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@ -1,12 +1,5 @@
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import { radians } from "./angle";
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import { line } from "./line";
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import {
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point,
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pointDistance,
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pointFromVector,
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pointRotateRads,
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} from "./point";
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import type { Ellipse, GenericPoint, Segment, Radians } from "./types";
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import { point, pointDistance, pointFromVector } from "./point";
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import type { Ellipse, GenericPoint, Segment } from "./types";
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import { PRECISION } from "./utils";
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import {
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vector,
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@ -27,13 +20,11 @@ import {
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*/
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export function ellipse<Point extends GenericPoint>(
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center: Point,
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angle: Radians,
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halfWidth: number,
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halfHeight: number,
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): Ellipse<Point> {
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return {
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center,
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angle,
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halfWidth,
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halfHeight,
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} as Ellipse<Point>;
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@ -50,22 +41,11 @@ export const ellipseIncludesPoint = <Point extends GenericPoint>(
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p: Point,
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ellipse: Ellipse<Point>,
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) => {
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const { center, angle, halfWidth, halfHeight } = ellipse;
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const translatedPoint = vectorAdd(
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vectorFromPoint(p),
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vectorScale(vectorFromPoint(center), -1),
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);
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const [rotatedPointX, rotatedPointY] = pointRotateRads(
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pointFromVector(translatedPoint),
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point(0, 0),
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radians(-angle),
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);
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const { center, halfWidth, halfHeight } = ellipse;
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const normalizedX = (p[0] - center[0]) / halfWidth;
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const normalizedY = (p[1] - center[1]) / halfHeight;
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return (
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(rotatedPointX / halfWidth) * (rotatedPointX / halfWidth) +
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(rotatedPointY / halfHeight) * (rotatedPointY / halfHeight) <=
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1
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);
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return normalizedX * normalizedX + normalizedY * normalizedY <= 1;
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};
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/**
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@ -97,21 +77,16 @@ export const ellipseDistanceFromPoint = <Point extends GenericPoint>(
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p: Point,
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ellipse: Ellipse<Point>,
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): number => {
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const { angle, halfWidth, halfHeight, center } = ellipse;
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const { halfWidth, halfHeight, center } = ellipse;
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const a = halfWidth;
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const b = halfHeight;
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const translatedPoint = vectorAdd(
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vectorFromPoint(p),
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vectorScale(vectorFromPoint(center), -1),
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);
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const [rotatedPointX, rotatedPointY] = pointRotateRads(
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pointFromVector(translatedPoint),
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point(0, 0),
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radians(-angle),
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);
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const px = Math.abs(rotatedPointX);
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const py = Math.abs(rotatedPointY);
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const px = Math.abs(translatedPoint[0]);
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const py = Math.abs(translatedPoint[1]);
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let tx = 0.707;
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let ty = 0.707;
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@ -140,11 +115,11 @@ export const ellipseDistanceFromPoint = <Point extends GenericPoint>(
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}
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const [minX, minY] = [
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a * tx * Math.sign(rotatedPointX),
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b * ty * Math.sign(rotatedPointY),
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a * tx * Math.sign(translatedPoint[0]),
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b * ty * Math.sign(translatedPoint[1]),
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];
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return pointDistance(point(rotatedPointX, rotatedPointY), point(minX, minY));
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return pointDistance(pointFromVector(translatedPoint), point(minX, minY));
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};
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/**
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@ -153,19 +128,13 @@ export const ellipseDistanceFromPoint = <Point extends GenericPoint>(
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*/
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export function ellipseSegmentInterceptPoints<Point extends GenericPoint>(
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e: Readonly<Ellipse<Point>>,
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l: Readonly<Segment<Point>>,
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s: Readonly<Segment<Point>>,
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): Point[] {
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const rx = e.halfWidth;
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const ry = e.halfHeight;
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const nonRotatedLine = line(
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pointRotateRads(l[0], e.center, radians(-e.angle)),
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pointRotateRads(l[1], e.center, radians(-e.angle)),
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);
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const dir = vectorFromPoint(nonRotatedLine[1], nonRotatedLine[0]);
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const diff = vector(
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nonRotatedLine[0][0] - e.center[0],
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nonRotatedLine[0][1] - e.center[1],
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);
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const dir = vectorFromPoint(s[1], s[0]);
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const diff = vector(s[0][0] - e.center[0], s[0][1] - e.center[1]);
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const mDir = vector(dir[0] / (rx * rx), dir[1] / (ry * ry));
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const mDiff = vector(diff[0] / (rx * rx), diff[1] / (ry * ry));
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@ -183,10 +152,8 @@ export function ellipseSegmentInterceptPoints<Point extends GenericPoint>(
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if (0 <= t_a && t_a <= 1) {
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intersections.push(
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point(
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nonRotatedLine[0][0] +
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(nonRotatedLine[1][0] - nonRotatedLine[0][0]) * t_a,
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nonRotatedLine[0][1] +
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(nonRotatedLine[1][1] - nonRotatedLine[0][1]) * t_a,
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s[0][0] + (s[1][0] - s[0][0]) * t_a,
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s[0][1] + (s[1][1] - s[0][1]) * t_a,
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),
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);
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}
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@ -194,10 +161,8 @@ export function ellipseSegmentInterceptPoints<Point extends GenericPoint>(
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if (0 <= t_b && t_b <= 1) {
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intersections.push(
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point(
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nonRotatedLine[0][0] +
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(nonRotatedLine[1][0] - nonRotatedLine[0][0]) * t_b,
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nonRotatedLine[0][1] +
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(nonRotatedLine[1][1] - nonRotatedLine[0][1]) * t_b,
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s[0][0] + (s[1][0] - s[0][0]) * t_b,
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s[0][1] + (s[1][1] - s[0][1]) * t_b,
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),
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);
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}
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@ -206,16 +171,12 @@ export function ellipseSegmentInterceptPoints<Point extends GenericPoint>(
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if (0 <= t && t <= 1) {
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intersections.push(
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point(
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nonRotatedLine[0][0] +
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(nonRotatedLine[1][0] - nonRotatedLine[0][0]) * t,
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nonRotatedLine[0][1] +
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(nonRotatedLine[1][1] - nonRotatedLine[0][1]) * t,
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s[0][0] + (s[1][0] - s[0][0]) * t,
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s[0][1] + (s[1][1] - s[0][1]) * t,
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),
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);
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}
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}
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return intersections.map((point) =>
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pointRotateRads(point, e.center, e.angle),
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);
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return intersections;
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}
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Mark Tolmacs
4 months ago