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import * as math from '../../../utilities/math';
import type {
ISpline,
SplineProps,
SplineLineSegment,
ClosestControlPoint,
ClosestSplinePoint,
ClosestPoint,
ControlPointInfo,
SplineCurveSegment,
} from '../../../types';
type CurveSegmentDistanceSquared = {
curveSegmentIndex: number;
curveSegment: SplineCurveSegment;
distanceSquared: number;
};
/**
* Spline curve representation
*
* You can find more about splines in this video
* https://www.youtube.com/watch?v=jvPPXbo87ds&t=11m20s
*/
abstract class Spline implements ISpline {
private _controlPoints: Types.Point2[] = [];
private _resolution: number;
private _fixedResolution: boolean;
private _closed: boolean;
private _invalidated = false;
private _curveSegments: SplineCurveSegment[];
private _aabb: Types.AABB2;
private _length = 0;
constructor(props?: SplineProps) {
this._controlPoints = [];
this._resolution = props?.resolution ?? 20;
this._fixedResolution = props?.fixedResolution ?? false;
this._closed = props?.closed ?? false;
this._invalidated = true;
}
/**
* Return the control points array
*
* Any external access should be done through getControlPoints because it
* clones the points to make sure the data will not get changed by the caller
*/
protected get controlPoints(): Types.Point2[] {
return this._controlPoints;
}
/** Number of control points */
public get numControlPoints(): number {
return this._controlPoints.length;
}
/** Resolution of the spline curve (greater than or equal to 0) */
public get resolution(): number {
return this._resolution;
}
/** Set the resolution of the spline curve */
public set resolution(resolution: number) {
if (this._fixedResolution || this._resolution === resolution) {
return;
}
this._resolution = resolution;
this.invalidated = true;
}
/** Fixed resolution
*
* Linar spline is one of the splines that does not allow changing the resolution
* for better performance otherwise it would calculate and render 20 line segments
* instead of a single one..
*/
public get fixedResolution() {
return this._fixedResolution;
}
/** Flag that is set to true when the curve is already closed */
public get closed(): boolean {
return this._closed;
}
/** Set the curve as closed which connects the last to the first point */
public set closed(closed: boolean) {
if (this._closed === closed) {
return;
}
this._closed = closed;
this.invalidated = true;
}
/** Axis-aligned bounding box (minX, minY, maxX, maxY) */
public get aabb(): Types.AABB2 {
this._update();
return this._aabb;
}
/** Length of the spline curve in pixels */
public get length(): number {
this._update();
return this._length;
}
/**
* Flag that is set to true when the spline needs to be updated. The update
* runs automaticaly when needed (eg: getPolylinePoints).
*/
public get invalidated(): boolean {
return this._invalidated;
}
/**
* Sets the spline as invalid when curve segments need to be recalculated
* or as valid after recomputing the curves
*/
protected set invalidated(invalidated: boolean) {
this._invalidated = invalidated;
}
/**
* Bézier curves have tangent points connected to control points
* @returns True if the spline has tangent point or false otherwise
*/
public hasTangentPoints() {
return false;
}
/**
* Add a control point to the end of the array
* @param point - Control point (2D)
*/
public addControlPoint(point: Types.Point2): void {
this._controlPoints.push([point[0], point[1]]);
this.invalidated = true;
}
/**
* Add a list of control poits to the end of the array
* @param points - Control points to be added
*/
public addControlPoints(points: Types.Point2[]): void {
points.forEach((point) => this.addControlPoint(point));
}
/**
* Add a control point specifying its `u` value in Parameter Space which is a number from 0 to N
* where N is the number of curve segments. The integer part is the curve segment index and the
* decimal part is the `t` value on that curve segment.
