interlock.ts

import {InterlockPattern, SlotsPattern, TabsPattern} from './interlock_patterns.ts';
import * as kerfUtil from './kerf_util.ts';
import {Kerf} from './kerf_util.ts';
import {Turtle, TurtleFunc} from './turtle.ts';

export interface PartialTabsOptions {
  /** Kerf correction, affecting connection tightness. */
  kerf: Kerf;
  /**
   * How much the tabs protrude from the edge (typically equal to the thickness of the material).
   */
  tabWidth: number;
  /** To which side should the tabs go from the base line; or the edge of the material. */
  tabsDir: "right" | "left";
  /** Radius of the corners of the tabs, to make them slide in easier. */
  outerCornersRadius?: number;
  /**
   * Concave radius of the inner corners. It is recommended for materials that might break easily
   * due to tension, like acrylic.
   */
  innerCornersRadius?: number;
}
export interface TabsOptions extends Readonly<Required<PartialTabsOptions>> {}
export function tabsOptionsFromPartial({
  kerf,
  tabWidth,
  tabsDir,
  outerCornersRadius = 0,
  innerCornersRadius = 0,
}: PartialTabsOptions): TabsOptions {
  return {
    kerf,
    tabWidth,
    tabsDir,
    outerCornersRadius,
    innerCornersRadius,
  };
}

export interface PartialSlotsOptions {
  /** Kerf correction, affecting connection tightness. */
  kerf: Kerf;
  /** The width of the slots, typically corresponding with the thickness of the material. */
  slotWidth: number;
  /**
   * Kerf correction applied to slots width, or false to disable. By default true, which means
   * same as kerf.
   */
  slotWidthKerf?: boolean | Kerf;
  /**
   * Concave radius of the corners. It is recommended for materials that might break easily
   * due to tension, like acrylic.
   */
  innerCornersRadius?: number;
}
export interface SlotsOptions extends Readonly<Required<PartialSlotsOptions>> {
  readonly kerf: Kerf;
  readonly slotWidth: number;
  readonly slotWidthKerf: Kerf;
  readonly innerCornersRadius: number;
}
export function slotsOptionsFromPartial({
  kerf,
  slotWidth,
  slotWidthKerf: wKerfInput = true,
  innerCornersRadius = 0,
}: PartialSlotsOptions): SlotsOptions {
  const slotWidthKerf = wKerfInput === true ? kerf : wKerfInput || kerfUtil.ZERO;
  return {
    kerf,
    slotWidth,
    slotWidthKerf,
    innerCornersRadius,
  };
}

interface TabsArgs {
  pattern: TabsPattern;
  /**
   * Whether the edge starts and ends at the level of the tab (and not the base line).
   */
  onTabLevel?: boolean | "auto";
  /**
   * Whether the edge starts at the level of the tab (and not the base line).
   * Value `"auto"` means `true` if the pattern starts with a tab.
   */
  startOnTab?: boolean | "auto";
  /**
   * Whether the edge ends at the level of the tab (and not the base line).
   * Value `"auto"` means `true` if the pattern ends with a tab.
   */
  endOnTab?: boolean | "auto";
  options: PartialTabsOptions;
}

interface SlotsArgs {
  pattern: SlotsPattern;
  /** To which side of the base line should the slots go. */
  dir?: "right" | "left" | "center";
  /** Whether the end slots should be open. */
  open?: boolean;
  /** Whether to start with an opened slot. */
  startOpen?: boolean;
  /** Whether to end with an opened slot. */
  endOpen?: boolean;
  options: PartialSlotsOptions;
}

type ArgsWithOptionsSupplementInterface<Args extends TabsArgs | SlotsArgs> =
  Omit<Args, "options"> & {options?: Partial<Args["options"]>};

type ArgsWithOptionsSupplement<Args extends TabsArgs | SlotsArgs> =
  Args["pattern"] | ArgsWithOptionsSupplementInterface<Args>;

function isPattern<Args extends TabsArgs | SlotsArgs>(object: ArgsWithOptionsSupplement<Args>):
  object is Args["pattern"] {
  return object instanceof TabsPattern || object instanceof SlotsPattern;
}

