state : MotionStateNode) -> Unit raise MotionError#MotionStateMachine::add_transition
fn MotionStateMachine::add_transition(self : MotionStateMachine, transition : MotionStateTransition) -> Unit raise MotionError#MotionStateMachine::complete
#MotionStateMachine::current
#MotionStateMachine::has_state
#MotionStateMachine::is_transitioning
#MotionStateMachine::new
fn MotionStateMachine::new(states : Array[MotionStateNode], transitions? : Array[MotionStateTransition], initial? : String) -> MotionStateMachine raise MotionError#MotionStateMachine::reset
#MotionStateMachine::sample
#MotionStateMachine::sample_motion
#MotionStateMachine::state_value
#MotionStateMachine::states
#MotionStateMachine::transition_to
fn MotionStateMachine::transition_to(self : MotionStateMachine, target : String, now : Double, duration? : Double, curve? : Curve) -> Unit raise MotionErrorStart a transition at an arbitrary transport timestamp.
#MotionStateMachine::transitions
#MotionStateNode
A named scalar state used to model interaction modes and animation poses.
#MotionStateTransition
A directed transition between two named motion states.
#MotionStateTransition::curve
#MotionStateTransition::duration
#MotionStateTransition::from
#MotionStateTransition::to
#MotionTransport
pub struct MotionTransport {
position : Double
speed : Double
status : TransportStatus
direction : PlaybackDirection
range : TransportRange
markers : MarkerTimeline
} derive(Debug)A stateful transport clock for preview, timeline scrubbing, and export.
#MotionTransport::advance
fn MotionTransport::advance(self : MotionTransport, delta_seconds : Double) -> Array[MarkerHit] raise MotionErrorAdvance the clock and return markers crossed by this step.
#MotionTransport::clone_at
#MotionTransport::direction
#MotionTransport::fast_forward
#MotionTransport::is_at_boundary
#MotionTransport::markers
#MotionTransport::new
#MotionTransport::normalized_position
#MotionTransport::seek
#MotionTransport::seek_and_collect
fn MotionTransport::seek_and_collect(self : MotionTransport, position : Double) -> Array[MarkerHit] raise MotionError#MotionTransport::set_direction
#MotionTransport::set_speed
#Path2D
pub struct Path2D {
segments : Array[PathSegment2D]
lengths : Array[Double]
total_length : Double
} derive(Debug)A length-indexed composition of line and cubic path segments.
#Path2D::append
fn Path2D::append(self : Path2D, segment : PathSegment2D, samples_per_curve? : Int) -> Path2D raise MotionError#Path2D::new
fn Path2D::new(segments : Array[PathSegment2D], samples_per_curve? : Int) -> Path2D raise MotionError#Path2D::polyline
#Path2D::project
Approximate the nearest point by scanning each segment's polyline.
#Path2D::sample_by_distance
#PathBuilder2D
Builder for paths constructed from a start point and successive endpoints.
#PathBuilder2D::build
#PathBuilder2D::cubic_to
fn PathBuilder2D::cubic_to(self : PathBuilder2D, control_start : Point2, control_end : Point2, end : Point2) -> Unit#PathSegment2D
Geometric segment types that can be composed into a renderable path.
#PathSegment2D::bounds
#PathSegment2D::polyline
#PlaybackDirection
Direction of a transport clock.
#Point2
Two-dimensional point for UI and 2D media transforms.
#Point2Keyframe
A point keyframe for UI, camera, and sprite motion tracks.
#Point2Track
A validated 2D point track with the same boundary policies as ScalarTrack.
#Point2Track::new
#Point2Track::sample
#Point2Track::sample_many
fn Point2Track::sample_many(self : Point2Track, count : Int, mode? : Extrapolation) -> Array[Point2] raise MotionError#Point3
Three-dimensional point for camera, scene, and 3D keyframe data.
#Point3Keyframe
A 3D keyframe for camera and scene transforms.
