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chore: Unify math types, utils and functions (#8389)
Co-authored-by: dwelle <5153846+dwelle@users.noreply.github.com>
This commit is contained in:
Márk Tolmács
GitHub
parent
e3d1dee9d0
commit
f4dd23fc31
98 changed files with 4291 additions and 3661 deletions
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@ -12,9 +12,30 @@
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* to pure shapes
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*/
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import type { Curve, LineSegment, Polygon, Radians } from "../../math";
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import {
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curve,
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lineSegment,
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point,
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pointDistance,
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pointFromArray,
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pointFromVector,
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pointRotateRads,
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polygon,
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polygonFromPoints,
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PRECISION,
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segmentsIntersectAt,
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vector,
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vectorAdd,
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vectorFromPoint,
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vectorScale,
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type GlobalPoint,
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type LocalPoint,
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} from "../../math";
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import { getElementAbsoluteCoords } from "../../excalidraw/element";
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import type {
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ElementsMap,
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ExcalidrawBindableElement,
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ExcalidrawDiamondElement,
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ExcalidrawElement,
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ExcalidrawEllipseElement,
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@ -28,67 +49,54 @@ import type {
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ExcalidrawSelectionElement,
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ExcalidrawTextElement,
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} from "../../excalidraw/element/types";
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import { angleToDegrees, close, pointAdd, pointRotate } from "./geometry";
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import { pointsOnBezierCurves } from "points-on-curve";
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import type { Drawable, Op } from "roughjs/bin/core";
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// a point is specified by its coordinate (x, y)
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export type Point = [number, number];
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export type Vector = Point;
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// a line (segment) is defined by two endpoints
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export type Line = [Point, Point];
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import { invariant } from "../../excalidraw/utils";
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// a polyline (made up term here) is a line consisting of other line segments
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// this corresponds to a straight line element in the editor but it could also
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// be used to model other elements
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export type Polyline = Line[];
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// cubic bezier curve with four control points
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export type Curve = [Point, Point, Point, Point];
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export type Polyline<Point extends GlobalPoint | LocalPoint> =
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LineSegment<Point>[];
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// a polycurve is a curve consisting of ther curves, this corresponds to a complex
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// curve on the canvas
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export type Polycurve = Curve[];
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// a polygon is a closed shape by connecting the given points
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// rectangles and diamonds are modelled by polygons
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export type Polygon = Point[];
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export type Polycurve<Point extends GlobalPoint | LocalPoint> = Curve<Point>[];
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// an ellipse is specified by its center, angle, and its major and minor axes
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// but for the sake of simplicity, we've used halfWidth and halfHeight instead
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// in replace of semi major and semi minor axes
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export type Ellipse = {
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export type Ellipse<Point extends GlobalPoint | LocalPoint> = {
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center: Point;
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angle: number;
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angle: Radians;
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halfWidth: number;
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halfHeight: number;
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};
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export type GeometricShape =
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export type GeometricShape<Point extends GlobalPoint | LocalPoint> =
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| {
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type: "line";
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data: Line;
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data: LineSegment<Point>;
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}
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| {
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type: "polygon";
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data: Polygon;
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data: Polygon<Point>;
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}
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| {
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type: "curve";
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data: Curve;
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data: Curve<Point>;
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}
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| {
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type: "ellipse";
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data: Ellipse;
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data: Ellipse<Point>;
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}
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| {
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type: "polyline";
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data: Polyline;
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data: Polyline<Point>;
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}
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| {
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type: "polycurve";
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data: Polycurve;
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data: Polycurve<Point>;
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};
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type RectangularElement =
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@ -102,32 +110,32 @@ type RectangularElement =
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| ExcalidrawSelectionElement;
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// polygon
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export const getPolygonShape = (
