"use strict";

class TrivialConnections {
	/**
	 * This class implements the {@link https://cs.cmu.edu/~kmcrane/Projects/TrivialConnections trivial connections} algorithm to compute a smooth
	 * 1-form vector fields on a surface mesh.
	 * @constructor module:Projects.TrivialConnections
	 * @param {module:Core.Geometry} geometry The input geometry of the mesh this class acts on.
	 * @property {Object} vertexIndex A dictionary mapping each vertex of the input mesh to a unique index.
	 * @property {Object} edgeIndex A dictionary mapping each edge of the input mesh to a unique index.
	 * @property {module:LinearAlgebra.DenseMatrix[]} bases The harmonic bases [γ1, γ2 ... γn] of the input mesh.
	 * @property {module:LinearAlgebra.SparseMatrix} P The period matrix of the input mesh.
	 * @property {module:LinearAlgebra.SparseMatrix} A The 0-form laplace matrix d0^T star1 d0 of the input mesh.
	 * @property {module:LinearAlgebra.SparseMatrix} hodge1 The hodge star 1-form matrix of the input mesh.
	 * @property {module:LinearAlgebra.SparseMatrix} d0 The exterior derivaitve 0-form matrix of the input mesh.
	 */
	constructor(geometry) {
		this.geometry = geometry;
		this.vertexIndex = indexElements(geometry.mesh.vertices);
		this.edgeIndex = indexElements(geometry.mesh.edges);

		// TODO: build harmonic bases
		this.bases = []; // placeholder

		// build period matrix
		this.P = this.buildPeriodMatrix();

		// TODO: store relevant DEC operators
		this.A = SparseMatrix.identity(1, 1); // placeholder
		this.hodge1 = SparseMatrix.identity(1, 1); // placeholder
		this.d0 = SparseMatrix.identity(1, 1); // placeholder
	}

	/**
	 * Builds the period matrix Pij = ∑_{ek ∈ li} (ξj)k, where li is the ith homology generator,
	 * ek is a dual edge in li and ξj is the jth harmonic 1-form basis.
	 * @private
	 * @method module:Projects.TrivialConnections#buildPeriodMatrix
	 * @returns {module:LinearAlgebra.SparseMatrix}
	 */
	buildPeriodMatrix() {
		// TODO

		return SparseMatrix.identity(1, 1); // placeholder
	}

	/**
	 * Checks whether Gauss Bonnet is satisfied, i.e., ∑singularity = χ.
	 * @private
	 * @method module:Projects.TrivialConnections#satisfyGaussBonnet
	 * @param {Object} singularity A dictionary mapping each vertex of the input mesh
	 * to either 0 or 1, where 1 indicates that the vertex is a singularity and 0
	 * indicates that it is not.
	 * @returns {boolean}
	 */
	satisfyGaussBonnet(singularity) {
		let sum = 0;
		let mesh = this.geometry.mesh;
		for (let v of mesh.vertices) {
			sum += singularity[v];
		}

		return Math.abs(mesh.eulerCharacteristic() - sum) < 1e-8;
	}

	/**
	 * Computes the dual 0-form potential β by solving the system d𝛿β = -K + 2π * singularity.
	 * @private
	 * @method module:Projects.TrivialConnections#computeCoExactComponent
	 * @param {Object} singularity A dictionary mapping each vertex of the input mesh
	 * to either 0 or 1, where 1 indicates that the vertex is a singularity and 0
	 * indicates that it is not.
	 * @returns {module:LinearAlgebra.DenseMatrix} The coexact component 𝛿β.
	 */
	computeCoExactComponent(singularity) {
		// TODO

		return DenseMatrix.zeros(1, 1); // placeholder
	}

	/**
	 * Given an initial angle αi in face i, this function computes the new angle
	 * αj in the neighboring face j as αj = αi - θij + θji, where θij and θji are
	 * the angles between the shared edge e and an arbitrary but fixed reference direction
	 * in faces i and j. Repeating this procedure for n consecutive dual edges in a
	 * generator gives a sequence of angles α0 , . . . , αn with a resulting total
	 * angle defect equal to αn - α0. This corresponds to transporting a vector around
	 * a generator by unfolding, sliding and refolding it across neighboring faces
	 * without any extra in plane rotation.
	 * @private
	 * @method module:Projects.TrivialConnections#transportNoRotation
	 * @param {Object} h A halfedge lying on the shared edge between face i and j.
	 * @param {number} alphaI The initial angle αi.
	 * @returns {number}
	 */
	transportNoRotation(h, alphaI = 0) {
		let u = this.geometry.vector(h);

		let [e1, e2] = this.geometry.orthonormalBases(h.face);
		let thetaIJ = Math.atan2(u.dot(e2), u.dot(e1));

		let [f1, f2] = this.geometry.orthonormalBases(h.twin.face);
		let thetaJI = Math.atan2(u.dot(f2), u.dot(f1));

		return alphaI - thetaIJ + thetaJI;
	}

	/**
	 * Computes the harmonic component γ = ∑_{i = 1, ..., 2g} zi ξi by solving
	 * the system Pz = v - ∑𝛿β. v - ∑𝛿β should be normalized to lie between -π and π.
	 * @private
	 * @method module:Projects.TrivialConnections#computeHarmonicComponent
	 * @param {module:LinearAlgebra.DenseMatrix} deltaBeta The coexact component 𝛿β.
	 * @returns {module:LinearAlgebra.DenseMatrix}
	 */
	computeHarmonicComponent(deltaBeta) {
		// TODO

		return DenseMatrix.zeros(1, 1); // placeholder
	}

	/**
	 * Computes the dual 1-form connections φ = 𝛿β + γ.
	 * @method module:Projects.TrivialConnections#computeConnections
	 * @param {Object} singularity A dictionary mapping each vertex of the input mesh
	 * to either 0 or 1, where 1 indicates that the vertex is a singularity and 0
	 * indicates that it is not.
	 * @returns {module:LinearAlgebra.DenseMatrix}
	 */
	computeConnections(singularity) {
		if (!this.satisfyGaussBonnet(singularity)) {
			alert("Singularities do not add up to the euler characteristic of the mesh");
			return undefined;
		}

		// TODO

		return undefined; // placeholder
	}
}