#Point3Track
#Point3Track::new
#Point3Track::sample
#Point3Track::sample_many
fn Point3Track::sample_many(self : Point3Track, count : Int, mode? : Extrapolation) -> Array[Point3] raise MotionError#RetimeMap
pub struct RetimeMap {
segments : Array[RetimeSegment]
input_start : Double
input_end : Double
output_start : Double
output_end : Double
} derive(Debug)#RetimeMap::map
Map a source timestamp to presentation time. Gaps clamp to the adjacent
segment, which is deterministic for scrubbing and export.
#RetimeMap::new
#RetimeMap::sample
#RetimeMap::scale_output
#RetimeMap::shift_output
#RetimeMapBuilder
Build a map by appending non-overlapping source and presentation ranges.
#RetimeMapBuilder::add
fn RetimeMapBuilder::add(self : RetimeMapBuilder, segment : RetimeSegment) -> RetimeMapBuilder raise MotionError#RetimeMapBuilder::build
#RetimeSegment
A monotone time remapping segment. Input and output intervals are kept
explicit so media editors can preserve source timestamps while changing
presentation speed.
#RetimeSegment::contains_input
#RetimeSegment::contains_output
#RetimeSegment::derivative
#RetimeSegment::input_duration
#RetimeSegment::output_duration
#Rgba
RGBA color stored in the normalized [0, 1] range.
#RgbaKeyframe
A color keyframe track for gradients, fades, and compositing timelines.
#RgbaTrack
#RgbaTrack::new
fn RgbaTrack::new(frames : Array[RgbaKeyframe], premultiplied? : Bool) -> RgbaTrack raise MotionError#RgbaTrack::sample
#RgbaTrack::sample_many
fn RgbaTrack::sample_many(self : RgbaTrack, count : Int, mode? : Extrapolation) -> Array[Rgba] raise MotionError#SamplePoint
#SamplingConfig
pub struct SamplingConfig {
start : Double
end : Double
frame_rate : Double
include_end : Bool
} derive(Debug)Deterministic sampling window for rendering or offline export.
#SamplingConfig::new
fn SamplingConfig::new(start : Double, end : Double, frame_rate : Double, include_end? : Bool) -> SamplingConfig raise MotionError#ScalarChannel
pub struct ScalarChannel {
name : String
track : ScalarTrack
enabled : Bool
weight : Double
offset : Double
} derive(Debug)A named scalar channel with editor-friendly activation and weighting.
#ScalarChannel::sample
#ScalarChannel::with_enabled
#ScalarChannel::with_offset
fn ScalarChannel::with_offset(self : ScalarChannel, offset : Double) -> ScalarChannel raise MotionError#ScalarChannel::with_weight
fn ScalarChannel::with_weight(self : ScalarChannel, weight : Double) -> ScalarChannel raise MotionError#ScalarTrack
A validated, immutable-at-the-API scalar track.
#ScalarTrack::map_values
fn ScalarTrack::map_values(self : ScalarTrack, mapper : (Double) -> Double) -> ScalarTrack raise MotionErrorTransform values without changing timing or curves.
#ScalarTrack::new
Build a scalar track from strictly increasing keyframes.
#ScalarTrack::sample
Sample at an arbitrary time using the selected boundary policy.
#ScalarTrack::sample_motion
fn ScalarTrack::sample_motion(self : ScalarTrack, time : Double, mode? : Extrapolation) -> MotionSample#ScalarTrack::sample_values
fn ScalarTrack::sample_values(self : ScalarTrack, times : Array[Double], mode? : Extrapolation) -> Array[Double]#ScalarTrack::scale_time
Scale a track's time axis around its first keyframe.
#ScalarTrack::shift
Move a track in time while preserving its segment curves.
#ScalarTrack::trim
fn ScalarTrack::trim(self : ScalarTrack, start : Double, end : Double) -> ScalarTrack raise MotionErrorCopy a time range, adding interpolated boundary frames when needed.
#ScalarTrack::value_range
#ScalarTrack::velocity
Estimate velocity with a central difference that respects track duration.