function makeExportedFunc<Args extends TabsArgs | SlotsArgs>(base: TurtleFunc<[Args]>):
  ExportedFunc<Args> {
  function funcFromArgs(args: Args): TurtleFunc {
    return t => base(t, args);
  }
  function funcFromOpts(options: Args["options"]):
    TurtleFunc<[ArgsWithOptionsSupplement<Args>]> {
    return (t, argsSupplement) => {
      const argsSuppl: ArgsWithOptionsSupplementInterface<Args> = isPattern(argsSupplement) ?
        {pattern: argsSupplement} as ArgsWithOptionsSupplementInterface<Args> :
        argsSupplement;
      return base(t, {
        ...argsSuppl,
        options: {
          ...options,
          ...argsSuppl.options,
        } satisfies Args["options"],
      } as Args);
    };
  }
  function isTurtleArgs(args: Parameters<typeof base | typeof funcFromArgs | typeof funcFromOpts>):
    args is Parameters<typeof base> {
    return args[0] instanceof Turtle;
  }
  function isArgsParams(args: Parameters<typeof funcFromArgs | typeof funcFromOpts>):
    args is Parameters<typeof funcFromArgs> {
    const [arg] = args;
    return Object.hasOwn(arg, "pattern") && Object.hasOwn(arg, "options");
  }
  function func(...args: Parameters<typeof base>): ReturnType<typeof base>;
  function func(...args: Parameters<typeof funcFromArgs>): ReturnType<typeof funcFromArgs>;
  function func(...args: Parameters<typeof funcFromOpts>): ReturnType<typeof funcFromOpts>;
  function func(...args: Parameters<typeof base | typeof funcFromArgs | typeof funcFromOpts>) {
    if (isTurtleArgs(args))
      return base(...args);
    if (isArgsParams(args))
      return funcFromArgs(...args);
    return funcFromOpts(...args);
  }
  return func;
}

interface ProgressionBoundaryItem {
  kind: "boundary";
  boundary: "start" | "end";
  active: boolean;
}
interface ProgressionForwardItem {
  kind: "forward";
  active: boolean;
  length: number;
}
interface ProgressionActiveEdgeItem {
  kind: "activeEdge";
  newActive: boolean;
  useKerf: boolean;
}
type ProgressionItem =
  ProgressionForwardItem | ProgressionActiveEdgeItem | ProgressionBoundaryItem;

function patternProgression({pattern, startActive, endActive}: {
  pattern: InterlockPattern,
  startActive: boolean,
  endActive: boolean,
}) {
  let active = startActive;
  const items: ProgressionItem[] = [{
    kind: "boundary",
    boundary: "start",
    active,
  }];
  for (const item of pattern.items) {
    if (item.active !== active) {
      active = item.active;
      items.push({
        kind: "activeEdge",
        newActive: active,
        useKerf: items.length > 1,
      });
    }
    items.push({
      kind: "forward",
      active,
      length: item.length,
    });
  }
  if (endActive !== active) {
    active = endActive;
    items.push({
      kind: "activeEdge",
      newActive: active,
      useKerf: false,
    });
  }
  items.push({
    kind: "boundary",
    boundary: "end",
    active,
  });
  return items;
}

function signAbs(v: number) {
  if (v > 0)
    return [1, v];
  if (v < 0)
    return [-1, -v];
  return [0, 0];
}

function arcTurn(t: Turtle, rSign: number, rVal: number, d: number) {
  if (rVal === 0)
    return t.right(90 * d)
  else if (rSign > 0)
    return t.arcRight(90 * d, rVal * d)
  else
    return t.left(90 * d).arcRight(270 * d, rVal * d).left(90 * d);
}

