src/math/line.js
import {Point2D} from './point';
import {
isSimilar,
REAL_WORLD_EPSILON,
} from './matrix';
// doc imports
/* eslint-disable no-unused-vars */
import {ViewController} from '../app/viewController';
import {Scalar2D} from './scalar';
/* eslint-enable no-unused-vars */
/**
* Line shape.
*/
export class Line {
/**
* Line begin point.
*
* @type {Point2D}
*/
#begin;
/**
* Line end point.
*
* @type {Point2D}
*/
#end;
/**
* @param {Point2D} begin A Point2D representing the beginning
* of the line.
* @param {Point2D} end A Point2D representing the end of the line.
*/
constructor(begin, end) {
this.#begin = begin;
this.#end = end;
}
/**
* Get the begin point of the line.
*
* @returns {Point2D} The beginning point of the line.
*/
getBegin() {
return this.#begin;
}
/**
* Get the end point of the line.
*
* @returns {Point2D} The ending point of the line.
*/
getEnd() {
return this.#end;
}
/**
* Check for equality.
*
* @param {Line} rhs The object to compare to.
* @returns {boolean} True if both objects are equal.
*/
equals(rhs) {
return rhs !== null &&
this.getBegin().equals(rhs.getBegin()) &&
this.getEnd().equals(rhs.getEnd());
}
/**
* Get the line delta in the X direction.
*
* @returns {number} The delta in the X direction.
*/
getDeltaX() {
return this.getEnd().getX() - this.getBegin().getX();
}
/**
* Get the line delta in the Y direction.
*
* @returns {number} The delta in the Y direction.
*/
getDeltaY() {
return this.getEnd().getY() - this.getBegin().getY();
}
/**
* Get the length of the line.
*
* @returns {number} The length of the line.
*/
getLength() {
return Math.sqrt(
this.getDeltaX() * this.getDeltaX() +
this.getDeltaY() * this.getDeltaY()
);
}
/**
* Get the length of the line according to a spacing.
*
* @param {Scalar2D} spacing2D The 2D spacing.
* @returns {number} The length of the line with spacing
* or null for null spacings.
*/
getWorldLength(spacing2D) {
let wlen = null;
if (spacing2D !== null) {
const dxs = this.getDeltaX() * spacing2D.x;
const dys = this.getDeltaY() * spacing2D.y;
wlen = Math.sqrt(dxs * dxs + dys * dys);
}
return wlen;
}
/**
* Get the mid point of the line.
*
* @returns {Point2D} The mid point of the line.
*/
getMidpoint() {
return new Point2D(
(this.getBegin().getX() + this.getEnd().getX()) / 2,
(this.getBegin().getY() + this.getEnd().getY()) / 2
);
}
/**
* Get the centroid of the line.
*
* @returns {Point2D} THe centroid point.
*/
getCentroid() {
return this.getMidpoint();
}
/**
* Get the slope of the line.
*
* @returns {number} The slope of the line.
*/
getSlope() {
return this.getDeltaY() / this.getDeltaX();
}
/**
* Get the intercept of the line.
*
* @returns {number} The slope of the line.
*/
getIntercept() {
return (
this.getEnd().getX() * this.getBegin().getY() -
this.getBegin().getX() * this.getEnd().getY()
) / this.getDeltaX();
}
/**
* Get the inclination of the line.
*
* @returns {number} The inclination of the line.
*/
getInclination() {
// tan(theta) = slope
const angle =
Math.atan2(this.getDeltaY(), this.getDeltaX()) * 180 / Math.PI;
// shift?
return 180 - angle;
}
/**
* Quantify a line according to view information.
*
* @param {ViewController} viewController The associated view controller.
* @returns {object} A quantification object.
*/
quantify(viewController) {
const quant = {};
// length
const spacing2D = viewController.get2DSpacing();
const length = this.getWorldLength(spacing2D);
if (length !== null) {
quant.length = {value: length, unit: 'unit.mm'};
}
// return
return quant;
}
} // Line class
/**
* Get the angle between two lines in degree.
*
* @param {Line} line0 The first line.
* @param {Line} line1 The second line.
* @returns {number} The angle.
*/
export function getAngle(line0, line1) {
const dx0 = line0.getDeltaX();
const dy0 = line0.getDeltaY();
const dx1 = line1.getDeltaX();
const dy1 = line1.getDeltaY();
// dot = ||a||*||b||*cos(theta)
const dot = dx0 * dx1 + dy0 * dy1;
// cross = ||a||*||b||*sin(theta)
const det = dx0 * dy1 - dy0 * dx1;
// tan = sin / cos
const angle = Math.atan2(det, dot) * 180 / Math.PI;
// complementary angle
// shift?
return 360 - (180 - angle);
}
/**
* Check if two lines are orthogonal.
*
* @param {Line} line0 The first line.
* @param {Line} line1 The second line.
* @returns {boolean} True if both lines are orthogonal.