#ScalarTrack::with_curve
Return a track with a replacement curve on every segment.
#ScalarTrackBundle
pub struct ScalarTrackBundle {
channels : Array[ScalarChannel]
start_time : Double
end_time : Double
} derive(Debug)A group of synchronized scalar tracks for UI properties, camera channels,
or a compact control stream exported to a runtime.
#ScalarTrackBundle::channels
#ScalarTrackBundle::duration
#ScalarTrackBundle::end_time
#ScalarTrackBundle::find
#ScalarTrackBundle::new
#ScalarTrackBundle::sample
fn ScalarTrackBundle::sample(self : ScalarTrackBundle, time : Double, mode? : Extrapolation) -> BundleSample#ScalarTrackBundle::sample_many
fn ScalarTrackBundle::sample_many(self : ScalarTrackBundle, count : Int, mode? : Extrapolation) -> Array[BundleSample] raise MotionError#ScalarTrackBundle::set_enabled
fn ScalarTrackBundle::set_enabled(self : ScalarTrackBundle, name : String, enabled : Bool) -> ScalarTrackBundle raise MotionError#ScalarTrackBundle::set_weight
fn ScalarTrackBundle::set_weight(self : ScalarTrackBundle, name : String, weight : Double) -> ScalarTrackBundle raise MotionError#ScalarTrackBundle::start_time
#ScalarTrackBundle::with_channel
fn ScalarTrackBundle::with_channel(self : ScalarTrackBundle, channel : ScalarChannel) -> ScalarTrackBundle raise MotionError#ScalarTrackBundle::without
fn ScalarTrackBundle::without(self : ScalarTrackBundle, name : String) -> ScalarTrackBundle raise MotionError#ScalarTrackBundleBuilder
#ScalarTrackBundleBuilder::add
fn ScalarTrackBundleBuilder::add(self : ScalarTrackBundleBuilder, channel : ScalarChannel) -> ScalarTrackBundleBuilder raise MotionError#ScalarTrackBundleBuilder::build
fn ScalarTrackBundleBuilder::build(self : ScalarTrackBundleBuilder) -> ScalarTrackBundle raise MotionError#ScalarTrackBundleBuilder::length
#ScalarTrackBundleBuilder::remove
#SequenceBuilder
A mutable composition helper used by editors and importers.
#SequenceBuilder::build
#SequenceBuilder::remove_at
#SequenceSample
pub(all) struct SequenceSample {
time : Double
value : Double
index : Int
progress : Double
state : SequenceState
} derive(Debug)A sample from a TweenSequence, including the active segment index.
#SequenceState
Lifecycle state for a serial composition of scalar tweens.
#Spline2D
A Catmull-Rom spline over 2D control points.
tension=0 is the standard centripetal-free Catmull-Rom form. The
closed option connects the last control point back to the first one.
#Spline2D::new
fn Spline2D::new(points : Array[Point2], tension? : Double, closed? : Bool) -> Spline2D raise MotionError#Spline2D::polyline
#Spline2D::project
fn Spline2D::project(self : Spline2D, target : Point2, samples_per_segment? : Int) -> SplineProjectionFind the closest sampled point to a target, returning an approximate
normalized parameter and the actual point on the spline.
#Spline2D::sample_by_distance
#Spline2D::sample_many
#Spline3D
A Catmull-Rom spline over 3D control points for camera and scene motion.
#Spline3D::new
fn Spline3D::new(points : Array[Point3], tension? : Double, closed? : Bool) -> Spline3D raise MotionError#Spline3D::polyline
#Spline3D::sample_by_distance
#Spline3D::sample_many
#SplineProjection
A normalized projection on a spline, useful for path-following cameras.
#SpringSpec
pub struct SpringSpec {
stiffness : Double
damping : Double
mass : Double
initial_velocity : Double
} derive(Debug)Physical parameters for a damped spring response.
