| 1 |
- {"ast":null,"code":"import { Clamp, WithinEpsilon } from \"./math.scalar.functions.js\";\nimport { Vector2, Vector3, Quaternion, Matrix } from \"./math.vector.js\";\nimport { Epsilon } from \"./math.constants.js\";\n/**\n * Defines potential orientation for back face culling\n */\nexport var Orientation;\n(function (Orientation) {\n /**\n * Clockwise\n */\n Orientation[Orientation[\"CW\"] = 0] = \"CW\";\n /** Counter clockwise */\n Orientation[Orientation[\"CCW\"] = 1] = \"CCW\";\n})(Orientation || (Orientation = {}));\n/** Class used to represent a Bezier curve */\nexport class BezierCurve {\n /**\n * Returns the cubic Bezier interpolated value (float) at \"t\" (float) from the given x1, y1, x2, y2 floats\n * @param t defines the time\n * @param x1 defines the left coordinate on X axis\n * @param y1 defines the left coordinate on Y axis\n * @param x2 defines the right coordinate on X axis\n * @param y2 defines the right coordinate on Y axis\n * @returns the interpolated value\n */\n static Interpolate(t, x1, y1, x2, y2) {\n // Extract X (which is equal to time here)\n const f0 = 1 - 3 * x2 + 3 * x1;\n const f1 = 3 * x2 - 6 * x1;\n const f2 = 3 * x1;\n let refinedT = t;\n for (let i = 0; i < 5; i++) {\n const refinedT2 = refinedT * refinedT;\n const refinedT3 = refinedT2 * refinedT;\n const x = f0 * refinedT3 + f1 * refinedT2 + f2 * refinedT;\n const slope = 1.0 / (3.0 * f0 * refinedT2 + 2.0 * f1 * refinedT + f2);\n refinedT -= (x - t) * slope;\n refinedT = Math.min(1, Math.max(0, refinedT));\n }\n // Resolve cubic bezier for the given x\n return 3 * Math.pow(1 - refinedT, 2) * refinedT * y1 + 3 * (1 - refinedT) * Math.pow(refinedT, 2) * y2 + Math.pow(refinedT, 3);\n }\n}\n/**\n * Defines angle representation\n */\nexport class Angle {\n /**\n * Creates an Angle object of \"radians\" radians (float).\n * @param radians the angle in radians\n */\n constructor(radians) {\n this._radians = radians;\n if (this._radians < 0.0) {\n this._radians += 2.0 * Math.PI;\n }\n }\n /**\n * Get value in degrees\n * @returns the Angle value in degrees (float)\n */\n degrees() {\n return this._radians * 180.0 / Math.PI;\n }\n /**\n * Get value in radians\n * @returns the Angle value in radians (float)\n */\n radians() {\n return this._radians;\n }\n /**\n * Gets a new Angle object with a value of the angle (in radians) between the line connecting the two points and the x-axis\n * @param a defines first point as the origin\n * @param b defines point\n * @returns a new Angle\n */\n static BetweenTwoPoints(a, b) {\n const delta = b.subtract(a);\n const theta = Math.atan2(delta.y, delta.x);\n return new Angle(theta);\n }\n /**\n * Gets the angle between the two vectors\n * @param a defines first vector\n * @param b defines vector\n * @returns Returns an new Angle between 0 and PI\n */\n static BetweenTwoVectors(a, b) {\n let product = a.lengthSquared() * b.lengthSquared();\n if (product === 0) return new Angle(Math.PI / 2);\n product = Math.sqrt(product);\n let cosVal = a.dot(b) / product;\n cosVal = Clamp(cosVal, -1, 1);\n const angle = Math.acos(cosVal);\n return new Angle(angle);\n }\n /**\n * Gets a new Angle object from the given float in radians\n * @param radians defines the angle value in radians\n * @returns a new Angle\n */\n static FromRadians(radians) {\n return new Angle(radians);\n }\n /**\n * Gets a new Angle object from the given float in degrees\n * @param degrees defines the angle value in degrees\n * @returns a new Angle\n */\n static FromDegrees(degrees) {\n return new Angle(degrees * Math.PI / 180.0);\n }\n}\n/**\n * This represents an arc in a 2d space.\n */\nexport class Arc2 {\n /**\n * Creates an Arc object from the three given points : start, middle and end.\n * @param startPoint Defines the start point of the arc\n * @param midPoint Defines the middle point of the arc\n * @param endPoint Defines the end point of the arc\n */\n constructor( /** Defines the start point of the arc */\n startPoint, /** Defines the mid point of the arc */\n midPoint, /** Defines the end point of the arc */\n endPoint) {\n this.startPoint = startPoint;\n this.midPoint = midPoint;\n this.endPoint = endPoint;\n const temp = Math.pow(midPoint.x, 2) + Math.pow(midPoint.y, 2);\n const startToMid = (Math.pow(startPoint.x, 2) + Math.pow(startPoint.y, 2) - temp) / 2;\n const midToEnd = (temp - Math.pow(endPoint.x, 2) - Math.pow(endPoint.y, 2)) / 2;\n const det = (startPoint.x - midPoint.x) * (midPoint.y - endPoint.y) - (midPoint.x - endPoint.x) * (startPoint.y - midPoint.y);\n this.centerPoint = new Vector2((startToMid * (midPoint.y - endPoint.y) - midToEnd * (startPoint.y - midPoint.y)) / det, ((startPoint.x - midPoint.x) * midToEnd - (midPoint.x - endPoint.x) * startToMid) / det);\n this.radius = this.centerPoint.subtract(this.startPoint).length();\n this.startAngle = Angle.BetweenTwoPoints(this.centerPoint, this.startPoint);\n const a1 = this.startAngle.degrees();\n let a2 = Angle.BetweenTwoPoints(this.centerPoint, this.midPoint).degrees();\n let a3 = Angle.BetweenTwoPoints(this.centerPoint, this.endPoint).degrees();\n // angles correction\n if (a2 - a1 > +180.0) {\n a2 -= 360.0;\n }\n if (a2 - a1 < -180.0) {\n a2 += 360.0;\n }\n if (a3 - a2 > +180.0) {\n a3 -= 360.0;\n }\n if (a3 - a2 < -180.0) {\n a3 += 360.0;\n }\n this.orientation = a2 - a1 < 0 ? 0 /* Orientation.CW */ : 1 /* Orientation.CCW */;\n this.angle = Angle.FromDegrees(this.orientation === 0 /* Orientation.CW */ ? a1 - a3 : a3 - a1);\n }\n}\n/**\n * Represents a 2D path made up of multiple 2D points\n */\nexport class Path2 {\n /**\n * Creates a Path2 object from the starting 2D coordinates x and y.\n * @param x the starting points x value\n * @param y the starting points y value\n */\n constructor(x, y) {\n this._points = new Array();\n this._length = 0.0;\n /**\n * If the path start and end point are the same\n */\n this.closed = false;\n this._points.push(new Vector2(x, y));\n }\n /**\n * Adds a new segment until the given coordinates (x, y) to the current Path2.\n * @param x the added points x value\n * @param y the added points y value\n * @returns the updated Path2.\n */\n addLineTo(x, y) {\n if (this.closed) {\n return this;\n }\n const newPoint = new Vector2(x, y);\n const previousPoint = this._points[this._points.length - 1];\n this._points.push(newPoint);\n this._length += newPoint.subtract(previousPoint).length();\n return this;\n }\n /**\n * Adds _numberOfSegments_ segments according to the arc definition (middle point coordinates, end point coordinates, the arc start point being the current Path2 last point) to the current Path2.\n * @param midX middle point x value\n * @param midY middle point y value\n * @param endX end point x value\n * @param endY end point y value\n * @param numberOfSegments (default: 36)\n * @returns the updated Path2.\n */\n addArcTo(midX, midY, endX, endY, numberOfSegments = 36) {\n if (this.closed) {\n return this;\n }\n const startPoint = this._points[this._points.length - 1];\n const midPoint = new Vector2(midX, midY);\n const endPoint = new Vector2(endX, endY);\n const arc = new Arc2(startPoint, midPoint, endPoint);\n let increment = arc.angle.radians() / numberOfSegments;\n if (arc.orientation === 0 /* Orientation.CW */) {\n increment *= -1;\n }\n let currentAngle = arc.startAngle.radians() + increment;\n for (let i = 0; i < numberOfSegments; i++) {\n const x = Math.cos(currentAngle) * arc.radius + arc.centerPoint.x;\n const y = Math.sin(currentAngle) * arc.radius + arc.centerPoint.y;\n this.addLineTo(x, y);\n currentAngle += increment;\n }\n return this;\n }\n /**\n * Adds _numberOfSegments_ segments according to the quadratic curve definition to the current Path2.\n * @param controlX control point x value\n * @param controlY control point y value\n * @param endX end point x value\n * @param endY end point y value\n * @param numberOfSegments (default: 36)\n * @returns the updated Path2.\n */\n addQuadraticCurveTo(controlX, controlY, endX, endY, numberOfSegments = 36) {\n if (this.closed) {\n return this;\n }\n const equation = (t, val0, val1, val2) => {\n const res = (1.0 - t) * (1.0 - t) * val0 + 2.0 * t * (1.0 - t) * val1 + t * t * val2;\n return res;\n };\n const startPoint = this._points[this._points.length - 1];\n for (let i = 0; i <= numberOfSegments; i++) {\n const step = i / numberOfSegments;\n const x = equation(step, startPoint.x, controlX, endX);\n const y = equation(step, startPoint.y, controlY, endY);\n this.addLineTo(x, y);\n }\n return this;\n }\n /**\n * Adds _numberOfSegments_ segments according to the bezier curve definition to the current Path2.\n * @param originTangentX tangent vector at the origin point x value\n * @param originTangentY tangent vector at the origin point y value\n * @param destinationTangentX tangent vector at the destination point x value\n * @param destinationTangentY tangent vector at the destination point y value\n * @param endX end point x value\n * @param endY end point y value\n * @param numberOfSegments (default: 36)\n * @returns the updated Path2.\n */\n addBezierCurveTo(originTangentX, originTangentY, destinationTangentX, destinationTangentY, endX, endY, numberOfSegments = 36) {\n if (this.closed) {\n return this;\n }\n const equation = (t, val0, val1, val2, val3) => {\n const res = (1.0 - t) * (1.0 - t) * (1.0 - t) * val0 + 3.0 * t * (1.0 - t) * (1.0 - t) * val1 + 3.0 * t * t * (1.0 - t) * val2 + t * t * t * val3;\n return res;\n };\n const startPoint = this._points[this._points.length - 1];\n for (let i = 0; i <= numberOfSegments; i++) {\n const step = i / numberOfSegments;\n const x = equation(step, startPoint.x, originTangentX, destinationTangentX, endX);\n const y = equation(step, startPoint.y, originTangentY, destinationTangentY, endY);\n this.addLineTo(x, y);\n }\n return this;\n }\n /**\n * Defines if a given point is inside the polygon defines by the path\n * @param point defines the point to test\n * @returns true if the point is inside\n */\n isPointInside(point) {\n let isInside = false;\n const count = this._points.length;\n for (let p = count - 1, q = 0; q < count; p = q++) {\n let edgeLow = this._points[p];\n let edgeHigh = this._points[q];\n let edgeDx = edgeHigh.x - edgeLow.x;\n let edgeDy = edgeHigh.y - edgeLow.y;\n if (Math.abs(edgeDy) > Number.EPSILON) {\n // Not parallel\n if (edgeDy < 0) {\n edgeLow = this._points[q];\n edgeDx = -edgeDx;\n edgeHigh = this._points[p];\n edgeDy = -edgeDy;\n }\n if (point.y < edgeLow.y || point.y > edgeHigh.y) {\n continue;\n }\n if (point.y === edgeLow.y && point.x === edgeLow.x) {\n return true;\n } else {\n const perpEdge = edgeDy * (point.x - edgeLow.x) - edgeDx * (point.y - edgeLow.y);\n if (perpEdge === 0) {\n return true;\n }\n if (perpEdge < 0) {\n continue;\n }\n isInside = !isInside;\n }\n } else {\n // parallel or collinear\n if (point.y !