120 lines
2.9 KiB
TypeScript
120 lines
2.9 KiB
TypeScript
import { Point } from "./types";
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// https://stackoverflow.com/a/6853926/232122
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export function distanceBetweenPointAndSegment(
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x: number,
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y: number,
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x1: number,
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y1: number,
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x2: number,
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y2: number,
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) {
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const A = x - x1;
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const B = y - y1;
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const C = x2 - x1;
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const D = y2 - y1;
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const dot = A * C + B * D;
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const lenSquare = C * C + D * D;
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let param = -1;
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if (lenSquare !== 0) {
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// in case of 0 length line
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param = dot / lenSquare;
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}
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let xx, yy;
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if (param < 0) {
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xx = x1;
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yy = y1;
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} else if (param > 1) {
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xx = x2;
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yy = y2;
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} else {
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xx = x1 + param * C;
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yy = y1 + param * D;
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}
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const dx = x - xx;
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const dy = y - yy;
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return Math.hypot(dx, dy);
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}
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export function rotate(
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x1: number,
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y1: number,
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x2: number,
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y2: number,
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angle: number,
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) {
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// 𝑎′𝑥=(𝑎𝑥−𝑐𝑥)cos𝜃−(𝑎𝑦−𝑐𝑦)sin𝜃+𝑐𝑥
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// 𝑎′𝑦=(𝑎𝑥−𝑐𝑥)sin𝜃+(𝑎𝑦−𝑐𝑦)cos𝜃+𝑐𝑦.
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// https://math.stackexchange.com/questions/2204520/how-do-i-rotate-a-line-segment-in-a-specific-point-on-the-line
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return [
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(x1 - x2) * Math.cos(angle) - (y1 - y2) * Math.sin(angle) + x2,
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(x1 - x2) * Math.sin(angle) + (y1 - y2) * Math.cos(angle) + y2,
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];
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}
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export const getPointOnAPath = (point: Point, path: Point[]) => {
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const [px, py] = point;
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const [start, ...other] = path;
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let [lastX, lastY] = start;
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let kLine: number = 0;
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let idx: number = 0;
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// if any item in the array is true, it means that a point is
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// on some segment of a line based path
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const retVal = other.some(([x2, y2], i) => {
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// we always take a line when dealing with line segments
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const x1 = lastX;
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const y1 = lastY;
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lastX = x2;
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lastY = y2;
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// if a point is not within the domain of the line segment
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// it is not on the line segment
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if (px < x1 || px > x2) {
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return false;
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}
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// check if all points lie on the same line
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// y1 = kx1 + b, y2 = kx2 + b
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// y2 - y1 = k(x2 - x2) -> k = (y2 - y1) / (x2 - x1)
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// coefficient for the line (p0, p1)
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const kL = (y2 - y1) / (x2 - x1);
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// coefficient for the line segment (p0, point)
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const kP1 = (py - y1) / (px - x1);
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// coefficient for the line segment (point, p1)
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const kP2 = (py - y2) / (px - x2);
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// because we are basing both lines from the same starting point
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// the only option for collinearity is having same coefficients
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// using it for floating point comparisons
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const epsilon = 0.3;
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// if coefficient is more than an arbitrary epsilon,
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// these lines are nor collinear
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if (Math.abs(kP1 - kL) > epsilon && Math.abs(kP2 - kL) > epsilon) {
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return false;
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}
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// store the coefficient because we are goint to need it
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kLine = kL;
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idx = i;
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return true;
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});
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// Return a coordinate that is always on the line segment
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if (retVal === true) {
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return { x: point[0], y: kLine * point[0], segment: idx };
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}
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return null;
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};
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