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Prefer arrow functions (#2344)
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Lipis
GitHub
parent
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commit
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19 changed files with 304 additions and 336 deletions
277
src/ga.ts
277
src/ga.ts
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@ -22,22 +22,25 @@ export type Direction = NVector;
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export type Line = NVector;
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export type Transform = NVector;
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export function point(x: number, y: number): Point {
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return [0, 0, 0, 0, y, x, 1, 0];
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}
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export const point = (x: number, y: number): Point => [0, 0, 0, 0, y, x, 1, 0];
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export function origin(): Point {
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return [0, 0, 0, 0, 0, 0, 1, 0];
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}
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export const origin = (): Point => [0, 0, 0, 0, 0, 0, 1, 0];
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export function direction(x: number, y: number): Direction {
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export const direction = (x: number, y: number): Direction => {
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const norm = Math.hypot(x, y); // same as `inorm(direction(x, y))`
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return [0, 0, 0, 0, y / norm, x / norm, 0, 0];
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}
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};
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export function offset(x: number, y: number): Direction {
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return [0, 0, 0, 0, y, x, 0, 0];
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}
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export const offset = (x: number, y: number): Direction => [
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0,
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0,
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0,
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0,
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y,
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x,
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0,
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0,
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];
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/// This is the "implementation" part of the library
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@ -56,7 +59,7 @@ type NVector = readonly [
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const NVECTOR_BASE = ["1", "e0", "e1", "e2", "e01", "e20", "e12", "e012"];
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// Used to represent points, lines and transformations
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export function nvector(value: number = 0, index: number = 0): NVector {
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export const nvector = (value: number = 0, index: number = 0): NVector => {
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const result = [0, 0, 0, 0, 0, 0, 0, 0];
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if (index < 0 || index > 7) {
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throw new Error(`Expected \`index\` betwen 0 and 7, got \`${index}\``);
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@ -65,10 +68,10 @@ export function nvector(value: number = 0, index: number = 0): NVector {
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result[index] = value;
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}
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return (result as unknown) as NVector;
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}
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};
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const STRING_EPSILON = 0.000001;
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export function toString(nvector: NVector): string {
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export const toString = (nvector: NVector): string => {
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const result = nvector
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.map((value, index) =>
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Math.abs(value) > STRING_EPSILON
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@ -79,66 +82,58 @@ export function toString(nvector: NVector): string {
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.filter((representation) => representation != null)
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.join(" + ");
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return result === "" ? "0" : result;
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}
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};
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// Reverse the order of the basis blades.
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export function reverse(nvector: NVector): NVector {
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return [
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nvector[0],
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nvector[1],
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nvector[2],
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nvector[3],
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-nvector[4],
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-nvector[5],
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-nvector[6],
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-nvector[7],
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];
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}
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export const reverse = (nvector: NVector): NVector => [
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nvector[0],
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nvector[1],
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nvector[2],
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nvector[3],
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-nvector[4],
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-nvector[5],
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-nvector[6],
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-nvector[7],
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];
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// Poincare duality operator.
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export function dual(nvector: NVector): NVector {
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return [
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nvector[7],
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nvector[6],
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nvector[5],
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nvector[4],
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nvector[3],
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nvector[2],
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nvector[1],
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nvector[0],
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];
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}
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export const dual = (nvector: NVector): NVector => [
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nvector[7],
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nvector[6],
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nvector[5],
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nvector[4],
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nvector[3],
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nvector[2],
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nvector[1],
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nvector[0],
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];
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// Clifford Conjugation
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export function conjugate(nvector: NVector): NVector {
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return [
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nvector[0],
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-nvector[1],
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-nvector[2],
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-nvector[3],
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-nvector[4],
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-nvector[5],
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-nvector[6],
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nvector[7],
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];
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}
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export const conjugate = (nvector: NVector): NVector => [
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nvector[0],
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-nvector[1],
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-nvector[2],
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-nvector[3],
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-nvector[4],
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-nvector[5],
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-nvector[6],
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nvector[7],
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];
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// Main involution
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export function involute(nvector: NVector): NVector {
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return [
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nvector[0],
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-nvector[1],
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-nvector[2],
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-nvector[3],
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nvector[4],
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nvector[5],
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nvector[6],
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-nvector[7],
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];
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}
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export const involute = (nvector: NVector): NVector => [
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nvector[0],
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-nvector[1],
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-nvector[2],
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-nvector[3],
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nvector[4],
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nvector[5],
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nvector[6],
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-nvector[7],
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];
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// Multivector addition
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export function add(a: NVector, b: NVector | number): NVector {
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export const add = (a: NVector, b: NVector | number): NVector => {
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if (isNumber(b)) {
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return [a[0] + b, a[1], a[2], a[3], a[4], a[5], a[6], a[7]];
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}
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@ -152,10 +147,10 @@ export function add(a: NVector, b: NVector | number): NVector {
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a[6] + b[6],
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a[7] + b[7],
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];
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}
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};
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// Multivector subtraction
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export function sub(a: NVector, b: NVector | number): NVector {
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export const sub = (a: NVector, b: NVector | number): NVector => {
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if (isNumber(b)) {
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return [a[0] - b, a[1], a[2], a[3], a[4], a[5], a[6], a[7]];
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}
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@ -169,10 +164,10 @@ export function sub(a: NVector, b: NVector | number): NVector {
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a[6] - b[6],
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a[7] - b[7],
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];
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}
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};
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// The geometric product.