* @param u - `u` value in Parameter Space
*/
public addControlPointAtU(u: number): ControlPointInfo {
const lineSegment = this._getLineSegmentAt(u);
const { start: startPoint, end: endPoint } = lineSegment.points;
const curveSegmentIndex = Math.floor(u);
const curveSegment = this._curveSegments[curveSegmentIndex];
const t = u - Math.floor(curveSegmentIndex);
const controlPointPos: Types.Point2 = [
startPoint[0] + t * (endPoint[0] - startPoint[0]),
startPoint[1] + t * (endPoint[1] - startPoint[1]),
];
const insertIndex =
this._controlPoints.indexOf(curveSegment.controlPoints.p1) + 1;
this._controlPoints.splice(insertIndex, 0, controlPointPos);
this.invalidated = true;
return {
index: insertIndex,
point: controlPointPos,
};
}
/**
* Delete a control point given its index
* @param index - Control point index to be removed
* @returns True if the control point is removed or false otherwise
*/
public deleteControlPointByIndex(index: number): boolean {
const minControlPoints = this._closed ? 3 : 1;
const canDelete =
index >= 0 &&
index < this._controlPoints.length &&
this._controlPoints.length > minControlPoints;
if (!canDelete) {
return false;
}
this._controlPoints.splice(index, 1);
this.invalidated = true;
return true;
}
/**
* Remove all control points
*/
public clearControlPoints(): void {
this._controlPoints = [];
this.invalidated = true;
}
/**
* Replace all control points by some new ones
* @param points - Control points to be added to the array
*/
public setControlPoints(points: Types.Point2[]): void {
this.clearControlPoints();
this.addControlPoints(points);
}
/**
* Update the coordinate of a control point given its index
* @param index - Control point index
* @param newControlPoint - New control point
*/
public updateControlPoint(
index: number,
newControlPoint: Types.Point2
): void {
if (index < 0 || index >= this._controlPoints.length) {
throw new Error('Index out of bounds');
}
this._controlPoints[index] = [...newControlPoint];
this.invalidated = true;
}
/**
* Get a list with all control points. The control points are cloned to prevent
* any caller from changing them resulting in unexpected behaviors
* @returns - List of all control points
*/
public getControlPoints(): Types.Point2[] {
return this._controlPoints.map((controlPoint) => [
controlPoint[0],
controlPoint[1],
]);
}
/**
* Finds the closest control point given a 2D point
* @param point - Reference point
* @returns Closest control point
*/
public getClosestControlPoint(point: Types.Point2): ClosestControlPoint {
const controlPoints = this._controlPoints;
let minSquaredDist = Infinity;
let closestPointIndex = -1;
for (let i = 0, len = controlPoints.length; i < len; i++) {
const controlPoint = controlPoints[i];
const dx = point[0] - controlPoint[0];
const dy = point[1] - controlPoint[1];
const squaredDist = dx * dx + dy * dy;
if (squaredDist < minSquaredDist) {
minSquaredDist = squaredDist;
closestPointIndex = i;
}
}
return {
index: closestPointIndex,
point:
closestPointIndex === -1
? undefined
: [...controlPoints[closestPointIndex]],
distance: Math.sqrt(minSquaredDist),
};
}
/**
* Finds the closest control point given a 2D point and a maximum distance
* @param point - Reference 2D point
* @param maxDist - Maximum distance
* @returns Closest control point that is within the given range or undefined otherwise
*/
public getClosestControlPointWithinDistance(
point: Types.Point2,
maxDist: number
): ClosestControlPoint {
const closestControlPoint = this.getClosestControlPoint(point);
return closestControlPoint.distance <= maxDist
? closestControlPoint
: undefined;
}
/**
* Finds the closest point on the spline curve given 2D point
* @param point - Reference 2D point
* @returns Closest point on the spline curve
*/
public getClosestPoint(point: Types.Point2): ClosestSplinePoint {
this._update();
const curveSegmentsDistInfo =
this._getCurveSegmmentsDistanceSquaredInfo(point);
if (!curveSegmentsDistInfo.length) {
return;
}
// Sort the curves by distance because in most cases the closest point may be in the first
// curve segment and there is no need to check all next line segments if theirs curve segments'
// AABB is not closest compared to the minDist found saving a lot of cpu time.
