Jyotisha/frontend/src/lib/north-indian-chart-geometry.ts

/** North Indian (diamond) house polygons for a square of side S. */

export const CHART_SIZE = 400;

export type Point = Readonly<{ x: number; y: number }>;

const S = CHART_SIZE;
const H = S / 2;
const Q = S / 4;

/** House 1 is the top diamond; numbers run clockwise from there. */
export const HOUSE_POLYGONS: Readonly<Record<number, readonly Point[]>> = {
  1: [{ x: H, y: 0 }, { x: 3 * Q, y: Q }, { x: H, y: H }, { x: Q, y: Q }],
  2: [{ x: 0, y: 0 }, { x: H, y: 0 }, { x: Q, y: Q }],
  3: [{ x: 0, y: 0 }, { x: Q, y: Q }, { x: 0, y: H }],
  4: [{ x: 0, y: H }, { x: Q, y: Q }, { x: H, y: H }, { x: Q, y: 3 * Q }],
  5: [{ x: 0, y: H }, { x: Q, y: 3 * Q }, { x: 0, y: S }],
  6: [{ x: 0, y: S }, { x: Q, y: 3 * Q }, { x: H, y: S }],
  7: [{ x: H, y: S }, { x: Q, y: 3 * Q }, { x: H, y: H }, { x: 3 * Q, y: 3 * Q }],
  8: [{ x: H, y: S }, { x: 3 * Q, y: 3 * Q }, { x: S, y: S }],
  9: [{ x: S, y: S }, { x: 3 * Q, y: 3 * Q }, { x: S, y: H }],
  10: [{ x: S, y: H }, { x: 3 * Q, y: 3 * Q }, { x: H, y: H }, { x: 3 * Q, y: Q }],
  11: [{ x: S, y: H }, { x: 3 * Q, y: Q }, { x: S, y: 0 }],
  12: [{ x: S, y: 0 }, { x: 3 * Q, y: Q }, { x: H, y: 0 }],
};

export const HOUSE_NUMBERS = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] as const;

const CENTER: Point = { x: H, y: H };

export function polygonPoints(points: readonly Point[]): string {
  return points.map((point) => `${point.x},${point.y}`).join(" ");
}

export function polygonCentroid(points: readonly Point[]): Point {
  const areaTimes2 = points.reduce((sum, point, index) => {
    const next = points[(index + 1) % points.length];
    return sum + (point.x * next.y - next.x * point.y);
  }, 0);
  if (Math.abs(areaTimes2) < 1e-9) {
    const n = points.length || 1;
    return {
      x: points.reduce((sum, point) => sum + point.x, 0) / n,
      y: points.reduce((sum, point) => sum + point.y, 0) / n,
    };
  }
  const cx = points.reduce((sum, point, index) => {
    const next = points[(index + 1) % points.length];
    return sum + (point.x + next.x) * (point.x * next.y - next.x * point.y);
  }, 0) / (3 * areaTimes2);
  const cy = points.reduce((sum, point, index) => {
    const next = points[(index + 1) % points.length];
    return sum + (point.y + next.y) * (point.x * next.y - next.x * point.y);
  }, 0) / (3 * areaTimes2);
  return { x: cx, y: cy };
}

export function polygonArea(points: readonly Point[]): number {
  const sum = points.reduce((total, point, index) => {
    const next = points[(index + 1) % points.length];
    return total + (point.x * next.y - next.x * point.y);
  }, 0);
  return Math.abs(sum) / 2;
}

export function pointInPolygon(point: Point, polygon: readonly Point[]): boolean {
  let inside = false;
  for (let i = 0, j = polygon.length - 1; i < polygon.length; j = i, i += 1) {
    const a = polygon[i];
    const b = polygon[j];
    const intersect = (a.y > point.y) !== (b.y > point.y)
      && point.x < ((b.x - a.x) * (point.y - a.y)) / ((b.y - a.y) || Number.EPSILON) + a.x;
    if (intersect) inside = !inside;
  }
  return inside;
}

function distance(a: Point, b: Point): number {
  return Math.hypot(a.x - b.x, a.y - b.y);
}

function moveToward(from: Point, to: Point, distancePx: number): Point {
  const dx = to.x - from.x;
  const dy = to.y - from.y;
  const length = Math.hypot(dx, dy) || 1;
  return { x: from.x + (dx / length) * distancePx, y: from.y + (dy / length) * distancePx };
}

function rightAngleVertex(points: readonly Point[]): Point {
  for (let index = 0; index < points.length; index += 1) {
    const prev = points[(index + points.length - 1) % points.length];
    const vertex = points[index];
    const next = points[(index + 1) % points.length];
    const d1x = prev.x - vertex.x;
    const d1y = prev.y - vertex.y;
    const d2x = next.x - vertex.x;
    const d2y = next.y - vertex.y;
    if (Math.abs(d1x * d2x + d1y * d2y) < 1e-6) return vertex;
  }
  return points[0];
}

function innerVertex(points: readonly Point[]): Point {
  return points.reduce((best, point) => (distance(point, CENTER) < distance(best, CENTER) ? point : best));
}

/**
 * Where a house's planet symbols sit. The raw centroid crowds the sign number
 * in the triangular houses, so the group is nudged away from the vertex the
 * number hangs on — the centre for the four diamonds, the right angle for the
 * eight triangles.
 */
export function occupantAnchor(houseNumber: number): Point {
  const polygon = HOUSE_POLYGONS[houseNumber];
  const centroid = polygonCentroid(polygon);
  const isDiamond = polygon.length === 4;
  const anchorVertex = isDiamond ? innerVertex(polygon) : rightAngleVertex(polygon);
  const push = isDiamond ? 0.05 : 0.18;
  return {
    x: centroid.x + (centroid.x - anchorVertex.x) * push,
    y: centroid.y + (centroid.y - anchorVertex.y) * push,
  };
}

export function signNumberAnchor(houseNumber: number): Point {
  const polygon = HOUSE_POLYGONS[houseNumber];
  const centroid = polygonCentroid(polygon);
  if (polygon.length === 4) {
    return moveToward(innerVertex(polygon), centroid, 12);
  }
  return moveToward(rightAngleVertex(polygon), centroid, 14);
}