TypeScript polyhedra.Face類代碼示例

// Augment the following
function doAugment(
  polyhedron: Polyhedron,
  base: Face,
  augmentType: string,
  gyrate?: string,
) {
  const numSides = base.numSides;
  const augmentee = getAugmentee(augmentType, numSides);
  const underside = augmentee.faceWithNumSides(base.numSides);

  // Determine the orientations of the underside and the base
  const undersideRadius = underside.vertices[0].vec
    .sub(underside.centroid())
    .getNormalized();

  const baseIsAligned = isAligned(
    polyhedron,
    base,
    underside,
    isFastigium(augmentType, numSides) ? 'gyro' : gyrate,
    augmentType,
  );
  const offset = baseIsAligned ? 0 : 1;
  const baseRadius = base.vertices[offset].vec
    .sub(base.centroid())
    .getNormalized();

  // https://math.stackexchange.com/questions/624348/finding-rotation-axis-and-angle-to-align-two-oriented-vectors
  // Determine the transformation that rotates the underside orientation to the base orientation
  // TODO we probably want this as some sort of generic method
  const transformMatrix = getOrthonormalTransform(
    undersideRadius,
    underside.normal().getInverted(),
    baseRadius,
    base.normal(),
  );
  const transform = withOrigin(base.centroid(), u =>
    transformMatrix.applyTo(u),
  );

  // Scale and position the augmentee so that it lines up with the base
  const alignedVertices = augmentee.vertices.map(v => {
    return v.vec
      .sub(underside.centroid())
      .scale(base.sideLength() / augmentee.edgeLength())
      .add(base.centroid());
  });

  // Rotate the vertices so that they align with the base
  const rotatedVertices = alignedVertices.map(v => transform(v));

  const newAugmentee = augmentee.withChanges(solid =>
    solid.withVertices(rotatedVertices).withoutFaces([underside]),
  );
  return polyhedron.withChanges(solid =>
    solid.withoutFaces([base]).addPolyhedron(newAugmentee),
  );
}

export function isExpandedFace(
  polyhedron: Polyhedron,
  face: Face,
  nSides?: number,
) {
  const type = expansionType(polyhedron);
  if (typeof nSides === 'number' && face.numSides !== nSides) return false;
  if (!face.isValid()) return false;
  return _.every(face.adjacentFaces(), { numSides: edgeShape[type] });
}

// Return true if the base and augmentee are aligned
function isAligned(
  polyhedron: Polyhedron,
  base: Face,
  underside: Face,
  gyrate: string | undefined,
  augmentType: string,
) {
  if (augmentType === 'pyramid') return true;
  const baseType = getBaseType(base);
  if (baseType === 'pyramid' || baseType === 'antiprism') {
    return true;
  }

  if (baseType === 'prism' && Cap.getAll(polyhedron).length === 0) {
    return true;
  }

  if (baseType !== 'truncated' && _.isNil(gyrate)) {
    throw new Error(`Must define 'gyrate' for augmenting ${baseType} `);
  }

  const adjFace =
    baseType === 'prism' ? getOppositePrismFace(base) : base.adjacentFaces()[0];
  const alignedFace = getCyclic(underside.adjacentFaces(), -1);

  if (baseType === 'rhombicosidodecahedron') {
    const isOrtho = (adjFace.numSides !== 4) === (alignedFace.numSides !== 4);
    return isOrtho === (gyrate === 'ortho');
  }

  // It's orthogonal if triangle faces are aligned or non-triangle faces are aligned
  const isOrtho = (adjFace.numSides !== 3) === (alignedFace.numSides !== 3);

  if (baseType === 'truncated') {
    return !isOrtho;
  }

  // "ortho" or "gyro" is actually determined by whether the *tops* are aligned, not the bottoms
  // So for a cupola-rotunda, it's actually the opposite of everything else
  if (isCupolaRotunda(Cap.getAll(polyhedron)[0].type, augmentType)) {
    return isOrtho !== (gyrate === 'ortho');
  }

  return isOrtho === (gyrate === 'ortho');
}

function getFaceDistance(face1: Face, face2: Face) {
  let dist = 0;
  let current = [face1];
  while (!face2.inSet(current)) {
    dist++;
    current = flatMapUniq(current, face => face.adjacentFaces(), 'index');

    if (dist > 10) {
      throw new Error('we went toooooo far');
    }
  }
  return dist;
}

function getBaseType(base: Face) {
  const adjacentFaces = base.adjacentFaces();
  const adjacentFaceCounts = _(adjacentFaces)
    .map('numSides')
    .uniq()
    .value();
  if (setEquals(adjacentFaceCounts, [3, 4])) {
    return 'cupola';
  } else if (setEquals(adjacentFaceCounts, [4])) {
    return 'prism';
  } else if (setEquals(adjacentFaceCounts, [3])) {
    return _.intersection(adjacentFaces).length > 0 ? 'pyramid' : 'antiprism';
  } else if (setEquals(adjacentFaceCounts, [3, 5])) {
    return 'rotunda';
  } else if (setEquals(adjacentFaceCounts, [4, 5])) {
    return 'rhombicosidodecahedron';
  } else {
    return 'truncated';
  }
}

function getVertexToAdd(polyhedron: Polyhedron, face: Face) {
  const dist = getsharpenDist(polyhedron, face);
  return face.normalRay().getPointAtDistance(dist);
}

function calculatesharpenDist(face: Face, edge: Edge) {
  const apothem = face.apothem();
  const theta = Math.PI - edge.dihedralAngle();
  return apothem * Math.tan(theta);
}

function getAugmentAlignment(polyhedron: Polyhedron, face: Face) {
  const boundary = getSingle(Cap.getAll(polyhedron)).boundary();
  return isInverse(boundary.normal(), face.normal()) ? 'para' : 'meta';
}

 const alignedVertices = augmentee.vertices.map(v => {
   return v.vec
     .sub(underside.centroid())
     .scale(base.sideLength() / augmentee.edgeLength())
     .add(base.centroid());
 });