curveSegmentsDistInfo.sort(
(csA, csB) => csA.distanceSquared - csB.distanceSquared
);
let closestPoint: Types.Point2;
let closestPointCurveSegmentIndex = -1;
let minDistSquared = Infinity;
let minDistCurveSegment: SplineCurveSegment;
let minDistLineSegment: SplineLineSegment;
for (let i = 0; i < curveSegmentsDistInfo.length; i++) {
const curveSegmentDistInfo = curveSegmentsDistInfo[i];
// If the distance to curve segments' AABB is greater than the minDist
// it does not need to waste time verifying each line segment
if (curveSegmentDistInfo.distanceSquared > minDistSquared) {
continue;
}
const { curveSegmentIndex, curveSegment } = curveSegmentDistInfo;
const { lineSegments } = curveSegment;
for (let j = 0; j < lineSegments.length; j++) {
const lineSegment = lineSegments[j];
const { point: lineSegPoint, distanceSquared: lineSegDistSquared } =
math.lineSegment.distanceToPointSquaredInfo(
lineSegment.points.start,
lineSegment.points.end,
point
);
if (lineSegDistSquared < minDistSquared) {
minDistLineSegment = lineSegment;
closestPointCurveSegmentIndex = curveSegmentIndex;
minDistCurveSegment = curveSegmentDistInfo.curveSegment;
closestPoint = lineSegPoint;
minDistSquared = lineSegDistSquared;
}
}
}
const curveSegmentLengthToPoint =
minDistLineSegment.previousLineSegmentsLength +
math.point.distanceToPoint(minDistLineSegment.points.start, closestPoint);
const t = curveSegmentLengthToPoint / minDistCurveSegment.length;
const u = closestPointCurveSegmentIndex + t;
return {
point: closestPoint,
uValue: u,
distance: Math.sqrt(minDistSquared),
};
}
/**
* Finds the closest point on the straight line that connects all control points given a 2D point
* @param point - Reference point
* @returns Closest point on the straight line that connects all control points
*/
public getClosestPointOnControlPointLines(point: Types.Point2): ClosestPoint {
const linePoints = [...this._controlPoints];
if (this._closed) {
linePoints.push(this._controlPoints[0]);
}
if (!linePoints.length) {
return;
}
let closestPoint: Types.Point2;
let minDistSquared = Infinity;
let startPoint = linePoints[0];
for (let i = 1, len = linePoints.length; i < len; i++) {
const endPoint = linePoints[i];
const { point: lineSegPoint, distanceSquared: lineSegDistSquared } =
math.lineSegment.distanceToPointSquaredInfo(
startPoint,
endPoint,
point
);
if (lineSegDistSquared < minDistSquared) {
closestPoint = lineSegPoint;
minDistSquared = lineSegDistSquared;
}
startPoint = endPoint;
}
return {
point: closestPoint,
distance: Math.sqrt(minDistSquared),
};
}
/**
* Get all points necessary to draw a spline curve
* @returns Array with all points necessary to draw a spline curve
*/
public getPolylinePoints(): Types.Point2[] {
this._update();
return this._convertCurveSegmentsToPolyline(this._curveSegments);
}
/**
* Get all points necessary to draw the preview of the changes that shall be
* made to the spline if a new control point is added to it
* @param controlPointPreview - New control point preview
* @param closeDistance - Distance to the first control point to consider it a closed spline
* @returns Array with all points necessary to draw a spline curve preview
*/
public getPreviewPolylinePoints(
controlPointPreview: Types.Point2,
closeDistance: number
): Types.Point2[] {
if (this._closed) {
return [];
}
this._update();
// Check if the new control point would be close to the first one
// in order to create a preview of a closed spline
const closestControlPoint = this.getClosestControlPointWithinDistance(
controlPointPreview,
closeDistance
);
const closeSpline = closestControlPoint?.index === 0;
const previewCurveSegments = this.getPreviewCurveSegments(
controlPointPreview,
closeSpline
);
return previewCurveSegments?.length
? this._convertCurveSegmentsToPolyline(previewCurveSegments)
: [];
}
/**
* Checks if a point is near to the spline curve
* @param point - Reference point
* @param maxDist - Maximum allowed distance
* @returns True if the point is close to the spline curve or false otherwise
*/
public isPointNearCurve(point: Types.Point2, maxDist: number): boolean {
this._update();
const curveSegments = this._getCurveSegmmentsWithinDistance(point, maxDist);
const maxDistSquared = maxDist * maxDist;
// Check if the point is close to the spline and doest waste time checking each curve/line
for (let i = 0; i < curveSegments.length; i++) {
const { lineSegments } = curveSegments[i];
for (let j = 0; j < lineSegments.length; j++) {
const lineSegment = lineSegments[j];
const lineDistSquared = math.lineSegment.distanceToPointSquared(
lineSegment.points.start,
lineSegment.points.end,
point
);
if (lineDistSquared <= maxDistSquared) {
return true;
}
}
}
return false;
}
/**
* Checks if a 2D point is inside the spline curve.
