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

/**
 * Copyright (c) 2018-2020 mol* contributors, licensed under MIT, See LICENSE file for more info.
 *
 * @author David Sehnal <david.sehnal@gmail.com>
 * @author Alexander Rose <alexander.rose@weirdbyte.de>
 */

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

interface SpacegroupCell {
    /** Index into spacegroup data table */
    readonly index: number,
    readonly size: Vec3,
    readonly volume: number,
    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 {
    /** Hermann-Mauguin spacegroup name */
    readonly name: string,
    /** Spacegroup number from International Tables for Crystallography */
    readonly num: number,
    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) {
        if (!cell) return true;
        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 volume = size[0] * size[1] * size[2]

        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, volume, 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]));
        const name = SpacegroupName[cell.index]
        const num = SpacegroupNumber[cell.index]
        return { name, num, cell, operators };
    }

    const _ijkVec = Vec3();
    const _tempMat = Mat4();
    export function setOperatorMatrix(spacegroup: Spacegroup, index: number, i: number, j: number, k: number, target: Mat4) {
        Vec3.set(_ijkVec, i, j, k);

        Mat4.fromTranslation(_tempMat, _ijkVec);
        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, spgrOp: number, i: number, j: number, k: number): SymmetryOperator {
        const operator = setOperatorMatrix(spacegroup, spgrOp, i, j, k, Mat4.zero());
        return SymmetryOperator.create(`${spgrOp + 1}_${5 + i}${5 + j}${5 + k}`, operator, { hkl: Vec3.create(i, j, k), spgrOp });
    }

    const _translationRef = Vec3()
    const _translationRefSymop = Vec3()
    const _translationSymop = Vec3()
    export function setOperatorMatrixRef(spacegroup: Spacegroup, index: number, i: number, j: number, k: number, ref: Vec3, target: Mat4) {
        Vec3.set(_ijkVec, i, j, k);
        Vec3.floor(_translationRef, ref)

        Mat4.copy(target, spacegroup.operators[index])

        Vec3.floor(_translationRefSymop, Vec3.transformMat4(_translationRefSymop, ref, target))

        Mat4.getTranslation(_translationSymop, target)
        Vec3.sub(_translationSymop, _translationSymop, _translationRefSymop)
        Vec3.add(_translationSymop, _translationSymop, _translationRef)
        Vec3.add(_translationSymop, _translationSymop, _ijkVec)

        Mat4.setTranslation(target, _translationSymop)
        Mat4.mul(target, spacegroup.cell.fromFractional, target)
        Mat4.mul(target, target, spacegroup.cell.toFractional)
        return target
    }

    /**
     * Get Symmetry operator for transformation around the given
     * reference point `ref` in fractional coordinates
     */
    export function getSymmetryOperatorRef(spacegroup: Spacegroup, spgrOp: number, i: number, j: number, k: number, ref: Vec3) {
        const operator = setOperatorMatrixRef(spacegroup, spgrOp, i, j, k, ref, Mat4.zero());
        return SymmetryOperator.create(`${spgrOp + 1}_${5 + i}${5 + j}${5 + k}`, operator, { hkl: Vec3.create(i, j, k), spgrOp });
    }

    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 function getOperatorXyz(op: Mat4) {
        return [
            formatElement(getRotation(op[0], op[4], op[8]), getShift(op[12])),
            formatElement(getRotation(op[1], op[5], op[9]), getShift(op[13])),
            formatElement(getRotation(op[2], op[6], op[10]), getShift(op[14]))
        ].join(',')
    }

    function getRotation(x: number, y: number, z: number) {
        let r: string[] = []
        if (x > 0) r.push('+X')
        else if (x < 0) r.push('-X')
        if (y > 0) r.push('+Y')
        else if (y < 0) r.push('-Y')
        if (z > 0) r.push('+Z')
        else if (z < 0) r.push('-Z')

        if (r.length === 1) {
            return r[0].charAt(0) === '+' ? r[0].substr(1) : r[0]
        }
        if (r.length === 2) {
            const s0 = r[0].charAt(0)
            const s1 = r[1].charAt(0)
            if (s0 === '+') return `${r[0].substr(1)}${r[1]}`
            if (s1 === '+') return `${r[1].substr(1)}${r[0]}`
        }
        throw new Error(`unknown rotation '${r}', ${x} ${y} ${z}`)
    }

    function getShift(s: number) {
        switch (s) {
            case 1 / 2: return '1/2'
            case 1 / 4: return '1/4'
            case 3 / 4: return '3/4'
            case 1 / 3: return '1/3'
            case 2 / 3: return '2/3'
            case 1 / 6: return '1/6'
            case 5 / 6: return '5/6'
        }
        return ''
    }

    function formatElement(rotation: string, shift: string) {
        if (shift === '') return rotation
        if (rotation.length > 2) return `${rotation}+${shift}`
        return rotation.charAt(0) === '-' ? `${shift}${rotation}` : `${shift}+${rotation}`
    }
}

export { Spacegroup, SpacegroupCell }