#SpringSpec::is_settled
fn SpringSpec::is_settled(self : SpringSpec, start : Double, end : Double, time : Double, tolerance? : Double) -> Bool#SpringSpec::sample
fn SpringSpec::sample(self : SpringSpec, start : Double, end : Double, time : Double) -> MotionSample#SpringSpec::sample_many
fn SpringSpec::sample_many(self : SpringSpec, start : Double, end : Double, duration : Double, count : Int) -> Array[MotionSample] raise MotionError#SpringSpec::settle_time
#SpringSpec::value_at
Spring position for a unit step from start to end.
#SpringSpec::velocity_at
fn SpringSpec::velocity_at(self : SpringSpec, start : Double, end : Double, time : Double) -> Double#Tempo
Beat-based timing helper for music and rhythm-driven interactions.
#TimeWarp
A normalized time remapping used by editors and media exporters.
#TimeWarp::new
fn TimeWarp::new(curve : Curve, start : Double, end : Double, speed? : Double) -> TimeWarp raise MotionError#Timeline
A deterministic collection of named scalar tracks.
#Timeline::sample
Sample every enabled track at a timeline coordinate.
#Timeline::sample_window
fn Timeline::sample_window(self : Timeline, config : SamplingConfig, mode? : Extrapolation) -> Array[Array[TimelineValue]]Sample a timeline on a deterministic export grid.
#Timeline::set_enabled
#TimelineValue
#TrackBuilder
A mutable builder useful for editors that add frames interactively.
#TrackBuilder::build
#TrackBuilder::remove_at
#TrackBuilder::replace
#TrackSlot
pub struct TrackSlot {
name : String
track : ScalarTrack
offset : Double
enabled : Bool
} derive(Debug)A named scalar track placed on a shared media timeline.
#Transform2D
2D affine transform represented as translation, scale, rotation and skew.
#TransformKeyframe
A transform track that interpolates translation, scale, rotation, and skew.
#TransformTrack
pub struct TransformTrack {
frames : Array[TransformKeyframe]
shortest_rotation : Bool
} derive(Debug)#TransformTrack::keyframes
#TransformTrack::new
fn TransformTrack::new(frames : Array[TransformKeyframe], shortest_rotation? : Bool) -> TransformTrack raise MotionError#TransformTrack::sample
fn TransformTrack::sample(self : TransformTrack, time : Double, mode? : Extrapolation) -> Transform2D#TransformTrack::sample_many
fn TransformTrack::sample_many(self : TransformTrack, count : Int, mode? : Extrapolation) -> Array[Transform2D] raise MotionError#TransportFrame
A fixed-rate export iterator that emits frame times and marker events.
#TransportFrame::marker_hits
#TransportRange
A transport window with explicit in/out points for media scrubbing.
#TransportRange::clamp
#TransportRange::contains
#TransportRange::normalized
#TransportStatus
#Tween
pub struct Tween {
from : Double
to : Double
duration : Double
delay : Double
repeat_count : Int
mode : Extrapolation
curve : Curve
} derive(Debug)A scalar tween with delay, repeats, and optional ping-pong direction.
#Tween::new
fn Tween::new(from : Double, to : Double, duration : Double, delay? : Double, repeat_count? : Int, mode? : Extrapolation, curve? : Curve) -> Tween raise MotionError#Tween::sample
Sample a tween at wall-clock time. Time and duration use the same units.
#Tween::sample_many
#TweenSample
pub(all) struct TweenSample {
time : Double
value : Double
progress : Double
cycle : Int
state : TweenState
} derive(Debug)A value sample with enough metadata for a renderer or UI state machine.
#TweenSequence
A serial composition of Tweens with optional gaps between segments.
#TweenSequence::new
#TweenSequence::sample
Sample the sequence in wall-clock time. A gap holds the previous value.
#TweenSequence::sample_many
fn TweenSequence::sample_many(self : TweenSequence, count : Int) -> Array[SequenceSample] raise MotionError#TweenSequence::value_at
#TweenState
Lifecycle state of a tween sample.