== edgeLow.y) {\n continue;\n }\n if (edgeHigh.x <= point.x && point.x <= edgeLow.x || edgeLow.x <= point.x && point.x <= edgeHigh.x) {\n return true;\n }\n }\n }\n return isInside;\n }\n /**\n * Closes the Path2.\n * @returns the Path2.\n */\n close() {\n this.closed = true;\n return this;\n }\n /**\n * Gets the sum of the distance between each sequential point in the path\n * @returns the Path2 total length (float).\n */\n length() {\n let result = this._length;\n if (this.closed) {\n const lastPoint = this._points[this._points.length - 1];\n const firstPoint = this._points[0];\n result += firstPoint.subtract(lastPoint).length();\n }\n return result;\n }\n /**\n * Gets the area of the polygon defined by the path\n * @returns area value\n */\n area() {\n const n = this._points.length;\n let value = 0.0;\n for (let p = n - 1, q = 0; q < n; p = q++) {\n value += this._points[p].x * this._points[q].y - this._points[q].x * this._points[p].y;\n }\n return value * 0.5;\n }\n /**\n * Gets the points which construct the path\n * @returns the Path2 internal array of points.\n */\n getPoints() {\n return this._points;\n }\n /**\n * Retrieves the point at the distance aways from the starting point\n * @param normalizedLengthPosition the length along the path to retrieve the point from\n * @returns a new Vector2 located at a percentage of the Path2 total length on this path.\n */\n getPointAtLengthPosition(normalizedLengthPosition) {\n if (normalizedLengthPosition < 0 || normalizedLengthPosition > 1) {\n return Vector2.Zero();\n }\n const lengthPosition = normalizedLengthPosition * this.length();\n let previousOffset = 0;\n for (let i = 0; i < this._points.length; i++) {\n const j = (i + 1) % this._points.length;\n const a = this._points[i];\n const b = this._points[j];\n const bToA = b.subtract(a);\n const nextOffset = bToA.length() + previousOffset;\n if (lengthPosition >= previousOffset && lengthPosition <= nextOffset) {\n const dir = bToA.normalize();\n const localOffset = lengthPosition - previousOffset;\n return new Vector2(a.x + dir.x * localOffset, a.y + dir.y * localOffset);\n }\n previousOffset = nextOffset;\n }\n return Vector2.Zero();\n }\n /**\n * Creates a new path starting from an x and y position\n * @param x starting x value\n * @param y starting y value\n * @returns a new Path2 starting at the coordinates (x, y).\n */\n static StartingAt(x, y) {\n return new Path2(x, y);\n }\n}\n/**\n * Represents a 3D path made up of multiple 3D points\n * @see https://doc.babylonjs.com/features/featuresDeepDive/mesh/path3D\n */\nexport class Path3D {\n /**\n * new Path3D(path, normal, raw)\n * Creates a Path3D. A Path3D is a logical math object, so not a mesh.\n * please read the description in the tutorial : https://doc.babylonjs.com/features/featuresDeepDive/mesh/path3D\n * @param path an array of Vector3, the curve axis of the Path3D\n * @param firstNormal (options) Vector3, the first wanted normal to the curve. Ex (0, 1, 0) for a vertical normal.\n * @param raw (optional, default false) : boolean, if true the returned Path3D isn't normalized. Useful to depict path acceleration or speed.\n * @param alignTangentsWithPath (optional, default false) : boolean, if true the tangents will be aligned with the path.\n */\n constructor(\n /**\n * an array of Vector3, the curve axis of the Path3D\n */\n path, firstNormal = null, raw, alignTangentsWithPath = false) {\n this.path = path;\n this._curve = new Array();\n this._distances = new Array();\n this._tangents = new Array();\n this._normals = new Array();\n this._binormals = new Array();\n // holds interpolated point data\n this._pointAtData = {\n id: 0,\n point: Vector3.Zero(),\n previousPointArrayIndex: 0,\n position: 0,\n subPosition: 0,\n interpolateReady: false,\n interpolationMatrix: Matrix.Identity()\n };\n for (let p = 0; p < path.length; p++) {\n this._curve[p] = path[p].clone(); // hard copy\n }\n this._raw = raw || false;\n this._alignTangentsWithPath = alignTangentsWithPath;\n this._compute(firstNormal, alignTangentsWithPath);\n }\n /**\n * Returns the Path3D array of successive Vector3 designing its curve.\n * @returns the Path3D array of successive Vector3 designing its curve.\n */\n getCurve() {\n return this._curve;\n }\n /**\n * Returns the Path3D array of successive Vector3 designing its curve.\n * @returns the Path3D array of successive Vector3 designing its curve.\n */\n getPoints() {\n return this._curve;\n }\n /**\n * @returns the computed length (float) of the path.\n */\n length() {\n return this._distances[this._distances.length - 1];\n }\n /**\n * Returns an array populated with tangent vectors on each Path3D curve point.\n * @returns an array populated with tangent vectors on each Path3D curve point.\n */\n getTangents() {\n return this._tangents;\n }\n /**\n * Returns an array populated with normal vectors on each Path3D curve point.\n * @returns an array populated with normal vectors on each Path3D curve point.\n */\n getNormals() {\n return this._normals;\n }\n /**\n * Returns an array populated with binormal vectors on each Path3D curve point.\n * @returns an array populated with binormal vectors on each Path3D curve point.\n */\n getBinormals() {\n return this._binormals;\n }\n /**\n * Returns an array populated with distances (float) of the i-th point from the first curve point.\n * @returns an array populated with distances (float) of the i-th point from the first curve point.\n */\n getDistances() {\n return this._distances;\n }\n /**\n * Returns an interpolated point along this path\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @returns a new Vector3 as the point\n */\n getPointAt(position) {\n return this._updatePointAtData(position).point;\n }\n /**\n * Returns the tangent vector of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @param interpolated (optional, default false) : boolean, if true returns an interpolated tangent instead of the tangent of the previous path point.\n * @returns a tangent vector corresponding to the interpolated Path3D curve point, if not interpolated, the tangent is taken from the precomputed tangents array.\n */\n getTangentAt(position, interpolated = false) {\n this._updatePointAtData(position, interpolated);\n return interpolated ? Vector3.TransformCoordinates(Vector3.Forward(), this._pointAtData.interpolationMatrix) : this._tangents[this._pointAtData.previousPointArrayIndex];\n }\n /**\n * Returns the tangent vector of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @param interpolated (optional, default false) : boolean, if true returns an interpolated normal instead of the normal of the previous path point.\n * @returns a normal vector corresponding to the interpolated Path3D curve point, if not interpolated, the normal is taken from the precomputed normals array.\n */\n getNormalAt(position, interpolated = false) {\n this._updatePointAtData(position, interpolated);\n return interpolated ? Vector3.TransformCoordinates(Vector3.Right(), this._pointAtData.interpolationMatrix) : this._normals[this._pointAtData.previousPointArrayIndex];\n }\n /**\n * Returns the binormal vector of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @param interpolated (optional, default false) : boolean, if true returns an interpolated binormal instead of the binormal of the previous path point.\n * @returns a binormal vector corresponding to the interpolated Path3D curve point, if not interpolated, the binormal is taken from the precomputed binormals array.\n */\n getBinormalAt(position, interpolated = false) {\n this._updatePointAtData(position, interpolated);\n return interpolated ? Vector3.TransformCoordinates(Vector3.UpReadOnly, this._pointAtData.interpolationMatrix) : this._binormals[this._pointAtData.previousPointArrayIndex];\n }\n /**\n * Returns the distance (float) of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @returns the distance of the interpolated Path3D curve point at the specified position along this path.\n */\n getDistanceAt(position) {\n return this.length() * position;\n }\n /**\n * Returns the array index of the previous point of an interpolated point along this path\n * @param position the position of the point to interpolate along this path, from 0.0 to 1.0\n * @returns the array index\n */\n getPreviousPointIndexAt(position) {\n this._updatePointAtData(position);\n return this._pointAtData.previousPointArrayIndex;\n }\n /**\n * Returns the position of an interpolated point relative to the two path points it lies between, from 0.0 (point A) to 1.0 (point B)\n * @param position the position of the point to interpolate along this path, from 0.0 to 1.0\n * @returns the sub position\n */\n getSubPositionAt(position) {\n this._updatePointAtData(position);\n return this._pointAtData.subPosition;\n }\n /**\n * Returns the position of the closest virtual point on this path to an arbitrary Vector3, from 0.0 to 1.0\n * @param target the vector of which to get the closest position to\n * @returns the position of the closest virtual point on this path to the target vector\n */\n getClosestPositionTo(target) {\n let smallestDistance = Number.MAX_VALUE;\n let closestPosition = 0.0;\n for (let i = 0; i < this._curve.length - 1; i++) {\n const point = this._curve[i + 0];\n const tangent = this._curve[i + 1].subtract(point).normalize();\n const subLength = this._distances[i + 1] - this._distances[i + 0];\n const subPosition = Math.min(Math.max(Vector3.Dot(tangent, target.subtract(point).normalize()), 0.0) * Vector3.Distance(point, target) / subLength, 1.0);\n const distance = Vector3.Distance(point.add(tangent.scale(subPosition * subLength)), target);\n if (distance < smallestDistance) {\n smallestDistance = distance;\n closestPosition = (this._distances[i + 0] + subLength * subPosition) / this.length();\n }\n }\n return closestPosition;\n }\n /**\n * Returns a sub path (slice) of this path\n * @param start the position of the fist path point, from 0.0 to 1.0, or a negative value, which will get wrapped around from the end of the path to 0.0 to 1.0 values\n * @param end the position of the last path point, from 0.0 to 1.0, or a negative value, which will get wrapped around from the end of the path to 0.0 to 1.0 values\n * @returns a sub path (slice) of this path\n */\n slice(start = 0.0, end = 1.0) {\n if (start < 0.0) {\n start = 1 - start * -1.0 % 1.0;\n }\n if (end < 0.0) {\n end = 1 - end * -1.0 % 1.0;\n }\n if (start > end) {\n const _start = start;\n start = end;\n end = _start;\n }\n const curvePoints = this.getCurve();\n const startPoint = this.getPointAt(start);\n let startIndex = this.getPreviousPointIndexAt(start);\n const endPoint = this.getPointAt(end);\n const endIndex = this.getPreviousPointIndexAt(end) + 1;\n const slicePoints = [];\n if (start !