const TURTLE_TABS_BASE_FUNC: TurtleFunc<[TabsArgs]> = (t, {
  pattern,
  onTabLevel = false,
  startOnTab = onTabLevel,
  endOnTab = onTabLevel,
  options,
}) => {
  const {kerf, tabWidth, outerCornersRadius, innerCornersRadius} =
    tabsOptionsFromPartial(options);
  const progression = patternProgression({
    pattern: pattern.pattern,
    startActive: startOnTab === "auto" ? pattern.startsWithTab() : startOnTab,
    endActive: endOnTab === "auto" ? pattern.endsWithTab() : endOnTab,
  });
  const dirNum = options.tabsDir === "right" ? 1 :
    options.tabsDir === "left" ? -1 :
      options.tabsDir satisfies never;
  for (let i = 0; i + 2 < progression.length; i++) {
    const [prev, curr, next] = progression.slice(i, i + 3);
    if (curr.kind === "forward") {
      if (prev.kind === "boundary")
        t = t.forward(curr.length / 2);
      if (next.kind === "boundary")
        t = t.forward(curr.length / 2);
    } else if (curr.kind === "activeEdge") {
      const kerfCorrection = curr.useKerf ?
        kerf.oneSideInUnits * (curr.newActive ? -1 : 1) : 0;
      const preLen = (prev.kind === "forward" ? prev.length / 2 : 0) + kerfCorrection;
      const postLen = (next.kind === "forward" ? next.length / 2 : 0) - kerfCorrection;
      if (preLen < 0 || postLen < 0)
        throw new Error(`Kerf too big, negative edge`);
      const radii = curr.useKerf ? [-innerCornersRadius, outerCornersRadius] : [0, 0];
      if (!curr.newActive)
        radii.reverse();
      const neighs = [prev, next];
      const [[r1Sign, r1Val], [r2Sign, r2Val]] = radii.map((r, ri) =>
        signAbs(neighs[ri].kind === "boundary" ? 0 : r));
      const d = dirNum * (curr.newActive ? 1 : -1);
      t = t.forward(preLen - r1Val)
        .andThen(arcTurn, r1Sign, r1Val, d)
        .forward(tabWidth - r1Val - r2Val)
        .andThen(arcTurn, r2Sign, r2Val, -d)
        .forward(postLen - r2Val);
    }
  }
  return t;
}

const SLOT_DIR_VALUES = {
  "center": 0,
  "right": 1,
  "left": -1,
};

export function getSlotWidth(options: PartialSlotsOptions) {
  const {slotWidth, slotWidthKerf} = slotsOptionsFromPartial(options);
  return Math.max(0, slotWidth - 2 * slotWidthKerf.oneSideInUnits);
}

const TURTLE_SLOTS_BASE_FUNC: TurtleFunc<[SlotsArgs]> = (t, {
  pattern,
  dir = "center",
  open,
  startOpen = open ?? pattern.startsWithOpenSlot(),
  endOpen = open ?? pattern.endsWithOpenSlot(),
  options,
}) => {
  const {kerf, slotWidth, innerCornersRadius} = slotsOptionsFromPartial(options);
  const progression = patternProgression({
    pattern: pattern.pattern,
    startActive: startOpen,
    endActive: endOpen,
  });
  return t.branch(t => {
    t = t.withPenUp(t => t.strafeRight(slotWidth / 2 * SLOT_DIR_VALUES[dir]));
    const halfWid = getSlotWidth(options) / 2;
    for (const d of [1, -1])
      t = t.branch(t => {
        if (startOpen)
          t = t.withPenUp(t => t.strafeRight(halfWid * d));
        function fwd(t: Turtle, penDown: boolean, length: number) {
          return t.withPenDown(penDown, t => t.forward(length));
        }
        for (let i = 0; i + 2 < progression.length; i++) {
          const [prev, curr, next] = progression.slice(i, i + 3);
          if (curr.kind === "forward") {
            if (prev.kind === "boundary")
              t = t.andThen(fwd, curr.active, curr.length / 2);
            if (next.kind === "boundary")
              t = t.andThen(fwd, curr.active, curr.length / 2);
          } else if (curr.kind === "activeEdge") {
            const kerfCorrection = curr.useKerf ?
              kerf.oneSideInUnits * (curr.newActive ? 1 : -1) : 0;
            const preLen = (prev.kind === "forward" ? prev.length / 2 : 0) + kerfCorrection;
            const postLen = (next.kind === "forward" ? next.length / 2 : 0) - kerfCorrection;
            if (preLen < 0 || postLen < 0)
              throw new Error(`Kerf too big, negative edge`);
            const [rSign, rVal] = signAbs(-innerCornersRadius);
            if (curr.newActive)
              t = t.andThen(fwd, false, preLen)
                .right(90 * d)
                .forward(halfWid - rVal)
                .andThen(arcTurn, rSign, rVal, -d)
                .forward(postLen - rVal);
            else
              t = t.forward(preLen - rVal)
                .andThen(arcTurn, rSign, rVal, -d)
                .forward(halfWid - rVal)
                .right(90 * d)
                .andThen(fwd, false, postLen);
          }
        }
        return t;
      });
    return t;
  }).withPenUp(t =>
    t.forward(progression.reduce((s, i) => i.kind === "forward" ? s + i.length : s, 0)),
  );
}

export interface TurtleInterlockFunc<Args extends TabsArgs | SlotsArgs>
  extends TurtleFunc<[ArgsWithOptionsSupplement<Args>]> {}