#adaptive_sample
fn adaptive_sample(func : (Double) -> Double, start : Double, end : Double, config : AdaptiveSamplingConfig) -> AdaptiveSampleResult raise MotionErrorRecursively sample a scalar curve where curvature exceeds a tolerance.
#adaptive_sample_tween
fn adaptive_sample_tween(tween : Tween, start : Double, end : Double, config : AdaptiveSamplingConfig) -> AdaptiveSampleResult raise MotionError#all_easings
Enumerate the built-ins in a stable order for editors and documentation.
#analyze_easing
Inspect an arbitrary easing function using a fixed normalized grid.
#back_in
fn back_in(t : Double, overshoot? : Double) -> DoubleBack easing with configurable overshoot.
#bezier_clamped
Construct a curve while clamping its x controls to the CSS-valid range.
#blend
fn blend(first : (Double) -> Double, second : (Double) -> Double, amount~ : Double) -> ((Double) -> Double)Blend two curves with an amount in the closed interval [0, 1].
#blend_bundles
fn blend_bundles(first : ScalarTrackBundle, second : ScalarTrackBundle, amount : Double) -> ScalarTrackBundle raise MotionErrorBlend two bundles by channel name. Missing channels are carried through
from the bundle that contains them.
#blend_values
#bounce_out
fn bounce_out(t : Double) -> DoublePiecewise quadratic bounce used for UI and game motion.
#catmull_rom
fn catmull_rom(previous : Double, start : Double, end : Double, next : Double, t : Double, tension? : Double) -> DoubleCatmull-Rom interpolation across four scalar samples.
#catmull_rom_array
Cubic interpolation over a value array using clamped endpoint samples.
#catmull_rom_point2
#catmull_rom_point3
#classify_monotonicity
#compose
fn compose(outer : (Double) -> Double, inner : (Double) -> Double) -> ((Double) -> Double)Compose two curves. outer(inner(t)) is evaluated without intermediate arrays.
#compose_retime
fn compose_retime(first : RetimeMap, second : RetimeMap, samples_per_segment? : Int) -> RetimeMap raise MotionError#convolve_signal
Convolve a signal with a finite kernel, using edge replication.
#critically_damped_step
fn critically_damped_step(current : Double, target : Double, velocity : Double, response : Double, delta_time : Double) -> (Double, Double)#cubic_in_out
fn cubic_in_out(t : Double) -> DoubleCubic acceleration followed by deceleration.
#cubic_path2d
fn cubic_path2d(start : Point2, control_start : Point2, control_end : Point2, end : Point2) -> CubicPath2D#curve_lookup
fn curve_lookup(func : (Double) -> Double, start : Double, end : Double, count : Int) -> Array[SamplePoint] raise MotionErrorGenerate a lookup table with an explicit endpoint policy.
#decimate_samples
Downsample a sample array by keeping every nth frame and preserving the end.
#derivative_of
fn derivative_of(func : (Double) -> Double, t : Double, step? : Double) -> DoubleNumerically estimate a first derivative without allocating a sample buffer.
#differentiate
First difference of a sampled signal with an explicit time step.
#differentiate_signal
Differentiate a signal using central differences in the interior.
#easing
Return a first-class easing function for use in a sampler or a custom blend.
#elastic_in
fn elastic_in(t : Double, amplitude? : Double, period? : Double) -> DoubleElastic acceleration. Amplitude and period are normalized motion controls.
#enforce_monotonic
#first_crossing
Find the first time at which a sorted curve reaches a target value.
#gradient_stop
#hermite
fn hermite(start : Double, end : Double, tangent_start : Double, tangent_end : Double, t : Double) -> DoubleCubic Hermite interpolation. Tangents use the same units as values.
#integrate_analyzed_curve
Estimate the signed area under a curve using the trapezoidal rule.
#integrate_curve
fn integrate_curve(func : (Double) -> Double, samples : Int) -> DoubleIntegrate a normalized curve with the trapezoid rule.
#integrate_samples
Approximate the integral of a sampled scalar signal with trapezoids.
#interpolate_angle
fn interpolate_angle(start : Double, end : Double, t : Double) -> DoubleInterpolate an angle in radians along the shortest path.