== 0.0) {\n startIndex++;\n slicePoints.push(startPoint);\n }\n slicePoints.push(...curvePoints.slice(startIndex, endIndex));\n if (end !== 1.0 || start === 1.0) {\n slicePoints.push(endPoint);\n }\n return new Path3D(slicePoints, this.getNormalAt(start), this._raw, this._alignTangentsWithPath);\n }\n /**\n * Forces the Path3D tangent, normal, binormal and distance recomputation.\n * @param path path which all values are copied into the curves points\n * @param firstNormal which should be projected onto the curve\n * @param alignTangentsWithPath (optional, default false) : boolean, if true the tangents will be aligned with the path\n * @returns the same object updated.\n */\n update(path, firstNormal = null, alignTangentsWithPath = false) {\n for (let p = 0; p < path.length; p++) {\n this._curve[p].x = path[p].x;\n this._curve[p].y = path[p].y;\n this._curve[p].z = path[p].z;\n }\n this._compute(firstNormal, alignTangentsWithPath);\n return this;\n }\n // private function compute() : computes tangents, normals and binormals\n _compute(firstNormal, alignTangentsWithPath = false) {\n const l = this._curve.length;\n if (l < 2) {\n return;\n }\n // first and last tangents\n this._tangents[0] = this._getFirstNonNullVector(0);\n if (!this._raw) {\n this._tangents[0].normalize();\n }\n this._tangents[l - 1] = this._curve[l - 1].subtract(this._curve[l - 2]);\n if (!this._raw) {\n this._tangents[l - 1].normalize();\n }\n // normals and binormals at first point : arbitrary vector with _normalVector()\n const tg0 = this._tangents[0];\n const pp0 = this._normalVector(tg0, firstNormal);\n this._normals[0] = pp0;\n if (!this._raw) {\n this._normals[0].normalize();\n }\n this._binormals[0] = Vector3.Cross(tg0, this._normals[0]);\n if (!this._raw) {\n this._binormals[0].normalize();\n }\n this._distances[0] = 0.0;\n // normals and binormals : next points\n let prev; // previous vector (segment)\n let cur; // current vector (segment)\n let curTang; // current tangent\n // previous normal\n let prevNor; // previous normal\n let prevBinor; // previous binormal\n for (let i = 1; i < l; i++) {\n // tangents\n prev = this._getLastNonNullVector(i);\n if (i < l - 1) {\n cur = this._getFirstNonNullVector(i);\n this._tangents[i] = alignTangentsWithPath ? cur : prev.add(cur);\n this._tangents[i].normalize();\n }\n this._distances[i] = this._distances[i - 1] + this._curve[i].subtract(this._curve[i - 1]).length();\n // normals and binormals\n // http://www.cs.cmu.edu/afs/andrew/scs/cs/15-462/web/old/asst2camera.html\n curTang = this._tangents[i];\n prevBinor = this._binormals[i - 1];\n this._normals[i] = Vector3.Cross(prevBinor, curTang);\n if (!this._raw) {\n if (this._normals[i].length() === 0) {\n prevNor = this._normals[i - 1];\n this._normals[i] = prevNor.clone();\n } else {\n this._normals[i].normalize();\n }\n }\n this._binormals[i] = Vector3.Cross(curTang, this._normals[i]);\n if (!this._raw) {\n this._binormals[i].normalize();\n }\n }\n this._pointAtData.id = NaN;\n }\n // private function getFirstNonNullVector(index)\n // returns the first non null vector from index : curve[index + N].subtract(curve[index])\n _getFirstNonNullVector(index) {\n let i = 1;\n let nNVector = this._curve[index + i].subtract(this._curve[index]);\n while (nNVector.length() === 0 && index + i + 1 < this._curve.length) {\n i++;\n nNVector = this._curve[index + i].subtract(this._curve[index]);\n }\n return nNVector;\n }\n // private function getLastNonNullVector(index)\n // returns the last non null vector from index : curve[index].subtract(curve[index - N])\n _getLastNonNullVector(index) {\n let i = 1;\n let nLVector = this._curve[index].subtract(this._curve[index - i]);\n while (nLVector.length() === 0 && index > i + 1) {\n i++;\n nLVector = this._curve[index].subtract(this._curve[index - i]);\n }\n return nLVector;\n }\n // private function normalVector(v0, vt, va) :\n // returns an arbitrary point in the plane defined by the point v0 and the vector vt orthogonal to this plane\n // if va is passed, it returns the va projection on the plane orthogonal to vt at the point v0\n _normalVector(vt, va) {\n let normal0;\n let tgl = vt.length();\n if (tgl === 0.0) {\n tgl = 1.0;\n }\n if (va === undefined || va === null) {\n let point;\n if (!WithinEpsilon(Math.abs(vt.y) / tgl, 1.0, Epsilon)) {\n // search for a point in the plane\n point = new Vector3(0.0, -1.0, 0.0);\n } else if (!WithinEpsilon(Math.abs(vt.x) / tgl, 1.0, Epsilon)) {\n point = new Vector3(1.0, 0.0, 0.0);\n } else if (!WithinEpsilon(Math.abs(vt.z) / tgl, 1.0, Epsilon)) {\n point = new Vector3(0.0, 0.0, 1.0);\n } else {\n point = Vector3.Zero();\n }\n normal0 = Vector3.Cross(vt, point);\n } else {\n normal0 = Vector3.Cross(vt, va);\n Vector3.CrossToRef(normal0, vt, normal0);\n }\n normal0.normalize();\n return normal0;\n }\n /**\n * Updates the point at data for an interpolated point along this curve\n * @param position the position of the point along this curve, from 0.0 to 1.0\n * @param interpolateTNB\n * @interpolateTNB whether to compute the interpolated tangent, normal and binormal\n * @returns the (updated) point at data\n */\n _updatePointAtData(position, interpolateTNB = false) {\n // set an id for caching the result\n if (this._pointAtData.id === position) {\n if (!this._pointAtData.interpolateReady) {\n this._updateInterpolationMatrix();\n }\n return this._pointAtData;\n } else {\n this._pointAtData.id = position;\n }\n const curvePoints = this.getPoints();\n // clamp position between 0.0 and 1.0\n if (position <= 0.0) {\n return this._setPointAtData(0.0, 0.0, curvePoints[0], 0, interpolateTNB);\n } else if (position >= 1.0) {\n return this._setPointAtData(1.0, 1.0, curvePoints[curvePoints.length - 1], curvePoints.length - 1, interpolateTNB);\n }\n let previousPoint = curvePoints[0];\n let currentPoint;\n let currentLength = 0.0;\n const targetLength = position * this.length();\n for (let i = 1; i < curvePoints.length; i++) {\n currentPoint = curvePoints[i];\n const distance = Vector3.Distance(previousPoint, currentPoint);\n currentLength += distance;\n if (currentLength === targetLength) {\n return this._setPointAtData(position, 1.0, currentPoint, i, interpolateTNB);\n } else if (currentLength > targetLength) {\n const toLength = currentLength - targetLength;\n const diff = toLength / distance;\n const dir = previousPoint.subtract(currentPoint);\n const point = currentPoint.add(dir.scaleInPlace(diff));\n return this._setPointAtData(position, 1 - diff, point, i - 1, interpolateTNB);\n }\n previousPoint = currentPoint;\n }\n return this._pointAtData;\n }\n /**\n * Updates the point at data from the specified parameters\n * @param position where along the path the interpolated point is, from 0.0 to 1.0\n * @param subPosition\n * @param point the interpolated point\n * @param parentIndex the index of an existing curve point that is on, or else positionally the first behind, the interpolated point\n * @param interpolateTNB whether to compute the interpolated tangent, normal and binormal\n * @returns the (updated) point at data\n */\n _setPointAtData(position, subPosition, point, parentIndex, interpolateTNB) {\n this._pointAtData.point = point;\n this._pointAtData.position = position;\n this._pointAtData.subPosition = subPosition;\n this._pointAtData.previousPointArrayIndex = parentIndex;\n this._pointAtData.interpolateReady = interpolateTNB;\n if (interpolateTNB) {\n this._updateInterpolationMatrix();\n }\n return this._pointAtData;\n }\n /**\n * Updates the point at interpolation matrix for the tangents, normals and binormals\n */\n _updateInterpolationMatrix() {\n this._pointAtData.interpolationMatrix = Matrix.Identity();\n const parentIndex = this._pointAtData.previousPointArrayIndex;\n if (parentIndex !== this._tangents.length - 1) {\n const index = parentIndex + 1;\n const tangentFrom = this._tangents[parentIndex].clone();\n const normalFrom = this._normals[parentIndex].clone();\n const binormalFrom = this._binormals[parentIndex].clone();\n const tangentTo = this._tangents[index].clone();\n const normalTo = this._normals[index].clone();\n const binormalTo = this._binormals[index].clone();\n const quatFrom = Quaternion.RotationQuaternionFromAxis(normalFrom, binormalFrom, tangentFrom);\n const quatTo = Quaternion.RotationQuaternionFromAxis(normalTo, binormalTo, tangentTo);\n const quatAt = Quaternion.Slerp(quatFrom, quatTo, this._pointAtData.subPosition);\n quatAt.toRotationMatrix(this._pointAtData.interpolationMatrix);\n }\n }\n}\n/**\n * A Curve3 object is a logical object, so not a mesh, to handle curves in the 3D geometric space.\n * A Curve3 is designed from a series of successive Vector3.