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Ellipse refactor

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Signed-off-by: Mark Tolmacs <mark@lazycat.hu>
This commit is contained in:
Mark Tolmacs 2024-09-24 19:12:27 +02:00
parent 017047d15e
commit 3efa8735ef
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10 changed files with 301 additions and 217 deletions
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44
packages/utils/geometry/geometry.test.ts
View file

@ -1,4 +1,4 @@
import type { GlobalPoint, LineSegment, Polygon, Radians } from "../../math";
import type { GlobalPoint, LineSegment, Polygon } from "../../math";
import {
point,
lineSegment,
@ -7,7 +7,6 @@ import {
pointOnPolygon,
polygonIncludesPoint,
} from "../../math";
import { pointInEllipse, pointOnEllipse, type Ellipse } from "./shape";
describe("point and line", () => {
const s: LineSegment<GlobalPoint> = lineSegment(point(1, 0), point(1, 2));
@ -47,44 +46,3 @@ describe("point and polygon", () => {
expect(polygonIncludesPoint(point(3, 3), poly)).toBe(false);
});
});
describe("point and ellipse", () => {
const ellipse: Ellipse<GlobalPoint> = {
center: point(0, 0),
angle: 0 as Radians,
halfWidth: 2,
halfHeight: 1,
};
it("point on ellipse", () => {
[point(0, 1), point(0, -1), point(2, 0), point(-2, 0)].forEach((p) => {
expect(pointOnEllipse(p, ellipse)).toBe(true);
});
expect(pointOnEllipse(point(-1.4, 0.7), ellipse, 0.1)).toBe(true);
expect(pointOnEllipse(point(-1.4, 0.71), ellipse, 0.01)).toBe(true);
expect(pointOnEllipse(point(1.4, 0.7), ellipse, 0.1)).toBe(true);
expect(pointOnEllipse(point(1.4, 0.71), ellipse, 0.01)).toBe(true);
expect(pointOnEllipse(point(1, -0.86), ellipse, 0.1)).toBe(true);
expect(pointOnEllipse(point(1, -0.86), ellipse, 0.01)).toBe(true);
expect(pointOnEllipse(point(-1, -0.86), ellipse, 0.1)).toBe(true);
expect(pointOnEllipse(point(-1, -0.86), ellipse, 0.01)).toBe(true);
expect(pointOnEllipse(point(-1, 0.8), ellipse)).toBe(false);
expect(pointOnEllipse(point(1, -0.8), ellipse)).toBe(false);
});
it("point in ellipse", () => {
[point(0, 1), point(0, -1), point(2, 0), point(-2, 0)].forEach((p) => {
expect(pointInEllipse(p, ellipse)).toBe(true);
});
expect(pointInEllipse(point(-1, 0.8), ellipse)).toBe(true);
expect(pointInEllipse(point(1, -0.8), ellipse)).toBe(true);
expect(pointInEllipse(point(-1, 1), ellipse)).toBe(false);
expect(pointInEllipse(point(-1.4, 0.8), ellipse)).toBe(false);
});
});

