# CubicSegment A cubic bezier segment of a path. ## Constructors CubicSegment(s,cs,ce,e)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment) Constructs a cubic segment. `s` `[Vec](https://cuttle.xyz/learn/reference/Vec)` `cs` `[Vec](https://cuttle.xyz/learn/reference/Vec)` `ce` `[Vec](https://cuttle.xyz/learn/reference/Vec)` `e` `[Vec](https://cuttle.xyz/learn/reference/Vec)` CubicSegment.fromAnchors(startAnchor,endAnchor)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment) Constructs a cubic segment from two anchors. The `handleOut` of `startAnchor` and `handleIn` of `endAnchor` will be used, but the other handles will be ignored. `startAnchor` `[Anchor](https://cuttle.xyz/learn/reference/Anchor)` The first anchor of the segment `endAnchor` `[Anchor](https://cuttle.xyz/learn/reference/Anchor)` The second anchor of the segment CubicSegment.fromLineSegment(segment)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment) Constructs a cubic segment from a line segment. The control points of the cubic segment are calculated such that they lie on the line segment between `segment.s` and `segment.e`, evenly spaced in time at 1/3, 2/3, and 1 respectively. This keeps the segment linear with a constant derivative. `segment` `[LineSegment](https://cuttle.xyz/learn/reference/LineSegment)` A line segment to convert into a cubic segment ## Properties .s[Vec](https://cuttle.xyz/learn/reference/Vec) The start position .cs[Vec](https://cuttle.xyz/learn/reference/Vec) The first cubic "handle" position .ce[Vec](https://cuttle.xyz/learn/reference/Vec) The second cubic "handle" position .e[Vec](https://cuttle.xyz/learn/reference/Vec) The end position ## Methods .isLinear()→boolean Returns `true` if this segment is linear. A cubic segment is linear if its control points lie on the line segment between its start and end points, and they are evenly spaced. .isStraight(tolerance)→boolean `tolerance` `number` `GEOMETRIC_TOLERANCE` Returns `true` if this segment is straight. A cubic segment is straight if its control points lie on the line segment between its start and end points. .equals(segment)→boolean `segment` `[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)` Another cubic segment Returns `true` if this segment is exactly equal to `segment`. .copy(segment)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)chainable Sets the positions of this segments so that it equals `segment`. `segment` `[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)` .mix(segment,t)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)chainable Linearly interpolates this segment's control points to `segment`'s control points by the mixing factor `t`. `segment` `[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)` The cubic segment to interpolate to. `t` `number` The mixing factor between 0 and 1. .setFromAnchors(startAnchor,endAnchor)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)chainable Sets the positions of this segment from two anchors. `startAnchor` `[Anchor](https://cuttle.xyz/learn/reference/Anchor)` The first anchor `endAnchor` `[Anchor](https://cuttle.xyz/learn/reference/Anchor)` The second anchor .length()→number Returns the approximate arc length of the segment. .timeAtDistance(distance)→number `distance` `number` A positive distance Returns the approximate time at `distance` along the segment. If `distance` is greater than the length of the segment, this will return 1. Negative distances will return 0. .distanceAtTime(time)→number `time` `number` A segment time between 0 and 1 Returns the approximate distance along the segment at `time`. .positionAtTime(time)→[Vec](https://cuttle.xyz/learn/reference/Vec) `time` `number` A segment time between 0 and 1 Returns the position on the segment at `time`. .derivativeAtTime(time)→[Vec](https://cuttle.xyz/learn/reference/Vec) `time` `number` A segment time between 0 and 1 Returns the first derivative of the segment at `time`. The first derivative can also be thought of as the "velocity" of a point moving along the curve. .secondDerivativeAtTime(time)→[Vec](https://cuttle.xyz/learn/reference/Vec) `time` `number` A segment time between 0 and 1 Returns the second derivative of the segment at `time`. The second derivative can also be thought of as the "acceleration", or change in velocity of a point moving along the curve. .curvatureAtTime(time)→number `time` `number` A segment time between 0 and 1 Returns the curvature of the segment at `time`. Curvature describes how "bent" a segment is at a given point. It can be thought of as the reciprocal of the radius of a circle with the same curvature. To find the radius, one can use the formula `1 / curvature`. .tangentAtTime(time)→[Vec](https://cuttle.xyz/learn/reference/Vec) `time` `number` A segment time between 0 and 1 Returns a unit-length vector tangent to the segment at `time`. .normalAtTime(time)→[Vec](https://cuttle.xyz/learn/reference/Vec) `time` `number` A segment time between 0 and 1 Returns a unit-length vector perpendicular to the segment at `time`. .slice(startTime,endTime)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment) `startTime` `number` A segment time between 0 and 1 `endTime` `number` A segment time between 0 and 1 greater than `startTime` Returns A new cubic segment that is the subset of the segment between `startTime` and `endTime`. .splitAtTime(time)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)\[\] Splits the segment at a specific `time`. `time` `number` A segment time between 0 and 1 Returns two cubic segments. ## Methods inherited from [Geometry](https://cuttle.xyz/learn/reference/Geometry) .clone()→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment) Clone is useful when you need to make a