\n * @see https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves\n */\nexport class Curve3 {\n /**\n * Returns a Curve3 object along a Quadratic Bezier curve : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#quadratic-bezier-curve\n * @param v0 (Vector3) the origin point of the Quadratic Bezier\n * @param v1 (Vector3) the control point\n * @param v2 (Vector3) the end point of the Quadratic Bezier\n * @param nbPoints (integer) the wanted number of points in the curve\n * @returns the created Curve3\n */\n static CreateQuadraticBezier(v0, v1, v2, nbPoints) {\n nbPoints = nbPoints > 2 ? nbPoints : 3;\n const bez = [];\n const equation = (t, val0, val1, val2) => {\n const res = (1.0 - t) * (1.0 - t) * val0 + 2.0 * t * (1.0 - t) * val1 + t * t * val2;\n return res;\n };\n for (let i = 0; i <= nbPoints; i++) {\n bez.push(new Vector3(equation(i / nbPoints, v0.x, v1.x, v2.x), equation(i / nbPoints, v0.y, v1.y, v2.y), equation(i / nbPoints, v0.z, v1.z, v2.z)));\n }\n return new Curve3(bez);\n }\n /**\n * Returns a Curve3 object along a Cubic Bezier curve : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#cubic-bezier-curve\n * @param v0 (Vector3) the origin point of the Cubic Bezier\n * @param v1 (Vector3) the first control point\n * @param v2 (Vector3) the second control point\n * @param v3 (Vector3) the end point of the Cubic Bezier\n * @param nbPoints (integer) the wanted number of points in the curve\n * @returns the created Curve3\n */\n static CreateCubicBezier(v0, v1, v2, v3, nbPoints) {\n nbPoints = nbPoints > 3 ? nbPoints : 4;\n const bez = [];\n const equation = (t, val0, val1, val2, val3) => {\n const res = (1.0 - t) * (1.0 - t) * (1.0 - t) * val0 + 3.0 * t * (1.0 - t) * (1.0 - t) * val1 + 3.0 * t * t * (1.0 - t) * val2 + t * t * t * val3;\n return res;\n };\n for (let i = 0; i <= nbPoints; i++) {\n bez.push(new Vector3(equation(i / nbPoints, v0.x, v1.x, v2.x, v3.x), equation(i / nbPoints, v0.y, v1.y, v2.y, v3.y), equation(i / nbPoints, v0.z, v1.z, v2.z, v3.z)));\n }\n return new Curve3(bez);\n }\n /**\n * Returns a Curve3 object along a Hermite Spline curve : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#hermite-spline\n * @param p1 (Vector3) the origin point of the Hermite Spline\n * @param t1 (Vector3) the tangent vector at the origin point\n * @param p2 (Vector3) the end point of the Hermite Spline\n * @param t2 (Vector3) the tangent vector at the end point\n * @param nSeg (integer) the number of curve segments or nSeg + 1 points in the array\n * @returns the created Curve3\n */\n static CreateHermiteSpline(p1, t1, p2, t2, nSeg) {\n const hermite = [];\n const step = 1.0 / nSeg;\n for (let i = 0; i <= nSeg; i++) {\n hermite.push(Vector3.Hermite(p1, t1, p2, t2, i * step));\n }\n return new Curve3(hermite);\n }\n /**\n * Returns a Curve3 object along a CatmullRom Spline curve :\n * @param points (array of Vector3) the points the spline must pass through. At least, four points required\n * @param nbPoints (integer) the wanted number of points between each curve control points\n * @param closed (boolean) optional with default false, when true forms a closed loop from the points\n * @returns the created Curve3\n */\n static CreateCatmullRomSpline(points, nbPoints, closed) {\n const catmullRom = [];\n const step = 1.0 / nbPoints;\n let amount = 0.0;\n if (closed) {\n const pointsCount = points.length;\n for (let i = 0; i < pointsCount; i++) {\n amount = 0;\n for (let c = 0; c < nbPoints; c++) {\n catmullRom.push(Vector3.CatmullRom(points[i % pointsCount], points[(i + 1) % pointsCount], points[(i + 2) % pointsCount], points[(i + 3) % pointsCount], amount));\n amount += step;\n }\n }\n catmullRom.push(catmullRom[0]);\n } else {\n const totalPoints = [];\n totalPoints.push(points[0].clone());\n Array.prototype.push.apply(totalPoints, points);\n totalPoints.push(points[points.length - 1].clone());\n let i = 0;\n for (; i < totalPoints.length - 3; i++) {\n amount = 0;\n for (let c = 0; c < nbPoints; c++) {\n catmullRom.push(Vector3.CatmullRom(totalPoints[i], totalPoints[i + 1], totalPoints[i + 2], totalPoints[i + 3], amount));\n amount += step;\n }\n }\n i--;\n catmullRom.push(Vector3.CatmullRom(totalPoints[i], totalPoints[i + 1], totalPoints[i + 2], totalPoints[i + 3], amount));\n }\n return new Curve3(catmullRom);\n }\n /**\n * Returns a Curve3 object along an arc through three vector3 points:\n * The three points should not be colinear. When they are the Curve3 is empty.\n * @param first (Vector3) the first point the arc must pass through.\n * @param second (Vector3) the second point the arc must pass through.\n * @param third (Vector3) the third point the arc must pass through.\n * @param steps (number) the larger the number of steps the more detailed the arc.\n * @param closed (boolean) optional with default false, when true forms the chord from the first and third point\n * @param fullCircle Circle (boolean) optional with default false, when true forms the complete circle through the three points\n * @returns the created Curve3\n */\n static ArcThru3Points(first, second, third, steps = 32, closed = false, fullCircle = false) {\n const arc = [];\n const vec1 = second.subtract(first);\n const vec2 = third.subtract(second);\n const vec3 = first.subtract(third);\n const zAxis = Vector3.Cross(vec1, vec2);\n const len4 = zAxis.length();\n if (len4 < Math.pow(10, -8)) {\n return new Curve3(arc); // colinear points arc is empty\n }\n const len1_sq = vec1.lengthSquared();\n const len2_sq = vec2.lengthSquared();\n const len3_sq = vec3.lengthSquared();\n const len4_sq = zAxis.lengthSquared();\n const len1 = vec1.length();\n const len2 = vec2.length();\n const len3 = vec3.length();\n const radius = 0.5 * len1 * len2 * len3 / len4;\n const dot1 = Vector3.Dot(vec1, vec3);\n const dot2 = Vector3.Dot(vec1, vec2);\n const dot3 = Vector3.Dot(vec2, vec3);\n const a = -0.5 * len2_sq * dot1 / len4_sq;\n const b = -0.5 * len3_sq * dot2 / len4_sq;\n const c = -0.5 * len1_sq * dot3 / len4_sq;\n const center = first.scale(a).add(second.scale(b)).add(third.scale(c));\n const radiusVec = first.subtract(center);\n const xAxis = radiusVec.normalize();\n const yAxis = Vector3.Cross(zAxis, xAxis).normalize();\n if (fullCircle) {\n const dStep = 2 * Math.PI / steps;\n for (let theta = 0; theta <= 2 * Math.PI; theta += dStep) {\n arc.push(center.add(xAxis.scale(radius * Math.cos(theta)).add(yAxis.scale(radius * Math.sin(theta)))));\n }\n arc.push(first);\n } else {\n const dStep = 1 / steps;\n let theta = 0;\n let point = Vector3.Zero();\n do {\n point = center.add(xAxis.scale(radius * Math.cos(theta)).add(yAxis.scale(radius * Math.sin(theta))));\n arc.push(point);\n theta += dStep;\n } while (!point.equalsWithEpsilon(third, radius * dStep * 1.1));\n arc.push(third);\n if (closed) {\n arc.push(first);\n }\n }\n return new Curve3(arc);\n }\n /**\n * A Curve3 object is a logical object, so not a mesh, to handle curves in the 3D geometric space.\n * A Curve3 is designed from a series of successive Vector3.\n * Tuto : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#curve3-object\n * @param points points which make up the curve\n */\n constructor(points) {\n this._length = 0.0;\n this._points = points;\n this._length = this._computeLength(points);\n }\n /**\n * @returns the Curve3 stored array of successive Vector3\n */\n getPoints() {\n return this._points;\n }\n /**\n * @returns the computed length (float) of the curve.\n */\n length() {\n return this._length;\n }\n /**\n * Returns a new instance of Curve3 object : var curve = curveA.continue(curveB);\n * This new Curve3 is built by translating and sticking the curveB at the end of the curveA.\n * curveA and curveB keep unchanged.\n * @param curve the curve to continue from this curve\n * @returns the newly constructed curve\n */\n continue(curve) {\n const lastPoint = this._points[this._points.length - 1];\n const continuedPoints = this._points.slice();\n const curvePoints = curve.getPoints();\n for (let i = 1; i < curvePoints.length; i++) {\n continuedPoints.push(curvePoints[i].subtract(curvePoints[0]).add(lastPoint));\n }\n const continuedCurve = new Curve3(continuedPoints);\n return continuedCurve;\n }\n _computeLength(path) {\n let l = 0;\n for (let i = 1; i < path.length; i++) {\n l += path[i].subtract(path[i - 1]).length();\n }\n return l;\n }\n}","map":{"version":3,"names":["Clamp","WithinEpsilon","Vector2","Vector3","Quaternion","Matrix","Epsilon","Orientation","BezierCurve","Interpolate","t","x1","y1","x2","y2","f0","f1","f2","refinedT","i","refinedT2","refinedT3","x","slope","Math","min","max","pow","Angle","constructor","radians","_radians","PI","degrees","BetweenTwoPoints","a","b","delta","subtract","theta","atan2","y","BetweenTwoVectors","product","lengthSquared","sqrt","cosVal","dot","angle","acos","FromRadians","FromDegrees","Arc2","startPoint","midPoint","endPoint","temp","startToMid","midToEnd","det","centerPoint","radius","length","startAngle","a1","a2","a3","orientation","Path2","_points","Array","_length","closed","push","addLineTo","newPoint","previousPoint","addArcTo","midX","midY","endX","endY","numberOfSegments","arc","increment","currentAngle","cos","sin","addQuadraticCurveTo","controlX","controlY","equation","val0","val1","val2","res","step","addBezierCurveTo","originTangentX","originTangentY","destinationTangentX","destinationTangentY","val3","isPointInside","point","isInside","count","p","q","edgeLow","edgeHigh","edgeDx","edgeDy","abs","Number","EPSILON","perpEdge","close","result","lastPoint","firstPoint","area","n","value","getPoints","getPointAtLengthPosition","normalizedLengthPosition","Zero","lengthPosition","previousOffset","j","bToA","nextOffset","dir","normalize","localOffset","StartingAt","Path3D","path","firstNormal","raw","alignTangentsWithPath","_curve","_distances","_tangents","_normals","_binormals","_pointAtData","id","previousPointArrayIndex","position","subPosition","interpolateReady","interpolationMatrix","Identity","clone","_raw","_alignTangentsWithPath","_compute","getCurve","getTangents","getNormals","getBinormals","getDistances","getPointAt","_updatePointAtData","getTangentAt","interpolated","TransformCoordinates","Forward","getNormalAt","Right","getBinormalAt","UpReadOnly","getDistanceAt","getPreviousPointIndexAt","getSubPositionAt","getClosestPositionTo","target","smallestDistance","MAX_VALUE","closestPosition","tangent","subLength","Dot","Distance","distance","add","scale","slice","start","end","_start","curvePoints","startIndex","endIndex","slicePoints","update","z","l","_getFirstNonNullVector","tg0","pp0","_normalVector","Cross","prev","cur","curTang","prevNor","prevBinor","_getLastNonNullVector","NaN","index","nNVector","nLVector","vt","va","normal0","tgl","undefined","CrossToRef","interpolateTNB","_updateInterpolationMatrix","_setPointAtData","currentPoint","currentLength","targetLength","toLength","diff","scaleInPlace","parentIndex","tangentFrom","normalFrom","binormalFrom","tangentTo","normalTo","binormalTo","quatFrom","RotationQuaternionFromAxis","quatTo","quatAt","Slerp","toRotationMatrix","Curve3","CreateQuadraticBezier","v0","v1","v2","nbPoints","bez","CreateCubicBezier","v3","CreateHermiteSpline","p1","t1","p2","t2","nSeg","hermite","Hermite","CreateCatmullRomSpline","points","catmullRom","amount","pointsCount","c","CatmullRom","totalPoints","prototype","apply","ArcThru3Points","first","second","third","steps","fullCircle","vec1","vec2","vec3","zAxis","len4","len1_sq","len2_sq","len3_sq","len4_sq","len1","len2","len3","dot1","dot2","dot3","center","radiusVec","xAxis","yAxis","dStep","equalsWithEpsilon","_computeLength","continue","curve","continuedPoints","continuedCurve"],"sources":["F:/workspace/202226701027/huinongbao-app/node_modules/@babylonjs/core/Maths/math.path.js"],"sourcesContent":["import { Clamp, WithinEpsilon } from \"./math.scalar.functions.js\";\nimport { Vector2, Vector3, Quaternion, Matrix } from \"./math.vector.js\";\nimport { Epsilon } from \"./math.constants.js\";\n/**\n * Defines potential orientation for back face culling\n */\nexport var Orientation;\n(function (Orientation) {\n /**\n * Clockwise\n */\n Orientation[Orientation[\"CW\"] = 0] = \"CW\";\n /** Counter clockwise */\n Orientation[Orientation[\"CCW\"] = 1] = \"CCW\";\n})(Orientation || (Orientation = {}));\n/** Class used to represent a Bezier curve */\nexport class BezierCurve {\n /**\n * Returns the cubic Bezier interpolated value (float) at \"t\" (float) from the given x1, y1, x2, y2 floats\n * @param t defines the time\n * @param x1 defines the left coordinate on X axis\n * @param y1 defines the left coordinate on Y axis\n * @param x2 defines the right coordinate on X axis\n * @param y2 defines the right coordinate on Y axis\n * @returns the interpolated value\n */\n static Interpolate(t, x1, y1, x2, y2) {\n // Extract X (which is equal to time here)\n const f0 = 1 - 3 * x2 + 3 * x1;\n const f1 = 3 * x2 - 6 * x1;\n const f2 = 3 * x1;\n let refinedT = t;\n for (let i = 0; i < 5; i++) {\n const refinedT2 = refinedT * refinedT;\n const refinedT3 = refinedT2 * refinedT;\n const x = f0 * refinedT3 + f1 * refinedT2 + f2 * refinedT;\n const slope = 1.0 / (3.0 * f0 * refinedT2 + 2.0 * f1 * refinedT + f2);\n refinedT -= (x - t) * slope;\n refinedT = Math.min(1, Math.max(0, refinedT));\n }\n // Resolve cubic bezier for the given x\n return 3 * Math.pow(1 - refinedT, 2) * refinedT * y1 + 3 * (1 - refinedT) * Math.pow(refinedT, 2) * y2 + Math.pow(refinedT, 3);\n }\n}\n/**\n * Defines angle representation\n */\nexport class Angle {\n /**\n * Creates an Angle object of \"radians\" radians (float).\n * @param radians the angle in radians\n */\n constructor(radians) {\n this._radians = radians;\n if (this._radians < 0.0) {\n this._radians += 2.0 * Math.PI;\n }\n }\n /**\n * Get value in degrees\n * @returns the Angle value in degrees (float)\n */\n degrees() {\n return (this._radians * 180.0) / Math.PI;\n }\n /**\n * Get value in radians\n * @returns the Angle value in radians (float)\n */\n radians() {\n return this._radians;\n }\n /**\n * Gets a new Angle object with a value of the angle (in radians) between the line connecting the two points and the x-axis\n * @param a defines first point as the origin\n * @param b defines point\n * @returns a new Angle\n */\n static BetweenTwoPoints(a, b) {\n const delta = b.subtract(a);\n const theta = Math.atan2(delta.y, delta.x);\n return new Angle(theta);\n }\n /**\n * Gets the angle between the two vectors\n * @param a defines first vector\n * @param b defines vector\n * @returns Returns an new Angle between 0 and PI\n */\n static BetweenTwoVectors(a, b) {\n let product = a.lengthSquared() * b.lengthSquared();\n if (product === 0)\n return new Angle(Math.PI / 2);\n product = Math.sqrt(product);\n let cosVal = a.dot(b) / product;\n cosVal = Clamp(cosVal, -1, 1);\n const angle = Math.acos(cosVal);\n return new Angle(angle);\n }\n /**\n * Gets a new Angle object from the given float in radians\n * @param radians defines the angle value in radians\n * @returns a new Angle\n */\n static FromRadians(radians) {\n return new Angle(radians);\n }\n /**\n * Gets a new Angle object from the given float in degrees\n * @param degrees defines the angle value in degrees\n * @returns a new Angle\n */\n static FromDegrees(degrees) {\n return new Angle((degrees * Math.PI) / 180.0);\n }\n}\n/**\n * This represents an arc in a 2d space.\n */\nexport class Arc2 {\n /**\n * Creates an Arc object from the three given points : start, middle and end.\n * @param startPoint Defines the start point of the arc\n * @param midPoint Defines the middle point of the arc\n * @param endPoint Defines the end point of the arc\n */\n constructor(\n /** Defines the start point of the arc */\n startPoint, \n /** Defines the mid point of the arc */\n midPoint, \n /** Defines the end point of the arc */\n endPoint) {\n this.startPoint = startPoint;\n this.midPoint = midPoint;\n this.endPoint = endPoint;\n const temp = Math.pow(midPoint.x, 2) + Math.pow(midPoint.y, 2);\n const startToMid = (Math.pow(startPoint.x, 2) + Math.pow(startPoint.y, 2) - temp) / 2;\n const midToEnd = (temp - Math.pow(endPoint.x, 2) - Math.pow(endPoint.y, 2)) / 2;\n const det = (startPoint.x - midPoint.x) * (midPoint.y - endPoint.y) - (midPoint.x - endPoint.x) * (startPoint.y - midPoint.y);\n this.centerPoint = new Vector2((startToMid * (midPoint.y - endPoint.y) - midToEnd * (startPoint.y - midPoint.y)) / det, ((startPoint.x - midPoint.x) * midToEnd - (midPoint.x - endPoint.x) * startToMid) / det);\n this.radius = this.centerPoint.subtract(this.startPoint).length();\n this.startAngle = Angle.BetweenTwoPoints(this.centerPoint, this.startPoint);\n const a1 = this.startAngle.degrees();\n let a2 = Angle.BetweenTwoPoints(this.centerPoint, this.midPoint).degrees();\n let a3 = Angle.BetweenTwoPoints(this.centerPoint, this.endPoint).degrees();\n // angles correction\n if (a2 - a1 > +180.0) {\n a2 -= 360.0;\n }\n if (a2 - a1 < -180.0) {\n a2 += 360.0;\n }\n if (a3 - a2 > +180.0) {\n a3 -= 360.0;\n }\n if (a3 - a2 < -180.0) {\n a3 += 360.0;\n }\n this.orientation = a2 - a1 < 0 ? 0 /* Orientation.CW */ : 1 /* Orientation.CCW */;\n this.angle = Angle.FromDegrees(this.orientation === 0 /* Orientation.CW */ ? a1 - a3 : a3 - a1);\n }\n}\n/**\n * Represents a 2D path made up of multiple 2D points\n */\nexport class Path2 {\n /**\n * Creates a Path2 object from the starting 2D coordinates x and y.\n * @param x the starting points x value\n * @param y the starting points y value\n */\n constructor(x, y) {\n this._points = new Array();\n this._length = 0.0;\n /**\n * If the path start and end point are the same\n */\n this.closed = false;\n this._points.push(new Vector2(x, y));\n }\n /**\n * Adds a new segment until the given coordinates (x, y) to the current Path2.\n * @param x the added points x value\n * @param y the added points y value\n * @returns the updated Path2.\n */\n addLineTo(x, y) {\n if (this.closed) {\n return this;\n }\n const newPoint = new Vector2(x, y);\n const previousPoint = this._points[this._points.length - 1];\n this._points.push(newPoint);\n this._length += newPoint.subtract(previousPoint).length();\n return this;\n }\n /**\n * Adds _numberOfSegments_ segments according to the arc definition (middle point coordinates, end point coordinates, the arc start point being the current Path2 last point) to the current Path2.\n * @param midX middle point x value\n * @param midY middle point y value\n * @param endX end point x value\n * @param endY end point y value\n * @param numberOfSegments (default: 36)\n * @returns the updated Path2.\n */\n addArcTo(midX, midY, endX, endY, numberOfSegments = 36) {\n if (this.closed) {\n return this;\n }\n const startPoint = this._points[this._points.length - 1];\n const midPoint = new Vector2(midX, midY);\n const endPoint = new Vector2(endX, endY);\n const arc = new Arc2(startPoint, midPoint, endPoint);\n let increment = arc.angle.radians() / numberOfSegments;\n if (arc.orientation === 0 /* Orientation.CW */) {\n increment *= -1;\n }\n let currentAngle = arc.startAngle.radians() + increment;\n for (let i = 0; i < numberOfSegments; i++) {\n const x = Math.cos(currentAngle) * arc.radius + arc.centerPoint.x;\n const y = Math.sin(currentAngle) * arc.radius + arc.centerPoint.y;\n this.addLineTo(x, y);\n currentAngle += increment;\n }\n return this;\n }\n /**\n * Adds _numberOfSegments_ segments according to the quadratic curve definition to the current Path2.\n * @param controlX control point x value\n * @param controlY control point y value\n * @param endX end point x value\n * @param endY end point y value\n * @param numberOfSegments (default: 36)\n * @returns the updated Path2.\n */\n addQuadraticCurveTo(controlX, controlY, endX, endY, numberOfSegments = 36) {\n if (this.closed) {\n return this;\n }\n const equation = (t, val0, val1, val2) => {\n const res = (1.0 - t) * (1.0 - t) * val0 + 2.0 * t * (1.0 - t) * val1 + t * t * val2;\n return res;\n };\n const startPoint = this._points[this._points.length - 1];\n for (let i = 0; i <= numberOfSegments; i++) {\n const step = i / numberOfSegments;\n const x = equation(step, startPoint.x, controlX, endX);\n const y = equation(step, startPoint.y, controlY, endY);\n this.addLineTo(x, y);\n }\n return this;\n }\n /**\n * Adds _numberOfSegments_ segments according to the bezier curve definition to the current Path2.