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export function mul(a: NVector, b: NVector | number): NVector {
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export const mul = (a: NVector, b: NVector | number): NVector => {
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if (isNumber(b)) {
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return [
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a[0] * b,
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@ -223,112 +218,94 @@ export function mul(a: NVector, b: NVector | number): NVector {
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b[1] * a[6] +
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b[0] * a[7],
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];
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}
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};
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export function mulScalar(a: NVector, b: NVector): number {
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return b[0] * a[0] + b[2] * a[2] + b[3] * a[3] - b[6] * a[6];
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}
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export const mulScalar = (a: NVector, b: NVector): number =>
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b[0] * a[0] + b[2] * a[2] + b[3] * a[3] - b[6] * a[6];
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// The outer/exterior/wedge product.
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export function meet(a: NVector, b: NVector): NVector {
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return [
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b[0] * a[0],
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b[1] * a[0] + b[0] * a[1],
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b[2] * a[0] + b[0] * a[2],
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b[3] * a[0] + b[0] * a[3],
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b[4] * a[0] + b[2] * a[1] - b[1] * a[2] + b[0] * a[4],
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b[5] * a[0] - b[3] * a[1] + b[1] * a[3] + b[0] * a[5],
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b[6] * a[0] + b[3] * a[2] - b[2] * a[3] + b[0] * a[6],
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b[7] * a[0] +
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b[6] * a[1] +
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b[5] * a[2] +
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b[4] * a[3] +
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b[3] * a[4] +
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b[2] * a[5] +
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b[1] * a[6],
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];
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}
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export const meet = (a: NVector, b: NVector): NVector => [
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b[0] * a[0],
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b[1] * a[0] + b[0] * a[1],
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b[2] * a[0] + b[0] * a[2],
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b[3] * a[0] + b[0] * a[3],
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b[4] * a[0] + b[2] * a[1] - b[1] * a[2] + b[0] * a[4],
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b[5] * a[0] - b[3] * a[1] + b[1] * a[3] + b[0] * a[5],
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b[6] * a[0] + b[3] * a[2] - b[2] * a[3] + b[0] * a[6],
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b[7] * a[0] +
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b[6] * a[1] +
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b[5] * a[2] +
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b[4] * a[3] +
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b[3] * a[4] +
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b[2] * a[5] +
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b[1] * a[6],
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];
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// The regressive product.