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export const getPolygonShape = <Point extends GlobalPoint | LocalPoint>(
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element: RectangularElement,
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): GeometricShape => {
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): GeometricShape<Point> => {
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const { angle, width, height, x, y } = element;
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const angleInDegrees = angleToDegrees(angle);
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const cx = x + width / 2;
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const cy = y + height / 2;
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const center: Point = [cx, cy];
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const center: Point = point(cx, cy);
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let data: Polygon = [];
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let data: Polygon<Point>;
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if (element.type === "diamond") {
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data = [
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pointRotate([cx, y], angleInDegrees, center),
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pointRotate([x + width, cy], angleInDegrees, center),
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pointRotate([cx, y + height], angleInDegrees, center),
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pointRotate([x, cy], angleInDegrees, center),
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] as Polygon;
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data = polygon(
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pointRotateRads(point(cx, y), center, angle),
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pointRotateRads(point(x + width, cy), center, angle),
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pointRotateRads(point(cx, y + height), center, angle),
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pointRotateRads(point(x, cy), center, angle),
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);
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} else {
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data = [
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pointRotate([x, y], angleInDegrees, center),
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pointRotate([x + width, y], angleInDegrees, center),
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pointRotate([x + width, y + height], angleInDegrees, center),
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pointRotate([x, y + height], angleInDegrees, center),
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] as Polygon;
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data = polygon(
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pointRotateRads(point(x, y), center, angle),
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pointRotateRads(point(x + width, y), center, angle),
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pointRotateRads(point(x + width, y + height), center, angle),
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pointRotateRads(point(x, y + height), center, angle),
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);
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}
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return {
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@ -137,7 +145,7 @@ export const getPolygonShape = (
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};
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// return the selection box for an element, possibly rotated as well
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export const getSelectionBoxShape = (
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export const getSelectionBoxShape = <Point extends GlobalPoint | LocalPoint>(
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element: ExcalidrawElement,
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elementsMap: ElementsMap,
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padding = 10,
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@ -153,29 +161,29 @@ export const getSelectionBoxShape = (
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y1 -= padding;
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y2 += padding;
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const angleInDegrees = angleToDegrees(element.angle);
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const center: Point = [cx, cy];
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const topLeft = pointRotate([x1, y1], angleInDegrees, center);
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const topRight = pointRotate([x2, y1], angleInDegrees, center);
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const bottomLeft = pointRotate([x1, y2], angleInDegrees, center);
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const bottomRight = pointRotate([x2, y2], angleInDegrees, center);
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//const angleInDegrees = angleToDegrees(element.angle);
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const center = point(cx, cy);
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const topLeft = pointRotateRads(point(x1, y1), center, element.angle);
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const topRight = pointRotateRads(point(x2, y1), center, element.angle);
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const bottomLeft = pointRotateRads(point(x1, y2), center, element.angle);
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const bottomRight = pointRotateRads(point(x2, y2), center, element.angle);
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return {
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type: "polygon",
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data: [topLeft, topRight, bottomRight, bottomLeft],
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} as GeometricShape;
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} as GeometricShape<Point>;
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};
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// ellipse
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export const getEllipseShape = (
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export const getEllipseShape = <Point extends GlobalPoint | LocalPoint>(
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element: ExcalidrawEllipseElement,
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): GeometricShape => {
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): GeometricShape<Point> => {
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const { width, height, angle, x, y } = element;
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return {
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type: "ellipse",
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data: {
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center: [x + width / 2, y + height / 2],
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center: point(x + width / 2, y + height / 2),
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angle,
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halfWidth: width / 2,
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halfHeight: height / 2,
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@ -193,32 +201,34 @@ export const getCurvePathOps = (shape: Drawable): Op[] => {
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};
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// linear
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export const getCurveShape = (
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export const getCurveShape = <Point extends GlobalPoint | LocalPoint>(
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roughShape: Drawable,
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startingPoint: Point = [0, 0],
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angleInRadian: number,
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startingPoint: Point = point(0, 0),
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angleInRadian: Radians,
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center: Point,
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): GeometricShape => {
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const transform = (p: Point) =>
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pointRotate(
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[p[0] + startingPoint[0], p[1] + startingPoint[1]],