\n * @param originTangentX tangent vector at the origin point x value\n * @param originTangentY tangent vector at the origin point y value\n * @param destinationTangentX tangent vector at the destination point x value\n * @param destinationTangentY tangent vector at the destination point y value\n * @param endX end point x value\n * @param endY end point y value\n * @param numberOfSegments (default: 36)\n * @returns the updated Path2.\n */\n addBezierCurveTo(originTangentX, originTangentY, destinationTangentX, destinationTangentY, endX, endY, numberOfSegments = 36) {\n if (this.closed) {\n return this;\n }\n const equation = (t, val0, val1, val2, val3) => {\n const res = (1.0 - t) * (1.0 - t) * (1.0 - t) * val0 + 3.0 * t * (1.0 - t) * (1.0 - t) * val1 + 3.0 * t * t * (1.0 - t) * val2 + t * t * t * val3;\n return res;\n };\n const startPoint = this._points[this._points.length - 1];\n for (let i = 0; i <= numberOfSegments; i++) {\n const step = i / numberOfSegments;\n const x = equation(step, startPoint.x, originTangentX, destinationTangentX, endX);\n const y = equation(step, startPoint.y, originTangentY, destinationTangentY, endY);\n this.addLineTo(x, y);\n }\n return this;\n }\n /**\n * Defines if a given point is inside the polygon defines by the path\n * @param point defines the point to test\n * @returns true if the point is inside\n */\n isPointInside(point) {\n let isInside = false;\n const count = this._points.length;\n for (let p = count - 1, q = 0; q < count; p = q++) {\n let edgeLow = this._points[p];\n let edgeHigh = this._points[q];\n let edgeDx = edgeHigh.x - edgeLow.x;\n let edgeDy = edgeHigh.y - edgeLow.y;\n if (Math.abs(edgeDy) > Number.EPSILON) {\n // Not parallel\n if (edgeDy < 0) {\n edgeLow = this._points[q];\n edgeDx = -edgeDx;\n edgeHigh = this._points[p];\n edgeDy = -edgeDy;\n }\n if (point.y < edgeLow.y || point.y > edgeHigh.y) {\n continue;\n }\n if (point.y === edgeLow.y && point.x === edgeLow.x) {\n return true;\n }\n else {\n const perpEdge = edgeDy * (point.x - edgeLow.x) - edgeDx * (point.y - edgeLow.y);\n if (perpEdge === 0) {\n return true;\n }\n if (perpEdge < 0) {\n continue;\n }\n isInside = !isInside;\n }\n }\n else {\n // parallel or collinear\n if (point.y !== edgeLow.y) {\n continue;\n }\n if ((edgeHigh.x <= point.x && point.x <= edgeLow.x) || (edgeLow.x <= point.x && point.x <= edgeHigh.x)) {\n return true;\n }\n }\n }\n return isInside;\n }\n /**\n * Closes the Path2.\n * @returns the Path2.\n */\n close() {\n this.closed = true;\n return this;\n }\n /**\n * Gets the sum of the distance between each sequential point in the path\n * @returns the Path2 total length (float).\n */\n length() {\n let result = this._length;\n if (this.closed) {\n const lastPoint = this._points[this._points.length - 1];\n const firstPoint = this._points[0];\n result += firstPoint.subtract(lastPoint).length();\n }\n return result;\n }\n /**\n * Gets the area of the polygon defined by the path\n * @returns area value\n */\n area() {\n const n = this._points.length;\n let value = 0.0;\n for (let p = n - 1, q = 0; q < n; p = q++) {\n value += this._points[p].x * this._points[q].y - this._points[q].x * this._points[p].y;\n }\n return value * 0.5;\n }\n /**\n * Gets the points which construct the path\n * @returns the Path2 internal array of points.\n */\n getPoints() {\n return this._points;\n }\n /**\n * Retrieves the point at the distance aways from the starting point\n * @param normalizedLengthPosition the length along the path to retrieve the point from\n * @returns a new Vector2 located at a percentage of the Path2 total length on this path.\n */\n getPointAtLengthPosition(normalizedLengthPosition) {\n if (normalizedLengthPosition < 0 || normalizedLengthPosition > 1) {\n return Vector2.Zero();\n }\n const lengthPosition = normalizedLengthPosition * this.length();\n let previousOffset = 0;\n for (let i = 0; i < this._points.length; i++) {\n const j = (i + 1) % this._points.length;\n const a = this._points[i];\n const b = this._points[j];\n const bToA = b.subtract(a);\n const nextOffset = bToA.length() + previousOffset;\n if (lengthPosition >= previousOffset && lengthPosition <= nextOffset) {\n const dir = bToA.normalize();\n const localOffset = lengthPosition - previousOffset;\n return new Vector2(a.x + dir.x * localOffset, a.y + dir.y * localOffset);\n }\n previousOffset = nextOffset;\n }\n return Vector2.Zero();\n }\n /**\n * Creates a new path starting from an x and y position\n * @param x starting x value\n * @param y starting y value\n * @returns a new Path2 starting at the coordinates (x, y).\n */\n static StartingAt(x, y) {\n return new Path2(x, y);\n }\n}\n/**\n * Represents a 3D path made up of multiple 3D points\n * @see https://doc.babylonjs.com/features/featuresDeepDive/mesh/path3D\n */\nexport class Path3D {\n /**\n * new Path3D(path, normal, raw)\n * Creates a Path3D. A Path3D is a logical math object, so not a mesh.\n * please read the description in the tutorial : https://doc.babylonjs.com/features/featuresDeepDive/mesh/path3D\n * @param path an array of Vector3, the curve axis of the Path3D\n * @param firstNormal (options) Vector3, the first wanted normal to the curve. Ex (0, 1, 0) for a vertical normal.\n * @param raw (optional, default false) : boolean, if true the returned Path3D isn't normalized. Useful to depict path acceleration or speed.\n * @param alignTangentsWithPath (optional, default false) : boolean, if true the tangents will be aligned with the path.\n */\n constructor(\n /**\n * an array of Vector3, the curve axis of the Path3D\n */\n path, firstNormal = null, raw, alignTangentsWithPath = false) {\n this.path = path;\n this._curve = new Array();\n this._distances = new Array();\n this._tangents = new Array();\n this._normals = new Array();\n this._binormals = new Array();\n // holds interpolated point data\n this._pointAtData = {\n id: 0,\n point: Vector3.Zero(),\n previousPointArrayIndex: 0,\n position: 0,\n subPosition: 0,\n interpolateReady: false,\n interpolationMatrix: Matrix.Identity(),\n };\n for (let p = 0; p < path.length; p++) {\n this._curve[p] = path[p].clone(); // hard copy\n }\n this._raw = raw || false;\n this._alignTangentsWithPath = alignTangentsWithPath;\n this._compute(firstNormal, alignTangentsWithPath);\n }\n /**\n * Returns the Path3D array of successive Vector3 designing its curve.\n * @returns the Path3D array of successive Vector3 designing its curve.\n */\n getCurve() {\n return this._curve;\n }\n /**\n * Returns the Path3D array of successive Vector3 designing its curve.\n * @returns the Path3D array of successive Vector3 designing its curve.\n */\n getPoints() {\n return this._curve;\n }\n /**\n * @returns the computed length (float) of the path.\n */\n length() {\n return this._distances[this._distances.length - 1];\n }\n /**\n * Returns an array populated with tangent vectors on each Path3D curve point.\n * @returns an array populated with tangent vectors on each Path3D curve point.\n */\n getTangents() {\n return this._tangents;\n }\n /**\n * Returns an array populated with normal vectors on each Path3D curve point.\n * @returns an array populated with normal vectors on each Path3D curve point.\n */\n getNormals() {\n return this._normals;\n }\n /**\n * Returns an array populated with binormal vectors on each Path3D curve point.\n * @returns an array populated with binormal vectors on each Path3D curve point.\n */\n getBinormals() {\n return this._binormals;\n }\n /**\n * Returns an array populated with distances (float) of the i-th point from the first curve point.\n * @returns an array populated with distances (float) of the i-th point from the first curve point.\n */\n getDistances() {\n return this._distances;\n }\n /**\n * Returns an interpolated point along this path\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @returns a new Vector3 as the point\n */\n getPointAt(position) {\n return this._updatePointAtData(position).point;\n }\n /**\n * Returns the tangent vector of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @param interpolated (optional, default false) : boolean, if true returns an interpolated tangent instead of the tangent of the previous path point.\n * @returns a tangent vector corresponding to the interpolated Path3D curve point, if not interpolated, the tangent is taken from the precomputed tangents array.\n */\n getTangentAt(position, interpolated = false) {\n this._updatePointAtData(position, interpolated);\n return interpolated ? Vector3.TransformCoordinates(Vector3.Forward(), this._pointAtData.interpolationMatrix) : this._tangents[this._pointAtData.previousPointArrayIndex];\n }\n /**\n * Returns the tangent vector of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @param interpolated (optional, default false) : boolean, if true returns an interpolated normal instead of the normal of the previous path point.\n * @returns a normal vector corresponding to the interpolated Path3D curve point, if not interpolated, the normal is taken from the precomputed normals array.\n */\n getNormalAt(position, interpolated = false) {\n this._updatePointAtData(position, interpolated);\n return interpolated ? Vector3.TransformCoordinates(Vector3.Right(), this._pointAtData.interpolationMatrix) : this._normals[this._pointAtData.previousPointArrayIndex];\n }\n /**\n * Returns the binormal vector of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @param interpolated (optional, default false) : boolean, if true returns an interpolated binormal instead of the binormal of the previous path point.\n * @returns a binormal vector corresponding to the interpolated Path3D curve point, if not interpolated, the binormal is taken from the precomputed binormals array.\n */\n getBinormalAt(position, interpolated = false) {\n this._updatePointAtData(position, interpolated);\n return interpolated ? Vector3.TransformCoordinates(Vector3.UpReadOnly, this._pointAtData.interpolationMatrix) : this._binormals[this._pointAtData.previousPointArrayIndex];\n }\n /**\n * Returns the distance (float) of an interpolated Path3D curve point at the specified position along this path.