/**
 * A TurtleFunc that produces tabs or slots. It can also be used as a regular function taking
 * the args object, or only options, and returning a TurtleFunc that doesn't require specifying
 * the already specified parts.
 */
interface ExportedFunc<Args extends TabsArgs | SlotsArgs>
  extends TurtleFunc<[Args]> {
  (args: Args): TurtleFunc;
  (options: Args["options"]): TurtleInterlockFunc<Args>;
}

/** A turtle function that can produce tabs. */
export const turtleTabs: ExportedFunc<TabsArgs> = makeExportedFunc(TURTLE_TABS_BASE_FUNC);
/** A turtle function that can produce slots. */
export const turtleSlots: ExportedFunc<SlotsArgs> = makeExportedFunc(TURTLE_SLOTS_BASE_FUNC);

export interface TurtleTabsFunc extends TurtleInterlockFunc<TabsArgs> {}
export interface TurtleSlotsFunc extends TurtleInterlockFunc<SlotsArgs> {}

export type PartialInterlockOptions =
  | (PartialTabsOptions & PartialSlotsOptions)
  | (Omit<PartialTabsOptions & PartialSlotsOptions, "tabWidth" | "slotWidth"> &
    Partial<Pick<PartialTabsOptions & PartialSlotsOptions, "tabWidth" | "slotWidth">> & {
      materialThickness: number,
    });

export function tabsAndSlotsOptionsFromPartial(options: PartialInterlockOptions): {
  tabsOptions: TabsOptions,
  slotsOptions: SlotsOptions,
} {
  function noMaterialThickness(options: PartialInterlockOptions):
    options is PartialTabsOptions & PartialSlotsOptions {
    return !Object.hasOwn(options, "materialThickness");
  }
  const {tabs, slots} = noMaterialThickness(options) ? {tabs: options, slots: options} : {
    tabs: {
      ...options,
      tabWidth: options.tabWidth ?? options.materialThickness,
    },
    slots: {
      ...options,
      slotWidth: options.slotWidth ?? options.materialThickness,
    },
  };
  return {
    tabsOptions: tabsOptionsFromPartial(tabs),
    slotsOptions: slotsOptionsFromPartial(slots),
  };
}

/** Returns a pair of TurtleFunc's for tabs and for slots, given the options. */
export function turtleInterlock(options: PartialInterlockOptions) {
  const {tabsOptions, slotsOptions} = tabsAndSlotsOptionsFromPartial(options);
  return {
    tabsOptions,
    tabs: turtleTabs(tabsOptions),
    slotsOptions,
    slots: turtleSlots(slotsOptions),
  };
}

export function tabsPiece(args: TabsArgs) {
  return Turtle.create().andThen(TURTLE_TABS_BASE_FUNC, args).asPath();
}

export function slotsPiece(args: SlotsArgs) {
  return Turtle.create().andThen(TURTLE_SLOTS_BASE_FUNC, args).asPath();
}

export function turtleSlideSlotToSide(t: Turtle, {side, slot, options}: {
  side: "right" | "left",
  slot: number | SlotsPattern,
  options: PartialSlotsOptions,
}) {
  const wid = getSlotWidth(options);
  const pattern = typeof slot === "number" ? SlotsPattern.slide(slot) : slot;
  if (!pattern.startsWithSlot)
    throw new Error(`The pattern must start with a slot`);
  return t
    .withPenUp(t => t.forward(wid / 2))
    .branch(t => t
      .right(side === "right" ? 90 : side === "left" ? -90 : side satisfies never)
      .andThen(turtleSlots, {
        pattern,
        startOpen: true,
        options,
      })
    )
    .withPenUp(t => t.forward(wid / 2));
}