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angleToDegrees(angleInRadian),
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): GeometricShape<Point> => {
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const transform = (p: Point): Point =>
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pointRotateRads(
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point(p[0] + startingPoint[0], p[1] + startingPoint[1]),
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center,
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angleInRadian,
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);
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const ops = getCurvePathOps(roughShape);
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const polycurve: Polycurve = [];
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let p0: Point = [0, 0];
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const polycurve: Polycurve<Point> = [];
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let p0 = point<Point>(0, 0);
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for (const op of ops) {
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if (op.op === "move") {
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p0 = transform(op.data as Point);
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const p = pointFromArray<Point>(op.data);
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invariant(p != null, "Ops data is not a point");
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p0 = transform(p);
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}
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if (op.op === "bcurveTo") {
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const p1: Point = transform([op.data[0], op.data[1]]);
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const p2: Point = transform([op.data[2], op.data[3]]);
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const p3: Point = transform([op.data[4], op.data[5]]);
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polycurve.push([p0, p1, p2, p3]);
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const p1 = transform(point<Point>(op.data[0], op.data[1]));
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const p2 = transform(point<Point>(op.data[2], op.data[3]));
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const p3 = transform(point<Point>(op.data[4], op.data[5]));
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polycurve.push(curve<Point>(p0, p1, p2, p3));
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p0 = p3;
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}
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}
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@ -229,61 +239,72 @@ export const getCurveShape = (
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};
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};
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const polylineFromPoints = (points: Point[]) => {
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let previousPoint = points[0];
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const polyline: Polyline = [];
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const polylineFromPoints = <Point extends GlobalPoint | LocalPoint>(
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points: Point[],
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): Polyline<Point> => {
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let previousPoint: Point = points[0];
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const polyline: LineSegment<Point>[] = [];
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for (let i = 1; i < points.length; i++) {
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const nextPoint = points[i];
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polyline.push([previousPoint, nextPoint]);
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polyline.push(lineSegment<Point>(previousPoint, nextPoint));
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previousPoint = nextPoint;
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}
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return polyline;
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};
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export const getFreedrawShape = (
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export const getFreedrawShape = <Point extends GlobalPoint | LocalPoint>(
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element: ExcalidrawFreeDrawElement,
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center: Point,
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isClosed: boolean = false,
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): GeometricShape => {
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const angle = angleToDegrees(element.angle);
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): GeometricShape<Point> => {
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const transform = (p: Point) =>
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pointRotate(pointAdd(p, [element.x, element.y] as Point), angle, center);
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pointRotateRads(
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pointFromVector(
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vectorAdd(vectorFromPoint(p), vector(element.x, element.y)),
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),
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center,
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element.angle,
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);
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const polyline = polylineFromPoints(
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element.points.map((p) => transform(p as Point)),
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);
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return isClosed
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? {
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type: "polygon",
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data: close(polyline.flat()) as Polygon,
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}
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: {
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type: "polyline",
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data: polyline,
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};
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return (
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isClosed
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? {
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type: "polygon",
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data: polygonFromPoints(polyline.flat()),
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}
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: {
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type: "polyline",
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data: polyline,
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}
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) as GeometricShape<Point>;
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};
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export const getClosedCurveShape = (
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export const getClosedCurveShape = <Point extends GlobalPoint | LocalPoint>(
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element: ExcalidrawLinearElement,
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roughShape: Drawable,
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startingPoint: Point = [0, 0],
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angleInRadian: number,
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startingPoint: Point = point<Point>(0, 0),
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angleInRadian: Radians,
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center: Point,
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): GeometricShape => {
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): GeometricShape<Point> => {
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const transform = (p: Point) =>
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pointRotate(
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[p[0] + startingPoint[0], p[1] + startingPoint[1]],
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angleToDegrees(angleInRadian),
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pointRotateRads(