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export function join(a: NVector, b: NVector): NVector {
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return [
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joinScalar(a, b),
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a[1] * b[7] + a[4] * b[5] - a[5] * b[4] + a[7] * b[1],
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a[2] * b[7] - a[4] * b[6] + a[6] * b[4] + a[7] * b[2],
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a[3] * b[7] + a[5] * b[6] - a[6] * b[5] + a[7] * b[3],
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a[4] * b[7] + a[7] * b[4],
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a[5] * b[7] + a[7] * b[5],
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a[6] * b[7] + a[7] * b[6],
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a[7] * b[7],
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];
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}
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export const join = (a: NVector, b: NVector): NVector => [
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joinScalar(a, b),
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a[1] * b[7] + a[4] * b[5] - a[5] * b[4] + a[7] * b[1],
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a[2] * b[7] - a[4] * b[6] + a[6] * b[4] + a[7] * b[2],
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a[3] * b[7] + a[5] * b[6] - a[6] * b[5] + a[7] * b[3],
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a[4] * b[7] + a[7] * b[4],
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a[5] * b[7] + a[7] * b[5],
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a[6] * b[7] + a[7] * b[6],
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a[7] * b[7],
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];
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export function joinScalar(a: NVector, b: NVector): number {
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return (
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a[0] * b[7] +
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a[1] * b[6] +
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a[2] * b[5] +
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a[3] * b[4] +
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a[4] * b[3] +
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a[5] * b[2] +
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a[6] * b[1] +
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a[7] * b[0]
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);
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}
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export const joinScalar = (a: NVector, b: NVector): number =>
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a[0] * b[7] +
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a[1] * b[6] +
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a[2] * b[5] +
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a[3] * b[4] +
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a[4] * b[3] +
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a[5] * b[2] +
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a[6] * b[1] +
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a[7] * b[0];
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// The inner product.
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export function dot(a: NVector, b: NVector): NVector {
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return [
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b[0] * a[0] + b[2] * a[2] + b[3] * a[3] - b[6] * a[6],
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b[1] * a[0] +
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b[0] * a[1] -
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b[4] * a[2] +
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b[5] * a[3] +
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b[2] * a[4] -
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b[3] * a[5] -
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b[7] * a[6] -
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b[6] * a[7],
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b[2] * a[0] + b[0] * a[2] - b[6] * a[3] + b[3] * a[6],
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b[3] * a[0] + b[6] * a[2] + b[0] * a[3] - b[2] * a[6],
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b[4] * a[0] + b[7] * a[3] + b[0] * a[4] + b[3] * a[7],
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b[5] * a[0] + b[7] * a[2] + b[0] * a[5] + b[2] * a[7],
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b[6] * a[0] + b[0] * a[6],
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b[7] * a[0] + b[0] * a[7],
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];
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}
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export const dot = (a: NVector, b: NVector): NVector => [
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b[0] * a[0] + b[2] * a[2] + b[3] * a[3] - b[6] * a[6],
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b[1] * a[0] +
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b[0] * a[1] -
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b[4] * a[2] +
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b[5] * a[3] +
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b[2] * a[4] -
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b[3] * a[5] -
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b[7] * a[6] -
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b[6] * a[7],
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b[2] * a[0] + b[0] * a[2] - b[6] * a[3] + b[3] * a[6],
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b[3] * a[0] + b[6] * a[2] + b[0] * a[3] - b[2] * a[6],
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b[4] * a[0] + b[7] * a[3] + b[0] * a[4] + b[3] * a[7],
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b[5] * a[0] + b[7] * a[2] + b[0] * a[5] + b[2] * a[7],
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b[6] * a[0] + b[0] * a[6],
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b[7] * a[0] + b[0] * a[7],
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];
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export function norm(a: NVector): number {
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return Math.sqrt(
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Math.abs(a[0] * a[0] - a[2] * a[2] - a[3] * a[3] + a[6] * a[6]),
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);
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}
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export const norm = (a: NVector): number =>
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Math.sqrt(Math.abs(a[0] * a[0] - a[2] * a[2] - a[3] * a[3] + a[6] * a[6]));
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export function inorm(a: NVector): number {
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return Math.sqrt(
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Math.abs(a[7] * a[7] - a[5] * a[5] - a[4] * a[4] + a[1] * a[1]),
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);
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}
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export const inorm = (a: NVector): number =>
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Math.sqrt(Math.abs(a[7] * a[7] - a[5] * a[5] - a[4] * a[4] + a[1] * a[1]));
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export function normalized(a: NVector): NVector {
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export const normalized = (a: NVector): NVector => {
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const n = norm(a);
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if (n === 0 || n === 1) {
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return a;
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}
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const sign = a[6] < 0 ? -1 : 1;
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return mul(a, sign / n);
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}
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};
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export function inormalized(a: NVector): NVector {
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export const inormalized = (a: NVector): NVector => {
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const n = inorm(a);
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if (n === 0 || n === 1) {
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return a;
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}
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return mul(a, 1 / n);
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}
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};
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function isNumber(a: any): a is number {
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return typeof a === "number";
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}
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const isNumber = (a: any): a is number => typeof a === "number";
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export const E0: NVector = nvector(1, 1);
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export const E1: NVector = nvector(1, 2);
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