#interpolate_rgba
Interpolate straight in RGBA space, optionally preserving premultiplied alpha.
#interpolate_samples
Linear interpolation over a sorted adaptive sample.
#interpolate_scalar
fn interpolate_scalar(start : Double, end : Double, t : Double) -> DoubleScalar interpolation primitive.
#interpolate_transform
fn interpolate_transform(start : Transform2D, end : Transform2D, t : Double, shortest_rotation? : Bool) -> Transform2D#keyframe
#local_maxima
fn local_maxima(samples : Array[SamplePoint], prominence : Double) -> Array[SamplePoint] raise MotionErrorKeep local maxima with a configurable minimum prominence.
#lookup_value
Evaluate a table with linear interpolation and clamped boundaries.
#low_pass_signal
Apply a first-order exponential low-pass filter.
#map_curve_range
fn map_curve_range(samples : Array[SamplePoint], output_min : Double, output_max : Double) -> Array[SamplePoint]Compose a source curve with an output range.
#marker
#marker_cursor
#marker_sequence
fn marker_sequence(names : Array[String], start : Double, interval : Double) -> MarkerTimeline raise MotionErrorBuild a timeline from a regular sequence of marker names.
#maximum_sample_error
Return the largest absolute error between two aligned sample arrays.
#mirror
fn mirror(ease : (Double) -> Double) -> ((Double) -> Double)Reflect a curve around the center point, useful for reversible UI motion.
#monotone_envelope
Clamp a signal to a monotone non-decreasing envelope.
#motion_clip
fn motion_clip(name : String, track : ScalarTrack, markers? : MarkerTimeline, loop_mode? : ClipLoopMode) -> MotionClip raise MotionError#motion_profile
fn motion_profile(func : (Double) -> Double, samples : Int) -> Array[MotionSample] raise MotionErrorProduce value, velocity, and acceleration samples for a normalized curve.
#motion_state
#motion_transition
fn motion_transition(from : String, to : String, duration : Double, curve? : Curve) -> MotionStateTransition raise MotionError#moving_average
Moving-average smoothing for an already sampled scalar signal.
#normalize_samples
Normalize a signal to [0, 1]. Constant signals map to zero.
#path_cubic
fn path_cubic(start : Point2, control_start : Point2, control_end : Point2, end : Point2) -> PathSegment2D#percentile
Compute a percentile value from a copied and sorted scalar array.
#point2_dot
Dot product for planar tangent and normal calculations.
#point2_keyframe
fn point2_keyframe(time : Double, value~ : Point2, curve? : Curve) -> Point2Keyframe raise MotionError#point2_lerp_clamped
#point3_keyframe
fn point3_keyframe(time : Double, value~ : Point3, curve? : Curve) -> Point3Keyframe raise MotionError#point3_lerp_clamped
#polynomial_in
fn polynomial_in(t : Double, exponent~ : Double) -> DoublePolynomial easing with a caller-selected exponent.
#quad_in_out
fn quad_in_out(t : Double) -> DoubleQuadratic acceleration followed by deceleration.
#quart_in_out
fn quart_in_out(t : Double) -> DoubleQuartic acceleration followed by deceleration.
#quint_in_out
fn quint_in_out(t : Double) -> DoubleQuintic acceleration followed by deceleration.
#remap_value
fn remap_value(value : Double, source_min : Double, source_max : Double, target_min : Double, target_max : Double) -> Double#resample_adaptive
fn resample_adaptive(result : AdaptiveSampleResult, count : Int) -> Array[SamplePoint] raise MotionErrorResample an adaptive result at a fixed number of output points.
#resample_signal
Resample at a new step while preserving the signal's time span.
#rescale_time
#retime_linear
fn retime_linear(input_start : Double, input_end : Double, output_start : Double, output_end : Double) -> RetimeMap raise MotionError#retime_segment
fn retime_segment(input_start : Double, input_end : Double, output_start : Double, output_end : Double, curve? : Curve) -> RetimeSegment raise MotionError#reverse_samples
Reverse the time direction while preserving the original sample order in
the returned array, making it convenient for playback direction toggles.
