TmMolStar/src/mol-math/geometry/spacegroup/construction.ts

/**
 * Copyright (c) 2018 mol* contributors, licensed under MIT, See LICENSE file for more info.
 *
 * @author David Sehnal <david.sehnal@gmail.com>
 */

import { Vec3, Mat4 } from '../../linear-algebra'
import { SpacegroupName, TransformData, GroupData, getSpacegroupIndex, OperatorData, SpacegroupNames } from './tables'
import { SymmetryOperator } from '../../geometry';

interface SpacegroupCell {
    // zero based spacegroup number
    readonly index: number,
    readonly size: Vec3,
    readonly anglesInRadians: Vec3,
    /** Transfrom cartesian -> fractional coordinates within the cell */
    readonly toFractional: Mat4,
    /** Transfrom fractional coordinates within the cell -> cartesian */
    readonly fromFractional: Mat4
}

interface Spacegroup {
    readonly name: string,
    readonly cell: SpacegroupCell,
    readonly operators: ReadonlyArray<Mat4>
}

namespace SpacegroupCell {
    /** Create a 'P 1' with cellsize [1, 1, 1] */
    export const Zero: SpacegroupCell = create('P 1', Vec3.create(1, 1, 1), Vec3.create(Math.PI / 2, Math.PI / 2, Math.PI / 2));

    /** True if 'P 1' with cellsize [1, 1, 1] */
    export function isZero(cell: SpacegroupCell) {
        return cell.index === 0 && cell.size[0] === 1 && cell.size[1] === 1 && cell.size[1] === 1;
    }

    // returns Zero cell if the spacegroup does not exist
    export function create(nameOrNumber: number | string | SpacegroupName, size: Vec3, anglesInRadians: Vec3): SpacegroupCell {
        const index = getSpacegroupIndex(nameOrNumber);
        if (index < 0) {
            console.warn(`Unknown spacegroup '${nameOrNumber}', returning a 'P 1' with cellsize [1, 1, 1]`)
            return Zero;
        }

        const alpha = anglesInRadians[0];
        const beta = anglesInRadians[1];
        const gamma = anglesInRadians[2];

        const xScale = size[0], yScale = size[1], zScale = size[2];

        const z1 = Math.cos(beta);
        const z2 = (Math.cos(alpha) - Math.cos(beta) * Math.cos(gamma)) / Math.sin(gamma);
        const z3 = Math.sqrt(1.0 - z1 * z1 - z2 * z2);

        const x = [xScale, 0.0, 0.0];
        const y = [Math.cos(gamma) * yScale, Math.sin(gamma) * yScale, 0.0];
        const z = [z1 * zScale, z2 * zScale, z3 * zScale];

        const fromFractional = Mat4.ofRows([
            [x[0], y[0], z[0], 0],
            [0, y[1], z[1], 0],
            [0, 0, z[2], 0],
            [0, 0, 0, 1.0]
        ]);
        const toFractional = Mat4.invert(Mat4.zero(), fromFractional)!;

        return { index, size, anglesInRadians, toFractional, fromFractional };
    }
}


namespace Spacegroup {
    // P1 with [1, 1, 1] cell.
    export const ZeroP1 = create(SpacegroupCell.Zero);

    export function create(cell: SpacegroupCell): Spacegroup {
        const operators = GroupData[cell.index].map(i => getOperatorMatrix(OperatorData[i]));
        return { name: SpacegroupNames[cell.index], cell, operators };
    }

    const _tempVec = Vec3.zero(), _tempMat = Mat4.zero();
    export function updateOperatorMatrix(spacegroup: Spacegroup, index: number, i: number, j: number, k: number, target: Mat4) {
        _tempVec[0] = i;
        _tempVec[1] = j;
        _tempVec[2] = k;

        Mat4.fromTranslation(_tempMat, _tempVec);
        return Mat4.mul(target, Mat4.mul(target, Mat4.mul(target, spacegroup.cell.fromFractional, _tempMat), spacegroup.operators[index]), spacegroup.cell.toFractional);
    }

    export function getSymmetryOperator(spacegroup: Spacegroup, index: number, i: number, j: number, k: number): SymmetryOperator {
        const operator = updateOperatorMatrix(spacegroup, index, i, j, k, Mat4.zero());
        return SymmetryOperator.create(`${index + 1}_${5 + i}${5 + j}${5 + k}`, operator, { id: '', operList: [] }, '', Vec3.create(i, j, k));
    }

    function getOperatorMatrix(ids: number[]) {
        const r1 = TransformData[ids[0]];
        const r2 = TransformData[ids[1]];
        const r3 = TransformData[ids[2]];
        return Mat4.ofRows([r1, r2, r3, [0, 0, 0, 1]]);
    }
}

export { Spacegroup, SpacegroupCell }