\n * @param position the position of the point along this path, from 0.0 to 1.0\n * @returns the distance of the interpolated Path3D curve point at the specified position along this path.\n */\n getDistanceAt(position) {\n return this.length() * position;\n }\n /**\n * Returns the array index of the previous point of an interpolated point along this path\n * @param position the position of the point to interpolate along this path, from 0.0 to 1.0\n * @returns the array index\n */\n getPreviousPointIndexAt(position) {\n this._updatePointAtData(position);\n return this._pointAtData.previousPointArrayIndex;\n }\n /**\n * Returns the position of an interpolated point relative to the two path points it lies between, from 0.0 (point A) to 1.0 (point B)\n * @param position the position of the point to interpolate along this path, from 0.0 to 1.0\n * @returns the sub position\n */\n getSubPositionAt(position) {\n this._updatePointAtData(position);\n return this._pointAtData.subPosition;\n }\n /**\n * Returns the position of the closest virtual point on this path to an arbitrary Vector3, from 0.0 to 1.0\n * @param target the vector of which to get the closest position to\n * @returns the position of the closest virtual point on this path to the target vector\n */\n getClosestPositionTo(target) {\n let smallestDistance = Number.MAX_VALUE;\n let closestPosition = 0.0;\n for (let i = 0; i < this._curve.length - 1; i++) {\n const point = this._curve[i + 0];\n const tangent = this._curve[i + 1].subtract(point).normalize();\n const subLength = this._distances[i + 1] - this._distances[i + 0];\n const subPosition = Math.min((Math.max(Vector3.Dot(tangent, target.subtract(point).normalize()), 0.0) * Vector3.Distance(point, target)) / subLength, 1.0);\n const distance = Vector3.Distance(point.add(tangent.scale(subPosition * subLength)), target);\n if (distance < smallestDistance) {\n smallestDistance = distance;\n closestPosition = (this._distances[i + 0] + subLength * subPosition) / this.length();\n }\n }\n return closestPosition;\n }\n /**\n * Returns a sub path (slice) of this path\n * @param start the position of the fist path point, from 0.0 to 1.0, or a negative value, which will get wrapped around from the end of the path to 0.0 to 1.0 values\n * @param end the position of the last path point, from 0.0 to 1.0, or a negative value, which will get wrapped around from the end of the path to 0.0 to 1.0 values\n * @returns a sub path (slice) of this path\n */\n slice(start = 0.0, end = 1.0) {\n if (start < 0.0) {\n start = 1 - ((start * -1.0) % 1.0);\n }\n if (end < 0.0) {\n end = 1 - ((end * -1.0) % 1.0);\n }\n if (start > end) {\n const _start = start;\n start = end;\n end = _start;\n }\n const curvePoints = this.getCurve();\n const startPoint = this.getPointAt(start);\n let startIndex = this.getPreviousPointIndexAt(start);\n const endPoint = this.getPointAt(end);\n const endIndex = this.getPreviousPointIndexAt(end) + 1;\n const slicePoints = [];\n if (start !== 0.0) {\n startIndex++;\n slicePoints.push(startPoint);\n }\n slicePoints.push(...curvePoints.slice(startIndex, endIndex));\n if (end !== 1.0 || start === 1.0) {\n slicePoints.push(endPoint);\n }\n return new Path3D(slicePoints, this.getNormalAt(start), this._raw, this._alignTangentsWithPath);\n }\n /**\n * Forces the Path3D tangent, normal, binormal and distance recomputation.\n * @param path path which all values are copied into the curves points\n * @param firstNormal which should be projected onto the curve\n * @param alignTangentsWithPath (optional, default false) : boolean, if true the tangents will be aligned with the path\n * @returns the same object updated.\n */\n update(path, firstNormal = null, alignTangentsWithPath = false) {\n for (let p = 0; p < path.length; p++) {\n this._curve[p].x = path[p].x;\n this._curve[p].y = path[p].y;\n this._curve[p].z = path[p].z;\n }\n this._compute(firstNormal, alignTangentsWithPath);\n return this;\n }\n // private function compute() : computes tangents, normals and binormals\n _compute(firstNormal, alignTangentsWithPath = false) {\n const l = this._curve.length;\n if (l < 2) {\n return;\n }\n // first and last tangents\n this._tangents[0] = this._getFirstNonNullVector(0);\n if (!this._raw) {\n this._tangents[0].normalize();\n }\n this._tangents[l - 1] = this._curve[l - 1].subtract(this._curve[l - 2]);\n if (!this._raw) {\n this._tangents[l - 1].normalize();\n }\n // normals and binormals at first point : arbitrary vector with _normalVector()\n const tg0 = this._tangents[0];\n const pp0 = this._normalVector(tg0, firstNormal);\n this._normals[0] = pp0;\n if (!this._raw) {\n this._normals[0].normalize();\n }\n this._binormals[0] = Vector3.Cross(tg0, this._normals[0]);\n if (!this._raw) {\n this._binormals[0].normalize();\n }\n this._distances[0] = 0.0;\n // normals and binormals : next points\n let prev; // previous vector (segment)\n let cur; // current vector (segment)\n let curTang; // current tangent\n // previous normal\n let prevNor; // previous normal\n let prevBinor; // previous binormal\n for (let i = 1; i < l; i++) {\n // tangents\n prev = this._getLastNonNullVector(i);\n if (i < l - 1) {\n cur = this._getFirstNonNullVector(i);\n this._tangents[i] = alignTangentsWithPath ? cur : prev.add(cur);\n this._tangents[i].normalize();\n }\n this._distances[i] = this._distances[i - 1] + this._curve[i].subtract(this._curve[i - 1]).length();\n // normals and binormals\n // http://www.cs.cmu.edu/afs/andrew/scs/cs/15-462/web/old/asst2camera.html\n curTang = this._tangents[i];\n prevBinor = this._binormals[i - 1];\n this._normals[i] = Vector3.Cross(prevBinor, curTang);\n if (!this._raw) {\n if (this._normals[i].length() === 0) {\n prevNor = this._normals[i - 1];\n this._normals[i] = prevNor.clone();\n }\n else {\n this._normals[i].normalize();\n }\n }\n this._binormals[i] = Vector3.Cross(curTang, this._normals[i]);\n if (!this._raw) {\n this._binormals[i].normalize();\n }\n }\n this._pointAtData.id = NaN;\n }\n // private function getFirstNonNullVector(index)\n // returns the first non null vector from index : curve[index + N].subtract(curve[index])\n _getFirstNonNullVector(index) {\n let i = 1;\n let nNVector = this._curve[index + i].subtract(this._curve[index]);\n while (nNVector.length() === 0 && index + i + 1 < this._curve.length) {\n i++;\n nNVector = this._curve[index + i].subtract(this._curve[index]);\n }\n return nNVector;\n }\n // private function getLastNonNullVector(index)\n // returns the last non null vector from index : curve[index].subtract(curve[index - N])\n _getLastNonNullVector(index) {\n let i = 1;\n let nLVector = this._curve[index].subtract(this._curve[index - i]);\n while (nLVector.length() === 0 && index > i + 1) {\n i++;\n nLVector = this._curve[index].subtract(this._curve[index - i]);\n }\n return nLVector;\n }\n // private function normalVector(v0, vt, va) :\n // returns an arbitrary point in the plane defined by the point v0 and the vector vt orthogonal to this plane\n // if va is passed, it returns the va projection on the plane orthogonal to vt at the point v0\n _normalVector(vt, va) {\n let normal0;\n let tgl = vt.length();\n if (tgl === 0.0) {\n tgl = 1.0;\n }\n if (va === undefined || va === null) {\n let point;\n if (!WithinEpsilon(Math.abs(vt.y) / tgl, 1.0, Epsilon)) {\n // search for a point in the plane\n point = new Vector3(0.0, -1.0, 0.0);\n }\n else if (!WithinEpsilon(Math.abs(vt.x) / tgl, 1.0, Epsilon)) {\n point = new Vector3(1.0, 0.0, 0.0);\n }\n else if (!WithinEpsilon(Math.abs(vt.z) / tgl, 1.0, Epsilon)) {\n point = new Vector3(0.0, 0.0, 1.0);\n }\n else {\n point = Vector3.Zero();\n }\n normal0 = Vector3.Cross(vt, point);\n }\n else {\n normal0 = Vector3.Cross(vt, va);\n Vector3.CrossToRef(normal0, vt, normal0);\n }\n normal0.normalize();\n return normal0;\n }\n /**\n * Updates the point at data for an interpolated point along this curve\n * @param position the position of the point along this curve, from 0.0 to 1.0\n * @param interpolateTNB\n * @interpolateTNB whether to compute the interpolated tangent, normal and binormal\n * @returns the (updated) point at data\n */\n _updatePointAtData(position, interpolateTNB = false) {\n // set an id for caching the result\n if (this._pointAtData.id === position) {\n if (!this._pointAtData.interpolateReady) {\n this._updateInterpolationMatrix();\n }\n return this._pointAtData;\n }\n else {\n this._pointAtData.id = position;\n }\n const curvePoints = this.getPoints();\n // clamp position between 0.0 and 1.0\n if (position <= 0.0) {\n return this._setPointAtData(0.0, 0.0, curvePoints[0], 0, interpolateTNB);\n }\n else if (position >= 1.0) {\n return this._setPointAtData(1.0, 1.0, curvePoints[curvePoints.length - 1], curvePoints.length - 1, interpolateTNB);\n }\n let previousPoint = curvePoints[0];\n let currentPoint;\n let currentLength = 0.0;\n const targetLength = position * this.length();\n for (let i = 1; i < curvePoints.length; i++) {\n currentPoint = curvePoints[i];\n const distance = Vector3.Distance(previousPoint, currentPoint);\n currentLength += distance;\n if (currentLength === targetLength) {\n return this._setPointAtData(position, 1.0, currentPoint, i, interpolateTNB);\n }\n else if (currentLength > targetLength) {\n const toLength = currentLength - targetLength;\n const diff = toLength / distance;\n const dir = previousPoint.subtract(currentPoint);\n const point = currentPoint.add(dir.scaleInPlace(diff));\n return this._setPointAtData(position, 1 - diff, point, i - 1, interpolateTNB);\n }\n previousPoint = currentPoint;\n }\n return this._pointAtData;\n }\n /**\n * Updates the point at data from the specified parameters\n * @param position where along the path the interpolated point is, from 0.0 to 1.0\n * @param subPosition\n * @param point the interpolated point\n * @param parentIndex the index of an existing curve point that is on, or else positionally the first behind, the interpolated point\n * @param interpolateTNB whether to compute the interpolated tangent, normal and binormal\n * @returns the (updated) point at data\n */\n _setPointAtData(position, subPosition, point, parentIndex, interpolateTNB) {\n this._pointAtData.point = point;\n this._pointAtData.position = position;\n this._pointAtData.subPosition = subPosition;\n this._pointAtData.previousPointArrayIndex = parentIndex;\n this._pointAtData.interpolateReady = interpolateTNB;\n if (interpolateTNB) {\n this._updateInterpolationMatrix();\n }\n return this._pointAtData;\n }\n /**\n * Updates the point at interpolation matrix for the tangents, normals and binormals\n */\n _updateInterpolationMatrix() {\n this._pointAtData.interpolationMatrix = Matrix.Identity();\n const parentIndex = this._pointAtData.previousPointArrayIndex;\n if (parentIndex !