166
packages/utils/geometry/shape.ts
View file

@ -14,6 +14,8 @@
import type {
Curve,
Ellipse,
GenericPoint,
LineSegment,
Polygon,
Radians,
@ -23,18 +25,15 @@ import {
curve,
lineSegment,
point,
pointDistance,
pointFromArray,
pointFromVector,
pointRotateRads,
polygon,
polygonFromPoints,
PRECISION,
segmentsIntersectAt,
vector,
vectorAdd,
vectorFromPoint,
vectorScale,
type GlobalPoint,
type LocalPoint,
} from "../../math";
@ -70,19 +69,7 @@ export type Polyline<Point extends GlobalPoint | LocalPoint | ViewportPoint> =
export type Polycurve<Point extends GlobalPoint | LocalPoint | ViewportPoint> =
Curve<Point>[];
// an ellipse is specified by its center, angle, and its major and minor axes
// but for the sake of simplicity, we've used halfWidth and halfHeight instead
// in replace of semi major and semi minor axes
export type Ellipse<Point extends GlobalPoint | LocalPoint | ViewportPoint> = {
center: Point;
angle: Radians;
halfWidth: number;
halfHeight: number;
};
export type GeometricShape<
Point extends GlobalPoint | LocalPoint | ViewportPoint,
> =
export type GeometricShape<Point extends GenericPoint> =
| {
type: "line";
data: LineSegment<Point>;
@ -403,150 +390,3 @@ export const segmentIntersectRectangleElement = <
.map((s) => segmentsIntersectAt(segment, s))
.filter((i): i is Point => !!i);
};
const distanceToEllipse = <
Point extends LocalPoint | GlobalPoint | ViewportPoint,
>(
p: Point,
ellipse: Ellipse<Point>,
) => {
const { angle, halfWidth, halfHeight, center } = ellipse;
const a = halfWidth;
const b = halfHeight;
const translatedPoint = vectorAdd(
vectorFromPoint(p),
vectorScale(vectorFromPoint(center), -1),
);
const [rotatedPointX, rotatedPointY] = pointRotateRads(
pointFromVector(translatedPoint),
point(0, 0),
-angle as Radians,
);
const px = Math.abs(rotatedPointX);
const py = Math.abs(rotatedPointY);
let tx = 0.707;
let ty = 0.707;
for (let i = 0; i < 3; i++) {
const x = a * tx;
const y = b * ty;
const ex = ((a * a - b * b) * tx ** 3) / a;
const ey = ((b * b - a * a) * ty ** 3) / b;
const rx = x - ex;
const ry = y - ey;
const qx = px - ex;
const qy = py - ey;
const r = Math.hypot(ry, rx);
const q = Math.hypot(qy, qx);
tx = Math.min(1, Math.max(0, ((qx * r) / q + ex) / a));
ty = Math.min(1, Math.max(0, ((qy * r) / q + ey) / b));
const t = Math.hypot(ty, tx);
tx /= t;
ty /= t;
}
const [minX, minY] = [
a * tx * Math.sign(rotatedPointX),
b * ty * Math.sign(rotatedPointY),
];
return pointDistance(point(rotatedPointX, rotatedPointY), point(minX, minY));
};
export const pointOnEllipse = <
Point extends LocalPoint | GlobalPoint | ViewportPoint,
>(
point: Point,
ellipse: Ellipse<Point>,
threshold = PRECISION,
) => {
return distanceToEllipse(point, ellipse) <= threshold;
};
export const pointInEllipse = <
Point extends LocalPoint | GlobalPoint | ViewportPoint,
>(
p: Point,
ellipse: Ellipse<Point>,
) => {
const { center, angle, halfWidth, halfHeight } = ellipse;
const translatedPoint = vectorAdd(
vectorFromPoint(p),
vectorScale(vectorFromPoint(center), -1),
);
const [rotatedPointX, rotatedPointY] = pointRotateRads(
pointFromVector(translatedPoint),
point(0, 0),
-angle as Radians,
);
return (
(rotatedPointX / halfWidth) * (rotatedPointX / halfWidth) +
(rotatedPointY / halfHeight) * (rotatedPointY / halfHeight) <=
1
);
};
export const ellipseAxes = <Point extends LocalPoint | GlobalPoint>(
ellipse: Ellipse<Point>,
) => {
const widthGreaterThanHeight = ellipse.halfWidth > ellipse.halfHeight;
const majorAxis = widthGreaterThanHeight
? ellipse.halfWidth * 2
: ellipse.halfHeight * 2;
const minorAxis = widthGreaterThanHeight
? ellipse.halfHeight * 2
: ellipse.halfWidth * 2;
return {
majorAxis,
minorAxis,
};
};
export const ellipseFocusToCenter = <Point extends LocalPoint | GlobalPoint>(
ellipse: Ellipse<Point>,
) => {
const { majorAxis, minorAxis } = ellipseAxes(ellipse);
return Math.sqrt(majorAxis ** 2 - minorAxis ** 2);
};
export const ellipseExtremes = <Point extends LocalPoint | GlobalPoint>(
ellipse: Ellipse<Point>,
) => {
const { center, angle } = ellipse;
const { majorAxis, minorAxis } = ellipseAxes(ellipse);
const cos = Math.cos(angle);
const sin = Math.sin(angle);
const sqSum = majorAxis ** 2 + minorAxis ** 2;
const sqDiff = (majorAxis ** 2 - minorAxis ** 2) * Math.cos(2 * angle);
const yMax = Math.sqrt((sqSum - sqDiff) / 2);
const xAtYMax =
(yMax * sqSum * sin * cos) /
(majorAxis ** 2 * sin ** 2 + minorAxis ** 2 * cos ** 2);
const xMax = Math.sqrt((sqSum + sqDiff) / 2);
const yAtXMax =
(xMax * sqSum * sin * cos) /
(majorAxis ** 2 * cos ** 2 + minorAxis ** 2 * sin ** 2);
const centerVector = vectorFromPoint(center);
return [
vectorAdd(vector(xAtYMax, yMax), centerVector),
vectorAdd(vectorScale(vector(xAtYMax, yMax), -1), centerVector),
vectorAdd(vector(xMax, yAtXMax), centerVector),
vectorAdd(vector(xMax, yAtXMax), centerVector),
];
};