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import type { Polycurve, Polyline } from "./geometry/shape";
import {
pointInEllipse,
pointOnEllipse,
type GeometricShape,
} from "./geometry/shape";
import type { Curve } from "@excalidraw/math";
import {
lineSegment,
pointFrom,
polygonIncludesPoint,
pointOnLineSegment,
pointOnPolygon,
polygonFromPoints,
type GlobalPoint,
type LocalPoint,
type Polygon,
} from "@excalidraw/math";
// check if the given point is considered on the given shape's border
export const isPointOnShape = <Point extends GlobalPoint | LocalPoint>(
point: Point,
shape: GeometricShape<Point>,
tolerance = 0,
) => {
// get the distance from the given point to the given element
// check if the distance is within the given epsilon range
switch (shape.type) {
case "polygon":
return pointOnPolygon(point, shape.data, tolerance);
case "ellipse":
return pointOnEllipse(point, shape.data, tolerance);
case "line":
return pointOnLineSegment(point, shape.data, tolerance);
case "polyline":
return pointOnPolyline(point, shape.data, tolerance);
case "curve":
return pointOnCurve(point, shape.data, tolerance);
case "polycurve":
return pointOnPolycurve(point, shape.data, tolerance);
default:
throw Error(`shape ${shape} is not implemented`);
}
};
// check if the given point is considered inside the element's border
export const isPointInShape = <Point extends GlobalPoint | LocalPoint>(
point: Point,
shape: GeometricShape<Point>,
) => {
switch (shape.type) {
case "polygon":
return polygonIncludesPoint(point, shape.data);
case "line":
return false;
case "curve":
return false;
case "ellipse":
return pointInEllipse(point, shape.data);
case "polyline": {
const polygon = polygonFromPoints(shape.data.flat());
return polygonIncludesPoint(point, polygon);
}
case "polycurve": {
return false;
}
default:
throw Error(`shape ${shape} is not implemented`);
}
};
// check if the given element is in the given bounds
export const isPointInBounds = <Point extends GlobalPoint | LocalPoint>(
point: Point,
bounds: Polygon<Point>,
) => {
return polygonIncludesPoint(point, bounds);
};
const pointOnPolycurve = <Point extends LocalPoint | GlobalPoint>(
point: Point,
polycurve: Polycurve<Point>,
tolerance: number,
) => {
return polycurve.some((curve) => pointOnCurve(point, curve, tolerance));
};
const cubicBezierEquation = <Point extends LocalPoint | GlobalPoint>(
curve: Curve<Point>,
) => {
const [p0, p1, p2, p3] = curve;
// B(t) = p0 * (1-t)^3 + 3p1 * t * (1-t)^2 + 3p2 * t^2 * (1-t) + p3 * t^3
return (t: number, idx: number) =>
Math.pow(1 - t, 3) * p3[idx] +
3 * t * Math.pow(1 - t, 2) * p2[idx] +
3 * Math.pow(t, 2) * (1 - t) * p1[idx] +
p0[idx] * Math.pow(t, 3);
};
const polyLineFromCurve = <Point extends LocalPoint | GlobalPoint>(
curve: Curve<Point>,
segments = 10,
): Polyline<Point> => {
const equation = cubicBezierEquation(curve);
let startingPoint = [equation(0, 0), equation(0, 1)] as Point;
const lineSegments: Polyline<Point> = [];
let t = 0;
const increment = 1 / segments;
for (let i = 0; i < segments; i++) {
t += increment;
if (t <= 1) {
const nextPoint: Point = pointFrom(equation(t, 0), equation(t, 1));
lineSegments.push(lineSegment(startingPoint, nextPoint));
startingPoint = nextPoint;
}
}
return lineSegments;
};
export const pointOnCurve = <Point extends LocalPoint | GlobalPoint>(
point: Point,
curve: Curve<Point>,
threshold: number,
) => {
return pointOnPolyline(point, polyLineFromCurve(curve), threshold);
};
export const pointOnPolyline = <Point extends LocalPoint | GlobalPoint>(
point: Point,
polyline: Polyline<Point>,
threshold = 10e-5,
) => {
return polyline.some((line) => pointOnLineSegment(point, line, threshold));
};
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