+2
@@ -0,0 +1,2 @@
|
||||
import { Point } from './index.js';
|
||||
export declare function curveToBezier(pointsIn: Point[], curveTightness?: number): Point[];
|
||||
+35
@@ -0,0 +1,35 @@
|
||||
function clone(p) {
|
||||
return [...p];
|
||||
}
|
||||
export function curveToBezier(pointsIn, curveTightness = 0) {
|
||||
const len = pointsIn.length;
|
||||
if (len < 3) {
|
||||
throw new Error('A curve must have at least three points.');
|
||||
}
|
||||
const out = [];
|
||||
if (len === 3) {
|
||||
out.push(clone(pointsIn[0]), clone(pointsIn[1]), clone(pointsIn[2]), clone(pointsIn[2]));
|
||||
}
|
||||
else {
|
||||
const points = [];
|
||||
points.push(pointsIn[0], pointsIn[0]);
|
||||
for (let i = 1; i < pointsIn.length; i++) {
|
||||
points.push(pointsIn[i]);
|
||||
if (i === (pointsIn.length - 1)) {
|
||||
points.push(pointsIn[i]);
|
||||
}
|
||||
}
|
||||
const b = [];
|
||||
const s = 1 - curveTightness;
|
||||
out.push(clone(points[0]));
|
||||
for (let i = 1; (i + 2) < points.length; i++) {
|
||||
const cachedVertArray = points[i];
|
||||
b[0] = [cachedVertArray[0], cachedVertArray[1]];
|
||||
b[1] = [cachedVertArray[0] + (s * points[i + 1][0] - s * points[i - 1][0]) / 6, cachedVertArray[1] + (s * points[i + 1][1] - s * points[i - 1][1]) / 6];
|
||||
b[2] = [points[i + 1][0] + (s * points[i][0] - s * points[i + 2][0]) / 6, points[i + 1][1] + (s * points[i][1] - s * points[i + 2][1]) / 6];
|
||||
b[3] = [points[i + 1][0], points[i + 1][1]];
|
||||
out.push(b[1], b[2], b[3]);
|
||||
}
|
||||
}
|
||||
return out;
|
||||
}
|
||||
+3
@@ -0,0 +1,3 @@
|
||||
export declare type Point = [number, number];
|
||||
export declare function simplify(points: Point[], distance: number): Point[];
|
||||
export declare function pointsOnBezierCurves(points: Point[], tolerance?: number, distance?: number): Point[];
|
||||
+123
@@ -0,0 +1,123 @@
|
||||
// distance between 2 points
|
||||
function distance(p1, p2) {
|
||||
return Math.sqrt(distanceSq(p1, p2));
|
||||
}
|
||||
// distance between 2 points squared
|
||||
function distanceSq(p1, p2) {
|
||||
return Math.pow(p1[0] - p2[0], 2) + Math.pow(p1[1] - p2[1], 2);
|
||||
}
|
||||
// Sistance squared from a point p to the line segment vw
|
||||
function distanceToSegmentSq(p, v, w) {
|
||||
const l2 = distanceSq(v, w);
|
||||
if (l2 === 0) {
|
||||
return distanceSq(p, v);
|
||||
}
|
||||
let t = ((p[0] - v[0]) * (w[0] - v[0]) + (p[1] - v[1]) * (w[1] - v[1])) / l2;
|
||||
t = Math.max(0, Math.min(1, t));
|
||||
return distanceSq(p, lerp(v, w, t));
|
||||
}
|
||||
function lerp(a, b, t) {
|
||||
return [
|
||||
a[0] + (b[0] - a[0]) * t,
|
||||
a[1] + (b[1] - a[1]) * t,
|
||||
];
|
||||
}
|
||||
// Adapted from https://seant23.wordpress.com/2010/11/12/offset-bezier-curves/
|
||||
function flatness(points, offset) {
|
||||
const p1 = points[offset + 0];
|
||||
const p2 = points[offset + 1];
|
||||
const p3 = points[offset + 2];
|
||||
const p4 = points[offset + 3];
|
||||
let ux = 3 * p2[0] - 2 * p1[0] - p4[0];
|
||||
ux *= ux;
|
||||
let uy = 3 * p2[1] - 2 * p1[1] - p4[1];