#rgba_keyframe
#sample_function
fn sample_function(func : (Double) -> Double, start : Double, end : Double, count : Int) -> Array[SamplePoint] raise MotionErrorSample a function on a uniform grid. This is useful for waveform and curve previews.
#sample_track
fn sample_track(track : ScalarTrack, config : SamplingConfig, mode? : Extrapolation) -> Array[SamplePoint]#scalar_channel
fn scalar_channel(name : String, track : ScalarTrack, enabled? : Bool, weight? : Double, offset? : Double) -> ScalarChannel raise MotionError#scale_markers
Return a copy with marker times scaled around the origin.
#sequence_item
fn sequence_item(clip : MotionClip, start : Double, weight? : Double) -> ClipSequenceItem raise MotionError#shift_markers
Return a copy with all marker times shifted by an offset.
#simplify_samples
fn simplify_samples(samples : Array[SamplePoint], tolerance : Double) -> Array[SamplePoint] raise MotionErrorRemove samples that are within a scalar tolerance of their chord.
#smooth_damp
fn smooth_damp(current : Double, target : Double, velocity : Double, smooth_time : Double, delta_time : Double) -> (Double, Double)#smooth_signal
Create a centered moving average; edge windows are shortened rather than
padded, avoiding artificial impulses at clip boundaries.
#soft_limit
fn soft_limit(value : Double, minimum : Double, maximum : Double, softness : Double) -> DoubleApply a soft saturation instead of a hard clamp near both bounds.
#spring_spec
fn spring_spec(stiffness : Double, damping : Double, mass? : Double, initial_velocity? : Double) -> SpringSpec raise MotionError#threshold_crossings
fn threshold_crossings(samples : Array[SamplePoint], threshold : Double) -> Array[Double] raise MotionErrorFind crossings of a scalar threshold, using linear interpolation in each span.
#total_variation
Estimate total variation, which is useful for quantizing a motion signal.
#track_slot
#transform2d
fn transform2d(position~ : Point2, scale~ : Point2, rotation~ : Double, skew? : Double) -> Transform2D#transform_keyframe
fn transform_keyframe(time : Double, value~ : Transform2D, curve? : Curve) -> TransformKeyframe raise MotionError#transport_frame_count
#transport_frames
fn transport_frames(range : TransportRange, frame_rate : Double, markers? : MarkerTimeline) -> Array[TransportFrame] raise MotionError#transport_range
#transport_time_at_frame
Source Files
- adaptive_sampling.mbt
- bezier.mbt
- bezier_ops.mbt
- color_gradient.mbt
- color_space.mbt
- curve_analysis.mbt
- curve_pipeline.mbt
- diagnostics.mbt
- easing_bounce.mbt
- easing_derivatives.mbt
- easing_math.mbt
- easing_overshoot.mbt
- easing_polynomial.mbt
- easing_registry.mbt
- easing_special.mbt
- easing_types.mbt
- errors.mbt
- interpolate.mbt
- interpolate_types.mbt
- keyframe_track.mbt
- keyframe_types.mbt
- motion_clip.mbt
- motion_constraints.mbt
- motion_markers.mbt
- motion_math.mbt
- motion_state_machine.mbt
- motion_transport.mbt
- path.mbt
- path_geometry.mbt
- quantize.mbt
- retime_map.mbt
- sample_filters.mbt
- sampling.mbt
- sequence.mbt
- signal_processing.mbt
- spline.mbt
- spring.mbt
- time_warp.mbt
- timeline.mbt
- track_advanced.mbt
- track_bundle.mbt
- tween.mbt
- typed_tracks.mbt
A dependency-free MoonBit motion toolkit for media timelines, easing curves, cubic Bezier inversion, and scalar keyframes.
animationeasingtweenbezierkeyframemedia
0.1.0
MIT
Updated 4 hours ago
2 downloads