import type { Vec } from '@/utils/types'
import type { DodecaminxFace, DodecaminxOpposite } from './types'

export const dodecaminxFaces = [
  'u', 'l', 'f', 'r', 'bl', 'br', 'd', 'dl', 'dr', 'dbl', 'dbr', 'b',
] as const satisfies Vec<12, DodecaminxFace>

/**
 * This constant defines how faces are related to one another. Think of it as
 * an unfolded dodecahedron, with the U face oriented towards you.
 *
 * https://www.desmos.com/geometry/o8kuskawcb
 *
 * The related faces go clockwise around each target face, starting from the
 * target face's primary corner.
 *
 * The number associated with each relationship represents what edge of the
 * related face borders the target face.
 */
export const dodecaminxNet = {
  b: [
    ['bl', 4],
    ['dbl', 4],
    ['d', 4],
    ['dbr', 0],
    ['br', 4],
  ],
  bl: [
    ['br', 3],
    ['u', 4],
    ['l', 4],
    ['dbl', 0],
    ['b', 0],
  ],
  br: [
    ['dbr', 4],
    ['r', 4],
    ['u', 0],
    ['bl', 0],
    ['b', 4],
  ],
  d: [
    ['dbl', 3],
    ['dl', 4],
    ['dr', 0],
    ['dbr', 1],
    ['b', 2],
  ],
  dbl: [
    ['bl', 3],
    ['l', 3],
    ['dl', 0],
    ['d', 0],
    ['b', 1],
  ],
  dbr: [
    ['b', 3],
    ['d', 3],
    ['dr', 4],
    ['r', 0],
    ['br', 0],
  ],
  dl: [
    ['dbl', 2],
    ['l', 2],
    ['f', 2],
    ['dr', 1],
    ['d', 1],
  ],
  dr: [
    ['d', 2],
    ['dl', 3],
    ['f', 1],
    ['r', 1],
    ['dbr', 2],
  ],
  f: [
    ['r', 2],
    ['dr', 2],
    ['dl', 2],
    ['l', 1],
    ['u', 2],
  ],
  l: [
    ['u', 3],
    ['f', 3],
    ['dl', 1],
    ['dbl', 1],
    ['bl', 2],
  ],
  r: [
    ['dbr', 3],
    ['dr', 3],
    ['f', 0],
    ['u', 1],
    ['br', 1],
  ],
  u: [
    ['br', 2],
    ['r', 3],
    ['f', 4],
    ['l', 0],
    ['bl', 1],
  ],
} as const satisfies {
  [T in DodecaminxFace]: Vec<5, [Exclude<DodecaminxFace, T | DodecaminxOpposite<T>>, number]>
}

/**
 * Dodecaminx faces that are opposite one another.
 */
export const dodecaminxOpposites: {
  [T in DodecaminxFace]: DodecaminxOpposite<T>
} = {
  b: 'f',
  bl: 'dr',
  br: 'dl',
  d: 'u',
  dbl: 'r',
  dbr: 'l',
  dl: 'br',
  dr: 'bl',
  f: 'b',
  l: 'dbr',
  r: 'dbl',
  u: 'd',
}