*
* A point is inside a curve/polygon if the number of intersections between the horizontal
* ray emanating from the given point and to the right and the line segments is odd.
* https://www.eecs.umich.edu/courses/eecs380/HANDOUTS/PROJ2/InsidePoly.html
*
* @param point - 2D Point
* @returns True is the point is inside the spline curve or false otherwise
*/
public containsPoint(point: Types.Point2): boolean {
this._update();
const controlPoints = this._controlPoints;
if (controlPoints.length < 3) {
return false;
}
const curveSegments = [...this._curveSegments];
const closingCurveSegment =
this._getClosingCurveSegmentWithStraightLineSegment();
if (closingCurveSegment) {
curveSegments.push(closingCurveSegment);
}
let numIntersections = 0;
for (let i = 0; i < curveSegments.length; i++) {
const curveSegment = curveSegments[i];
const { aabb: curveSegAABB } = curveSegment;
const mayIntersectCurveSegment =
point[0] <= curveSegAABB.maxX &&
point[1] >= curveSegAABB.minY &&
point[1] < curveSegAABB.maxY;
// Skip all line segments if it is not possible to intersect the curve segment
if (!mayIntersectCurveSegment) {
continue;
}
const { lineSegments } = curveSegment;
for (let i = 0; i < lineSegments.length; i++) {
const lineSegment = lineSegments[i];
const { aabb: lineSegmentAABB } = lineSegment;
const mayIntersectLineSegment =
point[0] <= lineSegmentAABB.maxX &&
point[1] >= lineSegmentAABB.minY &&
point[1] < lineSegmentAABB.maxY;
if (mayIntersectLineSegment) {
const { start: p1, end: p2 } = lineSegment.points;
const isVerticalLine = p1[0] === p2[0];
const xIntersection =
((point[1] - p1[1]) * (p2[0] - p1[0])) / (p2[1] - p1[1]) + p1[0];
numIntersections +=
isVerticalLine || point[0] <= xIntersection ? 1 : 0;
}
}
}
return numIntersections % 2 === 1;
}
protected abstract getTransformMatrix(): number[];
protected abstract getSplineCurves(): SplineCurveSegment[];
protected abstract getPreviewCurveSegments(
controlPointPreview: Types.Point2,
closeSpline: boolean
): SplineCurveSegment[];
private _update() {
if (!this._invalidated) {
return;
}
const curveSegments = this.getSplineCurves();
let length = 0;
let minX = Infinity;
let minY = Infinity;
let maxX = -Infinity;
let maxY = -Infinity;
for (let i = 0, len = curveSegments.length; i < len; i++) {
const { aabb: curveSegAABB, length: curveSegLength } = curveSegments[i];
minX = minX <= curveSegAABB.minX ? minX : curveSegAABB.minX;
minY = minY <= curveSegAABB.minY ? minY : curveSegAABB.minY;
maxX = maxX >= curveSegAABB.maxX ? maxX : curveSegAABB.maxX;
maxY = maxY >= curveSegAABB.maxY ? maxY : curveSegAABB.maxY;
length += curveSegLength;
}
this._curveSegments = curveSegments;
this._aabb = { minX, minY, maxX, maxY };
this._length = length;
this._invalidated = false;
}
private _convertCurveSegmentsToPolyline(
curveSegments: SplineCurveSegment[]
): Types.Point2[] {
this._update();
const polylinePoints: Types.Point2[] = [];
curveSegments.forEach(({ lineSegments }, curveSegIndex) => {
lineSegments.forEach((lineSegment, lineSegIndex) => {
// Add the start point before adding all end points
if (curveSegIndex === 0 && lineSegIndex === 0) {
polylinePoints.push([...lineSegment.points.start]);
}
// Always add 1 because the first segment stored its start point at the first position
polylinePoints.push([...lineSegment.points.end]);
});
});
return polylinePoints;
}
/**