== this._tangents.length - 1) {\n const index = parentIndex + 1;\n const tangentFrom = this._tangents[parentIndex].clone();\n const normalFrom = this._normals[parentIndex].clone();\n const binormalFrom = this._binormals[parentIndex].clone();\n const tangentTo = this._tangents[index].clone();\n const normalTo = this._normals[index].clone();\n const binormalTo = this._binormals[index].clone();\n const quatFrom = Quaternion.RotationQuaternionFromAxis(normalFrom, binormalFrom, tangentFrom);\n const quatTo = Quaternion.RotationQuaternionFromAxis(normalTo, binormalTo, tangentTo);\n const quatAt = Quaternion.Slerp(quatFrom, quatTo, this._pointAtData.subPosition);\n quatAt.toRotationMatrix(this._pointAtData.interpolationMatrix);\n }\n }\n}\n/**\n * A Curve3 object is a logical object, so not a mesh, to handle curves in the 3D geometric space.\n * A Curve3 is designed from a series of successive Vector3.\n * @see https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves\n */\nexport class Curve3 {\n /**\n * Returns a Curve3 object along a Quadratic Bezier curve : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#quadratic-bezier-curve\n * @param v0 (Vector3) the origin point of the Quadratic Bezier\n * @param v1 (Vector3) the control point\n * @param v2 (Vector3) the end point of the Quadratic Bezier\n * @param nbPoints (integer) the wanted number of points in the curve\n * @returns the created Curve3\n */\n static CreateQuadraticBezier(v0, v1, v2, nbPoints) {\n nbPoints = nbPoints > 2 ? nbPoints : 3;\n const bez = [];\n const equation = (t, val0, val1, val2) => {\n const res = (1.0 - t) * (1.0 - t) * val0 + 2.0 * t * (1.0 - t) * val1 + t * t * val2;\n return res;\n };\n for (let i = 0; i <= nbPoints; i++) {\n bez.push(new Vector3(equation(i / nbPoints, v0.x, v1.x, v2.x), equation(i / nbPoints, v0.y, v1.y, v2.y), equation(i / nbPoints, v0.z, v1.z, v2.z)));\n }\n return new Curve3(bez);\n }\n /**\n * Returns a Curve3 object along a Cubic Bezier curve : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#cubic-bezier-curve\n * @param v0 (Vector3) the origin point of the Cubic Bezier\n * @param v1 (Vector3) the first control point\n * @param v2 (Vector3) the second control point\n * @param v3 (Vector3) the end point of the Cubic Bezier\n * @param nbPoints (integer) the wanted number of points in the curve\n * @returns the created Curve3\n */\n static CreateCubicBezier(v0, v1, v2, v3, nbPoints) {\n nbPoints = nbPoints > 3 ? nbPoints : 4;\n const bez = [];\n const equation = (t, val0, val1, val2, val3) => {\n const res = (1.0 - t) * (1.0 - t) * (1.0 - t) * val0 + 3.0 * t * (1.0 - t) * (1.0 - t) * val1 + 3.0 * t * t * (1.0 - t) * val2 + t * t * t * val3;\n return res;\n };\n for (let i = 0; i <= nbPoints; i++) {\n bez.push(new Vector3(equation(i / nbPoints, v0.x, v1.x, v2.x, v3.x), equation(i / nbPoints, v0.y, v1.y, v2.y, v3.y), equation(i / nbPoints, v0.z, v1.z, v2.z, v3.z)));\n }\n return new Curve3(bez);\n }\n /**\n * Returns a Curve3 object along a Hermite Spline curve : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#hermite-spline\n * @param p1 (Vector3) the origin point of the Hermite Spline\n * @param t1 (Vector3) the tangent vector at the origin point\n * @param p2 (Vector3) the end point of the Hermite Spline\n * @param t2 (Vector3) the tangent vector at the end point\n * @param nSeg (integer) the number of curve segments or nSeg + 1 points in the array\n * @returns the created Curve3\n */\n static CreateHermiteSpline(p1, t1, p2, t2, nSeg) {\n const hermite = [];\n const step = 1.0 / nSeg;\n for (let i = 0; i <= nSeg; i++) {\n hermite.push(Vector3.Hermite(p1, t1, p2, t2, i * step));\n }\n return new Curve3(hermite);\n }\n /**\n * Returns a Curve3 object along a CatmullRom Spline curve :\n * @param points (array of Vector3) the points the spline must pass through. At least, four points required\n * @param nbPoints (integer) the wanted number of points between each curve control points\n * @param closed (boolean) optional with default false, when true forms a closed loop from the points\n * @returns the created Curve3\n */\n static CreateCatmullRomSpline(points, nbPoints, closed) {\n const catmullRom = [];\n const step = 1.0 / nbPoints;\n let amount = 0.0;\n if (closed) {\n const pointsCount = points.length;\n for (let i = 0; i < pointsCount; i++) {\n amount = 0;\n for (let c = 0; c < nbPoints; c++) {\n catmullRom.push(Vector3.CatmullRom(points[i % pointsCount], points[(i + 1) % pointsCount], points[(i + 2) % pointsCount], points[(i + 3) % pointsCount], amount));\n amount += step;\n }\n }\n catmullRom.push(catmullRom[0]);\n }\n else {\n const totalPoints = [];\n totalPoints.push(points[0].clone());\n Array.prototype.push.apply(totalPoints, points);\n totalPoints.push(points[points.length - 1].clone());\n let i = 0;\n for (; i < totalPoints.length - 3; i++) {\n amount = 0;\n for (let c = 0; c < nbPoints; c++) {\n catmullRom.push(Vector3.CatmullRom(totalPoints[i], totalPoints[i + 1], totalPoints[i + 2], totalPoints[i + 3], amount));\n amount += step;\n }\n }\n i--;\n catmullRom.push(Vector3.CatmullRom(totalPoints[i], totalPoints[i + 1], totalPoints[i + 2], totalPoints[i + 3], amount));\n }\n return new Curve3(catmullRom);\n }\n /**\n * Returns a Curve3 object along an arc through three vector3 points:\n * The three points should not be colinear. When they are the Curve3 is empty.\n * @param first (Vector3) the first point the arc must pass through.\n * @param second (Vector3) the second point the arc must pass through.\n * @param third (Vector3) the third point the arc must pass through.\n * @param steps (number) the larger the number of steps the more detailed the arc.\n * @param closed (boolean) optional with default false, when true forms the chord from the first and third point\n * @param fullCircle Circle (boolean) optional with default false, when true forms the complete circle through the three points\n * @returns the created Curve3\n */\n static ArcThru3Points(first, second, third, steps = 32, closed = false, fullCircle = false) {\n const arc = [];\n const vec1 = second.subtract(first);\n const vec2 = third.subtract(second);\n const vec3 = first.subtract(third);\n const zAxis = Vector3.Cross(vec1, vec2);\n const len4 = zAxis.length();\n if (len4 < Math.pow(10, -8)) {\n return new Curve3(arc); // colinear points arc is empty\n }\n const len1_sq = vec1.lengthSquared();\n const len2_sq = vec2.lengthSquared();\n const len3_sq = vec3.lengthSquared();\n const len4_sq = zAxis.lengthSquared();\n const len1 = vec1.length();\n const len2 = vec2.length();\n const len3 = vec3.length();\n const radius = (0.5 * len1 * len2 * len3) / len4;\n const dot1 = Vector3.Dot(vec1, vec3);\n const dot2 = Vector3.Dot(vec1, vec2);\n const dot3 = Vector3.Dot(vec2, vec3);\n const a = (-0.5 * len2_sq * dot1) / len4_sq;\n const b = (-0.5 * len3_sq * dot2) / len4_sq;\n const c = (-0.5 * len1_sq * dot3) / len4_sq;\n const center = first.scale(a).add(second.scale(b)).add(third.scale(c));\n const radiusVec = first.subtract(center);\n const xAxis = radiusVec.normalize();\n const yAxis = Vector3.Cross(zAxis, xAxis).normalize();\n if (fullCircle) {\n const dStep = (2 * Math.PI) / steps;\n for (let theta = 0; theta <= 2 * Math.PI; theta += dStep) {\n arc.push(center.add(xAxis.scale(radius * Math.cos(theta)).add(yAxis.scale(radius * Math.sin(theta)))));\n }\n arc.push(first);\n }\n else {\n const dStep = 1 / steps;\n let theta = 0;\n let point = Vector3.Zero();\n do {\n point = center.add(xAxis.scale(radius * Math.cos(theta)).add(yAxis.scale(radius * Math.sin(theta))));\n arc.push(point);\n theta += dStep;\n } while (!point.equalsWithEpsilon(third, radius * dStep * 1.1));\n arc.push(third);\n if (closed) {\n arc.push(first);\n }\n }\n return new Curve3(arc);\n }\n /**\n * A Curve3 object is a logical object, so not a mesh, to handle curves in the 3D geometric space.\n * A Curve3 is designed from a series of successive Vector3.\n * Tuto : https://doc.babylonjs.com/features/featuresDeepDive/mesh/drawCurves#curve3-object\n * @param points points which make up the curve\n */\n constructor(points) {\n this._length = 0.0;\n this._points = points;\n this._length = this._computeLength(points);\n }\n /**\n * @returns the Curve3 stored array of successive Vector3\n */\n getPoints() {\n return this._points;\n }\n /**\n * @returns the computed length (float) of the curve.\n */\n length() {\n return this._length;\n }\n /**\n * Returns a new instance of Curve3 object : var curve = curveA.continue(curveB);\n * This new Curve3 is built by translating and sticking the curveB at the end of the curveA.\n * curveA and curveB keep unchanged.\n * @param curve the curve to continue from this curve\n * @returns the newly constructed curve\n */\n continue(curve) {\n const lastPoint = this._points[this._points.length - 1];\n const continuedPoints = this._points.slice();\n const curvePoints = curve.getPoints();\n for (let i = 1; i < curvePoints.length; i++) {\n continuedPoints.push(curvePoints[i].subtract(curvePoints[0]).add(lastPoint));\n }\n const continuedCurve = new Curve3(continuedPoints);\n return continuedCurve;\n }\n _computeLength(path) {\n let l = 0;\n for (let i = 1; i < path.length; i++) {\n l += path[i].subtract(path[i - 1]).length();\n }\n return l;\n 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