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| var sqrt = Math.sqrt,
min = Math.min,
max = Math.max,
abs = Math.abs;
/**
* Calculate the square (power to two) of a number.
*
* @param {Number} n
*
* @return {Number}
*/
function sq(n) {
return Math.pow(n, 2);
}
/**
* Get distance between two points.
*
* @param {Point} p1
* @param {Point} p2
*
* @return {Number}
*/
function getDistance(p1, p2) {
return sqrt(sq(p1.x - p2.x) + sq(p1.y - p2.y));
}
/**
* Return the attachment of the given point on the specified line.
*
* The attachment is either a bendpoint (attached to the given point)
* or segment (attached to a location on a line segment) attachment:
*
* ```javascript
* var pointAttachment = {
* type: 'bendpoint',
* bendpointIndex: 3,
* position: { x: 10, y: 10 } // the attach point on the line
* };
*
* var segmentAttachment = {
* type: 'segment',
* segmentIndex: 2,
* relativeLocation: 0.31, // attach point location between 0 (at start) and 1 (at end)
* position: { x: 10, y: 10 } // the attach point on the line
* };
* ```
*
* @param {Point} point
* @param {Array<Point>} line
*
* @return {Object} attachment
*/
export function getAttachment(point, line) {
var idx = 0,
segmentStart,
segmentEnd,
segmentStartDistance,
segmentEndDistance,
attachmentPosition,
minDistance,
intersections,
attachment,
attachmentDistance,
closestAttachmentDistance,
closestAttachment;
for (idx = 0; idx < line.length - 1; idx++) {
segmentStart = line[idx];
segmentEnd = line[idx + 1];
if (pointsEqual(segmentStart, segmentEnd)) {
intersections = [ segmentStart ];
} else {
segmentStartDistance = getDistance(point, segmentStart);
segmentEndDistance = getDistance(point, segmentEnd);
minDistance = min(segmentStartDistance, segmentEndDistance);
intersections = getCircleSegmentIntersections(segmentStart, segmentEnd, point, minDistance);
}
Iif (intersections.length < 1) {
throw new Error('expected between [1, 2] circle -> line intersections');
}
// one intersection -> bendpoint attachment
if (intersections.length === 1) {
attachment = {
type: 'bendpoint',
position: intersections[0],
segmentIndex: idx,
bendpointIndex: pointsEqual(segmentStart, intersections[0]) ? idx : idx + 1
};
}
// two intersections -> segment attachment
if (intersections.length === 2) {
attachmentPosition = mid(intersections[0], intersections[1]);
attachment = {
type: 'segment',
position: attachmentPosition,
segmentIndex: idx,
relativeLocation: getDistance(segmentStart, attachmentPosition) / getDistance(segmentStart, segmentEnd)
};
}
attachmentDistance = getDistance(attachment.position, point);
if (!closestAttachment || closestAttachmentDistance > attachmentDistance) {
closestAttachment = attachment;
closestAttachmentDistance = attachmentDistance;
}
}
return closestAttachment;
}
/**
* Gets the intersection between a circle and a line segment.
*
* @param {Point} s1 segment start
* @param {Point} s2 segment end
* @param {Point} cc circle center
* @param {Number} cr circle radius
*
* @return {Array<Point>} intersections
*/
function getCircleSegmentIntersections(s1, s2, cc, cr) {
var baX = s2.x - s1.x;
var baY = s2.y - s1.y;
var caX = cc.x - s1.x;
var caY = cc.y - s1.y;
var a = baX * baX + baY * baY;
var bBy2 = baX * caX + baY * caY;
var c = caX * caX + caY * caY - cr * cr;
var pBy2 = bBy2 / a;
var q = c / a;
var disc = pBy2 * pBy2 - q;
// check against negative value to work around
// negative, very close to zero results (-4e-15)
// being produced in some environments
Iif (disc < 0 && disc > -0.000001) {
disc = 0;
}
Iif (disc < 0) {
return [];
}
// if disc == 0 ... dealt with later
var tmpSqrt = sqrt(disc);
var abScalingFactor1 = -pBy2 + tmpSqrt;
var abScalingFactor2 = -pBy2 - tmpSqrt;
var i1 = {
x: s1.x - baX * abScalingFactor1,
y: s1.y - baY * abScalingFactor1
};
if (disc === 0) { // abScalingFactor1 == abScalingFactor2
return [ i1 ];
}
var i2 = {
x: s1.x - baX * abScalingFactor2,
y: s1.y - baY * abScalingFactor2
};
// return only points on line segment
return [ i1, i2 ].filter(function(p) {
return isPointInSegment(p, s1, s2);
});
}
function isPointInSegment(p, segmentStart, segmentEnd) {
return (
fenced(p.x, segmentStart.x, segmentEnd.x) &&
fenced(p.y, segmentStart.y, segmentEnd.y)
);
}
function fenced(n, rangeStart, rangeEnd) {
// use matching threshold to work around
// precisison errors in intersection computation
return (
n >= min(rangeStart, rangeEnd) - EQUAL_THRESHOLD &&
n <= max(rangeStart, rangeEnd) + EQUAL_THRESHOLD
);
}
/**
* Calculate mid of two points.
*
* @param {Point} p1
* @param {Point} p2
*
* @return {Point}
*/
function mid(p1, p2) {
return {
x: (p1.x + p2.x) / 2,
y: (p1.y + p2.y) / 2
};
}
var EQUAL_THRESHOLD = 0.1;
function pointsEqual(p1, p2) {
return (
abs(p1.x - p2.x) <= EQUAL_THRESHOLD &&
abs(p1.y - p2.y) <= EQUAL_THRESHOLD
);
}
|