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Line and segment intersection

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Mark Tolmacs 2024-09-30 14:00:52 +02:00
parent f347281c21
commit b7f504796b
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3 changed files with 157 additions and 29 deletions
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82
packages/math/segment.ts
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@ -1,3 +1,4 @@
import { lineIntersectsSegment } from "./line";
import {
isPoint,
pointCenter,
@ -5,7 +6,7 @@ import {
pointRotateRads,
pointsEqual,
} from "./point";
import type { GenericPoint, Segment, Radians } from "./types";
import type { GenericPoint, Segment, Radians, Line } from "./types";
import { PRECISION } from "./utils";
import {
vectorAdd,
@ -38,17 +39,21 @@ export function segmentFromPointArray<P extends GenericPoint>(
}
/**
* Determines if the provided value is a segment
*
* @param segment
* @returns
* @param value The candidate
* @returns Returns TRUE if the provided value is a segment
*/
export const isSegment = <Point extends GenericPoint>(
segment: unknown,
): segment is Segment<Point> =>
Array.isArray(segment) &&
segment.length === 2 &&
isPoint(segment[0]) &&
isPoint(segment[0]);
export function isSegment<Point extends GenericPoint>(
value: unknown,
): value is Segment<Point> {
return (
Array.isArray(value) &&
segment.length === 2 &&
isPoint(value[0]) &&
isPoint(value[0])
);
}
/**
* Return the coordinates resulting from rotating the given line about an origin by an angle in radians
@ -59,25 +64,25 @@ export const isSegment = <Point extends GenericPoint>(
* @param origin
* @returns
*/
export const segmentRotate = <Point extends GenericPoint>(
export function segmentRotate<Point extends GenericPoint>(
l: Segment<Point>,
angle: Radians,
origin?: Point,
): Segment<Point> => {
): Segment<Point> {
return segment(
pointRotateRads(l[0], origin || pointCenter(l[0], l[1]), angle),
pointRotateRads(l[1], origin || pointCenter(l[0], l[1]), angle),
);
};
}
/**
* Calculates the point two line segments with a definite start and end point
* intersect at.
*/
export const segmentsIntersectAt = <Point extends GenericPoint>(
export function segmentsIntersectAt<Point extends GenericPoint>(
a: Readonly<Segment<Point>>,
b: Readonly<Segment<Point>>,
): Point | null => {
): Point | null {
const a0 = vectorFromPoint(a[0]);
const a1 = vectorFromPoint(a[1]);
const b0 = vectorFromPoint(b[0]);
@ -105,26 +110,41 @@ export const segmentsIntersectAt = <Point extends GenericPoint>(
}
return null;
};
}
export const segmentIncludesPoint = <Point extends GenericPoint>(
/**
* Determnines if a point lies on a segment
*
* @param point
* @param s
* @param threshold
* @returns
*/
export function segmentIncludesPoint<Point extends GenericPoint>(
point: Point,
line: Segment<Point>,
s: Segment<Point>,
threshold = PRECISION,
) => {
const distance = segmentDistanceToPoint(point, line);
) {
const distance = segmentDistanceToPoint(point, s);
if (distance === 0) {
return true;
}
return distance < threshold;
};
}
export const segmentDistanceToPoint = <Point extends GenericPoint>(
/**
* Returns the shortest distance from a point to a segment.
*
* @param p
* @param s
* @returns
*/
export function segmentDistanceToPoint<Point extends GenericPoint>(
p: Point,
s: Segment<Point>,
) => {
): number {
const [x, y] = p;
const [[x1, y1], [x2, y2]] = s;
@ -157,4 +177,18 @@ export const segmentDistanceToPoint = <Point extends GenericPoint>(
const dx = x - xx;
const dy = y - yy;
return Math.sqrt(dx * dx + dy * dy);
};
}
/**
* Returns the intersection point between a segment and a line, if any
*
* @param s
* @param l
* @returns
*/
export function segmentIntersectsLine<Point extends GenericPoint>(
s: Segment<Point>,
l: Line<Point>,
): Point | null {
return lineIntersectsSegment(l, s);
}