|
||||
uy *= uy;
|
||||
let vx = 3 * p3[0] - 2 * p4[0] - p1[0];
|
||||
vx *= vx;
|
||||
let vy = 3 * p3[1] - 2 * p4[1] - p1[1];
|
||||
vy *= vy;
|
||||
if (ux < vx) {
|
||||
ux = vx;
|
||||
}
|
||||
if (uy < vy) {
|
||||
uy = vy;
|
||||
}
|
||||
return ux + uy;
|
||||
}
|
||||
function getPointsOnBezierCurveWithSplitting(points, offset, tolerance, newPoints) {
|
||||
const outPoints = newPoints || [];
|
||||
if (flatness(points, offset) < tolerance) {
|
||||
const p0 = points[offset + 0];
|
||||
if (outPoints.length) {
|
||||
const d = distance(outPoints[outPoints.length - 1], p0);
|
||||
if (d > 1) {
|
||||
outPoints.push(p0);
|
||||
}
|
||||
}
|
||||
else {
|
||||
outPoints.push(p0);
|
||||
}
|
||||
outPoints.push(points[offset + 3]);
|
||||
}
|
||||
else {
|
||||
// subdivide
|
||||
const t = .5;
|
||||
const p1 = points[offset + 0];
|
||||
const p2 = points[offset + 1];
|
||||
const p3 = points[offset + 2];
|
||||
const p4 = points[offset + 3];
|
||||
const q1 = lerp(p1, p2, t);
|
||||
const q2 = lerp(p2, p3, t);
|
||||
const q3 = lerp(p3, p4, t);
|
||||
const r1 = lerp(q1, q2, t);
|
||||
const r2 = lerp(q2, q3, t);
|
||||
const red = lerp(r1, r2, t);
|
||||
getPointsOnBezierCurveWithSplitting([p1, q1, r1, red], 0, tolerance, outPoints);
|
||||
getPointsOnBezierCurveWithSplitting([red, r2, q3, p4], 0, tolerance, outPoints);
|
||||
}
|
||||
return outPoints;
|
||||
}
|
||||
export function simplify(points, distance) {
|
||||
return simplifyPoints(points, 0, points.length, distance);
|
||||
}
|
||||
// Ramer–Douglas–Peucker algorithm
|
||||
// https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm
|
||||
function simplifyPoints(points, start, end, epsilon, newPoints) {
|
||||
const outPoints = newPoints || [];
|
||||
// find the most distance point from the endpoints
|
||||
const s = points[start];
|
||||
const e = points[end - 1];
|
||||
let maxDistSq = 0;
|
||||
let maxNdx = 1;
|
||||
for (let i = start + 1; i < end - 1; ++i) {
|
||||
const distSq = distanceToSegmentSq(points[i], s, e);
|
||||
if (distSq > maxDistSq) {
|
||||
maxDistSq = distSq;
|
||||
maxNdx = i;
|
||||
}
|
||||
}
|
||||
// if that point is too far, split
|
||||
if (Math.sqrt(maxDistSq) > epsilon) {
|
||||
simplifyPoints(points, start, maxNdx + 1, epsilon, outPoints);
|
||||
simplifyPoints(points, maxNdx, end, epsilon, outPoints);
|
||||
}
|
||||
else {
|
||||
if (!outPoints.length) {
|
||||
outPoints.push(s);
|
||||
}
|
||||
outPoints.push(e);
|
||||
}
|
||||
return outPoints;
|
||||
}
|
||||
export function pointsOnBezierCurves(points, tolerance = 0.15, distance) {
|
||||
const newPoints = [];
|
||||
const numSegments = (points.length - 1) / 3;
|
||||
for (let i = 0; i < numSegments; i++) {
|
||||
const offset = i * 3;
|
||||
getPointsOnBezierCurveWithSplitting(points, offset, tolerance, newPoints);
|
||||
}
|
||||
if (distance && distance > 0) {
|
||||
return simplifyPoints(newPoints, 0, newPoints.length, distance);
|
||||
}
|
||||
return newPoints;
|
||||
}
|
||||
Reference in New Issue
Block a user