* Returns all curve segments and theirs respective squared distance to a given point
* @param point - Reference point
* @returns Curve segments and theirs respective squared distance to a given point
*/
private _getCurveSegmmentsDistanceSquaredInfo(
point: Types.Point2
): CurveSegmentDistanceSquared[] {
this._update();
const curveSegmentsDistanceSquared: CurveSegmentDistanceSquared[] = [];
const { _curveSegments: curveSegments } = this;
for (let i = 0; i < curveSegments.length; i++) {
const curveSegment = curveSegments[i];
const distanceSquared = math.aabb.distanceToPointSquared(
curveSegment.aabb,
point
);
curveSegmentsDistanceSquared.push({
curveSegmentIndex: i,
curveSegment,
distanceSquared,
});
}
return curveSegmentsDistanceSquared;
}
private _getCurveSegmmentsWithinDistance(
point: Types.Point2,
maxDist: number
): SplineCurveSegment[] {
this._update();
const maxDistSquared = maxDist * maxDist;
// Does not waste time checking each curve segment if the point is not event
// close to the spline's AABB
if (math.aabb.distanceToPointSquared(this.aabb, point) > maxDistSquared) {
return [];
}
const curveSegmentsDistance =
this._getCurveSegmmentsDistanceSquaredInfo(point);
const curveSegmentsWithinRange: SplineCurveSegment[] = [];
for (let i = 0, len = curveSegmentsDistance.length; i < len; i++) {
const { curveSegment, distanceSquared: curveSegmentDistSquared } =
curveSegmentsDistance[i];
if (curveSegmentDistSquared <= maxDistSquared) {
curveSegmentsWithinRange.push(curveSegment);
}
}
return curveSegmentsWithinRange;
}
private _getLineSegmentAt(u: number): SplineLineSegment {
this._update();
const curveSegmentIndex = Math.floor(u);
const t = u - curveSegmentIndex;
const curveSegment = this._curveSegments[curveSegmentIndex];
const { lineSegments } = curveSegment;
const pointLength = curveSegment.length * t;
for (let i = 0; i < lineSegments.length; i++) {
const lineSegment = lineSegments[i];
const lengthEnd =
lineSegment.previousLineSegmentsLength + lineSegment.length;
if (
pointLength >= lineSegment.previousLineSegmentsLength &&
pointLength <= lengthEnd
) {
return lineSegment;
}
}
}
/**
* Creates a curve segment with a single line segment connecting the start and end control points
* @returns A curve segment that closes the spline
*/
private _getClosingCurveSegmentWithStraightLineSegment(): SplineCurveSegment {
if (this.closed) {
return;
}
const controlPoints = this._controlPoints;
const startControlPoint = controlPoints[0];
const endControlPoint = controlPoints[controlPoints.length - 1];
// The only properties needed are `points` and `aabb`. All the other ones may undefined
const closingLineSegment: SplineLineSegment = {
points: {
start: [...startControlPoint],
end: [...endControlPoint],
},
aabb: {
minX: Math.min(startControlPoint[0], endControlPoint[0]),
minY: Math.min(startControlPoint[1], endControlPoint[1]),
maxX: Math.max(startControlPoint[0], endControlPoint[0]),
maxY: Math.max(startControlPoint[1], endControlPoint[1]),
},
} as SplineLineSegment;
// The only properties needed are `lineSegments` and `aabb`. All the other ones may undefined
return {
aabb: {
minX: closingLineSegment.aabb.minX,
minY: closingLineSegment.aabb.minY,
maxX: closingLineSegment.aabb.maxX,
maxY: closingLineSegment.aabb.maxY,
},
lineSegments: [closingLineSegment],
} as SplineCurveSegment;
}
}
export { Spline as default, Spline };
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