*/
export function areOrthogonal(line0, line1) {
const dx0 = line0.getDeltaX();
const dy0 = line0.getDeltaY();
const dx1 = line1.getDeltaX();
const dy1 = line1.getDeltaY();
// dot = ||a||*||b||*cos(theta)
return (dx0 * dx1 + dy0 * dy1) === 0;
}
/**
* Check if a point is in a line coordinate range.
*
* @param {Point2D} point The input point.
* @param {Line} line The input line.
* @returns {boolean} True if the input point is in the line coordinate range.
*/
export function isPointInLineRange(point, line) {
const minX = Math.min(line.getBegin().getX(), line.getEnd().getX());
const maxX = Math.max(line.getBegin().getX(), line.getEnd().getX());
const minY = Math.min(line.getBegin().getY(), line.getEnd().getY());
const maxY = Math.max(line.getBegin().getY(), line.getEnd().getY());
return point.getX() >= minX &&
point.getX() <= maxX &&
point.getY() >= minY &&
point.getY() <= maxY;
}
/**
* Get a perpendicular line to an input one at a given point.
*
* @param {Line} line The line to be perpendicular to.
* @param {Point2D} point The middle point of the perpendicular line.
* @param {number} length The length of the perpendicular line.
* @param {Scalar2D} [spacing] Optional image spacing, default to [1,1].
* @returns {Line} The perpendicular line.
*/
export function getPerpendicularLine(line, point, length, spacing) {
if (typeof spacing === 'undefined') {
spacing = {x: 1, y: 1};
}
const sx2 = spacing.x * spacing.x;
const sy2 = spacing.y * spacing.y;
// a0 * a1 = -1 (in square space)
const perpSlope = -sx2 / (sy2 * line.getSlope());
// y0 = a1*x0 + b1 -> b1 = y0 - a1*x0
const prepIntercept = point.getY() - perpSlope * point.getX();
// return
return getLineFromEquation(perpSlope, prepIntercept, point, length, spacing);
}
/**
* Get a perpendicular line to an input one at a given distance
* of its begin point.
*
* @param {Line} line The line to be perpendicular to.
* @param {number} distance The distance to the input line begin point.
* @param {number} length The length of the perpendicular line.
* @param {Scalar2D} [spacing] Optional image spacing, default to [1,1].
* @returns {Line} The perpendicular line.
*/
export function getPerpendicularLineAtDistance(
line, distance, length, spacing) {
// get a line along the input one and centered on begin point
const lineFromEq = getLineFromEquation(
line.getSlope(),
line.getIntercept(),
line.getBegin(),
distance,
spacing
);
// select the point on the input line
let startPoint;
if (isPointInLineRange(lineFromEq.getBegin(), line)) {
startPoint = lineFromEq.getBegin();
} else {
startPoint = lineFromEq.getEnd();
}
// use it as base for a perpendicular line
return getPerpendicularLine(line, startPoint, length, spacing);
}
/**
* Get a line from an equation, a middle point and a length.
*
* @param {number} slope The line slope.
* @param {number} intercept The line intercept.
* @param {Point2D} point The middle point of the line.
* @param {number} length The line length.
* @param {Scalar2D} [spacing] Optional image spacing, default to [1,1].
* @returns {Line} The resulting line.
*/
export function getLineFromEquation(slope, intercept, point, length, spacing) {
if (typeof spacing === 'undefined') {
spacing = {x: 1, y: 1};
}
// begin point
let beginX = 0;
let beginY = 0;
// end point
let endX = 0;
let endY = 0;
if (isSimilar(slope, 0, REAL_WORLD_EPSILON)) {
// slope = ~0 -> horizontal input line
beginX = point.getX() - length / (2 * spacing.x);
beginY = point.getY();
endX = point.getX() + length / (2 * spacing.x);
endY = point.getY();
} else if (Math.abs(slope) > 1e6) {
// slope = ~(+/-)Infinity -> vertical input line
beginX = point.getX();
beginY = point.getY() - length / (2 * spacing.y);
endX = point.getX();
endY = point.getY() + length / (2 * spacing.y);
} else {
const sx2 = spacing.x * spacing.x;
const sy2 = spacing.y * spacing.y;
// 1. [length] sx^2 * (x - x0)^2 + sy^2 * (y - y0)^2 = d^2
// 2. [slope] a = (y - y0) / (x - x0) -> y - y0 = a*(x - x0)
// -> sx^2 * (x - x0)^2 + sy^2 * a^2 * (x - x0)^2 = d^2
// -> (x - x0)^2 = d^2 / (sx^2 + sy^2 * a^2)
// -> x = x0 +- d / sqrt(sx^2 + sy^2 * a^2)
// length is the distance between begin and end,
// point is half way between both -> d = length / 2
const dx = length / (2 * Math.sqrt(sx2 + sy2 * slope * slope));
// begin point
beginX = point.getX() - dx;
beginY = slope * beginX + intercept;
// end point
endX = point.getX() + dx;
endY = slope * endX + intercept;
}
return new Line(
new Point2D(beginX, beginY),
new Point2D(endX, endY));
}