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53 lines
1.8 KiB
TypeScript
53 lines
1.8 KiB
TypeScript
import * as GA from "./ga";
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import type { Line, Point } from "./ga";
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/**
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* A line is stored as an array `[0, c, a, b, 0, 0, 0, 0]` representing:
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* c * e0 + a * e1 + b*e2
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*
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* This maps to a standard formula `a * x + b * y + c`.
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*
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* `(-b, a)` corresponds to a 2D vector parallel to the line. The lines
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* have a natural orientation, corresponding to that vector.
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*
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* The magnitude ("norm") of the line is `sqrt(a ^ 2 + b ^ 2)`.
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* `c / norm(line)` is the oriented distance from line to origin.
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*/
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// Returns line with direction (x, y) through origin
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export const vector = (x: number, y: number): Line =>
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GA.normalized([0, 0, -y, x, 0, 0, 0, 0]);
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// For equation ax + by + c = 0.
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export const equation = (a: number, b: number, c: number): Line =>
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GA.normalized([0, c, a, b, 0, 0, 0, 0]);
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export const through = (from: Point, to: Point): Line =>
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GA.normalized(GA.join(to, from));
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export const orthogonal = (line: Line, point: Point): Line =>
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GA.dot(line, point);
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// Returns a line perpendicular to the line through `against` and `intersection`
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// going through `intersection`.
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export const orthogonalThrough = (against: Point, intersection: Point): Line =>
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orthogonal(through(against, intersection), intersection);
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export const parallel = (line: Line, distance: number): Line => {
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const result = line.slice();
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result[1] -= distance;
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return result as unknown as Line;
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};
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export const parallelThrough = (line: Line, point: Point): Line =>
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orthogonal(orthogonal(point, line), point);
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export const distance = (line1: Line, line2: Line): number =>
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GA.inorm(GA.meet(line1, line2));
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export const angle = (line1: Line, line2: Line): number =>
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Math.acos(GA.dot(line1, line2)[0]);
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// The orientation of the line
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export const sign = (line: Line): number => Math.sign(line[1]);
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