change to geometry without changing the original. ``` const transformedPath = path.clone().transform({ rotation: 45 }); ``` Returns A deep copy of this geometry .isValid()→boolean Returns `true` if this geometry is valid, or `false` otherwise. .affineTransform(affineMatrix)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)chainable Spatially transforms this geometry by an affine transformation matrix. Affine matrices can represent any 2-dimensional transformation that keeps lines parallel. `affineMatrix` `[AffineMatrix](https://cuttle.xyz/learn/reference/AffineMatrix)` .affineTransformWithoutTranslation(affineMatrix)→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)chainable Spatially transforms this geometry by an affine transformation matrix, excluding translation. Only rotation, scale, and skew transformations will be applied. `affineMatrix` `[AffineMatrix](https://cuttle.xyz/learn/reference/AffineMatrix)` .reverse()→[CubicSegment](https://cuttle.xyz/learn/reference/CubicSegment)chainable Reverses this cubic segment. Swaps the start and end points of the segment as well as their corresponding control points. .closestPoint(point,areaOfInterest)→([ClosestPointResultWithTime](https://cuttle.xyz/learn/reference/interfaces#ClosestPointResultWithTime) | undefined) `point` `[Vec](https://cuttle.xyz/learn/reference/Vec)` The target point `areaOfInterest` `[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox)` optional If supplied, only results inside this bounding box will be returned. This can save a lot of computation if you only need to find closest points within a small area. Typically `areaOfInterest` is centered on `point`, but this isn't required. Returns The closest point to `point` that lies on this geometry, or `undefined` if no point is found. .boundingBox()→[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox) Returns the smallest axis-aligned bounding box that contains this geometry. .looseBoundingBox()→[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox) The loose bounding box may not be the smallest possible, but it's usually cheaper to compute. Use this when the exact bounding box isn't required. Returns an axis-aligned bounding box that contains this geometry. .isContainedByBoundingBox(box)→boolean Geometry is contained by a bounding box if no part of it lies beyond it's minimum and maximum. `box` `[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox)` .isIntersectedByBoundingBox(box)→boolean Geometry intersects a bounding box if part of the geometry crosses the boundary between the inside and outside of the box. `box` `[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox)` .isOverlappedByBoundingBox(box)→boolean Geometry is overlapped by a bounding box if a point can be chosen that is indside both the geometry and the box. Geometry is overlapped by a bounding box if it's contained inside, or intersected by it. `box` `[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox)` .isValid(a)→ `a` `unknown` Returns `true` if `geom` is valid geometry .transform(transform)→thischainable Transforms this geometry. A transform can optionally specify any of `position`, `rotation`, `scale`, `skew` and `origin`. `origin` defines the center (in pre-transform coordinates) of the transformation for `rotation`, `scale` and `skew`. ``` // Simple translation geometry.translate({ position: Vec(1, 0), }); // Rotation and scale geometry.transform({ rotation: 45, scale: 2, }); // Complicated transform geometry.transform({ position: Vec(1, 1), rotation: 180, scale: Vec(2, 1), skew: 45, origin: Vec(-0.5, 0.5), }; ``` `transform` `[TransformArgs](https://cuttle.xyz/learn/reference/interfaces#TransformArgs)` .intersectionsWith(geometries,areaOfInterest)→[IntersectionResult](https://cuttle.xyz/learn/reference/interfaces#IntersectionResult)\[\] `geometries` `[Geometry](https://cuttle.xyz/learn/reference/Geometry)[]` An array of geometries to intersect with. `areaOfInterest` `[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox)` optional If supplied, only intersection results inside this bounding box will be returned. This can save a lot of computation if you only need to find intersections within a small area. Returns An array of intersections between this geometry and `geometries` .overlapsWith(geometries,areaOfInterest,tolerance)→[OverlapResult](https://cuttle.xyz/learn/reference/OverlapResult)\[\] `geometries` `[Geometry](https://cuttle.xyz/learn/reference/Geometry)[]` An array of geometries to find overlaps with. `areaOfInterest` `[BoundingBox](https://cuttle.xyz/learn/reference/BoundingBox)` optional If supplied, input geometry will be filtered so that only parts that intersect this bounding box will be tested. This can save a lot of time if only need to find overlaps within a small area. `tolerance` `number` optional The maximum distance apart two segments can be to be considered overlapping. Returns An array of overlaps between this geometry and `geometries` .distanceToIntersect(targetGeometry,direction,options)→(number | undefined) `targetGeometry` `[Geometry](https://cuttle.xyz/learn/reference/Geometry)` The geometry to move toward. `direction` `[Vec](https://cuttle.xyz/learn/reference/Vec)` The direction to move in. This should point towards the target geometry, otherwise no intersection may be found. `options` `[DistanceToIntersectOptions](https://cuttle.xyz/learn/reference/interfaces#DistanceToIntersectOptions)` optional Returns approximately the smallest distance to move until this geometry intersects the target geometry. If `minOverlap` is specified, the distance to move until the geometry overlaps by some minimum width will be returned instead. Returns `undefined` if no intersection is found.