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point(p[0] + startingPoint[0], p[1] + startingPoint[1]),
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center,
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angleInRadian,
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);
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if (element.roundness === null) {
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return {
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type: "polygon",
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data: close(element.points.map((p) => transform(p as Point))),
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data: polygonFromPoints(
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element.points.map((p) => transform(p as Point)) as Point[],
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),
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};
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}
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@ -295,27 +316,218 @@ export const getClosedCurveShape = (
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if (operation.op === "move") {
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odd = !odd;
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if (odd) {
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points.push([operation.data[0], operation.data[1]]);
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points.push(point(operation.data[0], operation.data[1]));
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}
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} else if (operation.op === "bcurveTo") {
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if (odd) {
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points.push([operation.data[0], operation.data[1]]);
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points.push([operation.data[2], operation.data[3]]);
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points.push([operation.data[4], operation.data[5]]);
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points.push(point(operation.data[0], operation.data[1]));
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points.push(point(operation.data[2], operation.data[3]));
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points.push(point(operation.data[4], operation.data[5]));
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}
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} else if (operation.op === "lineTo") {
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if (odd) {
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points.push([operation.data[0], operation.data[1]]);
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points.push(point(operation.data[0], operation.data[1]));
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}
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}
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}
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const polygonPoints = pointsOnBezierCurves(points, 10, 5).map((p) =>
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transform(p),
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);
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transform(p as Point),
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) as Point[];
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return {
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type: "polygon",
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data: polygonPoints,
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data: polygonFromPoints<Point>(polygonPoints),
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};
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};
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/**
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* Determine intersection of a rectangular shaped element and a
|
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* line segment.
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*
|
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* @param element The rectangular element to test against
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* @param segment The segment intersecting the element
|
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* @param gap Optional value to inflate the shape before testing
|
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* @returns An array of intersections
|
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*/
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// TODO: Replace with final rounded rectangle code
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export const segmentIntersectRectangleElement = <
|
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Point extends LocalPoint | GlobalPoint,
|
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>(
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element: ExcalidrawBindableElement,
|
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segment: LineSegment<Point>,
|
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gap: number = 0,
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): Point[] => {
|
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const bounds = [
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element.x - gap,
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element.y - gap,
|
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element.x + element.width + gap,
|
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element.y + element.height + gap,
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];
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const center = point(
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(bounds[0] + bounds[2]) / 2,
|
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(bounds[1] + bounds[3]) / 2,
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);
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return [
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lineSegment(
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pointRotateRads(point(bounds[0], bounds[1]), center, element.angle),
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pointRotateRads(point(bounds[2], bounds[1]), center, element.angle),
|
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),
|
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lineSegment(
|
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pointRotateRads(point(bounds[2], bounds[1]), center, element.angle),
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pointRotateRads(point(bounds[2], bounds[3]), center, element.angle),
|
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),
|
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lineSegment(
|
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pointRotateRads(point(bounds[2], bounds[3]), center, element.angle),
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pointRotateRads(point(bounds[0], bounds[3]), center, element.angle),
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),
|
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lineSegment(
|
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pointRotateRads(point(bounds[0], bounds[3]), center, element.angle),
|
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pointRotateRads(point(bounds[0], bounds[1]), center, element.angle),
|
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),
|
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]
|
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.map((s) => segmentsIntersectAt(segment, s))
|
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.filter((i): i is Point => !!i);
|
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};
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|
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const distanceToEllipse = <Point extends LocalPoint | GlobalPoint>(
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p: Point,
|
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ellipse: Ellipse<Point>,
|
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) => {
|
||||
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;
|
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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>(
|
||||
point: Point,
|
||||
ellipse: Ellipse<Point>,
|
||||
threshold = PRECISION,
|
||||
) => {
|
||||
return distanceToEllipse(point, ellipse) <= threshold;
|
||||
};
|
||||
|
||||
export const pointInEllipse = <Point extends LocalPoint | GlobalPoint>(
|
||||
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),
|
||||
];
|
||||
};
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue