Started structure data model

src/structure/data.ts

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+/**
+ * Copyright (c) 2017 molio contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+export type Table<Data> = { rowCount: number } & { [E in keyof Data]: ArrayLike<Data[E]> }
+export type DataTable<Data> = { data: any } & Table<Data & { dataIndex: number }>
+
+export interface Position { x: number, y: number, z: number }
+export interface Positions extends Table<Position> {}
+
+export interface Atom {
+    name: string,
+    elementSymbol: string,
+    altLoc: string | null,
+}
+export interface Atoms extends DataTable<Atom> { }
+
+export interface Residue {
+    key: number,
+    name: string,
+    seqNumber: number,
+    insCode: string | null,
+    isHet: number
+}
+export interface Residues extends DataTable<Residue> { }
+
+export interface Chain { key: number, id: string }
+export interface Chains extends DataTable<Chain> { }
+
+export interface Entity { key: number, id: string }
+export interface Entities extends DataTable<Entity> { }
+
+export interface SecondaryStructure {
+
+}
+export interface SecondaryStructures extends Table<SecondaryStructure> {
+
+}

src/structure/model.ts

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+/**
+ * Copyright (c) 2017 molio contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+import * as Data from './data'
+import { Vec3, Mat4 } from '../utils/linear-algebra'
+
+
+/** Unit = essentially a list of residues (usually a chain) */
+export interface Unit extends Readonly<{
+    /** The static part (essentially residue annotations) */
+    structre: Unit.Structure,
+    /** 3D arrangement that often changes with time. */
+    conformation: Unit.Conformation
+}> { }
+
+export namespace Unit {
+    export interface ResidueLayer extends Readonly<{
+        data: Data.Residues,
+        /** Indices into the data table. */
+        index: ArrayLike<number>,
+        /** Offsets of atoms in the residue layer. start = offsets[i], endExclusive = offsets[i + 1] */
+        offset: ArrayLike<number>
+    }> { }
+
+    export interface AtomLayer extends Readonly<{
+        data: Data.Atoms,
+        /** Indices into the data table. */
+        index: ArrayLike<number>,
+        /** Index of a residue in the corresponding residue layer. */
+        residue: number
+    }> { }
+
+    /** Represent the th */
+    export interface Structure extends Readonly<{
+        /** A globally unique number for this instance (to easily determine unique structures within a model) */
+        key: number,
+        /** Reference to the Data.Entities table */
+        entity: number,
+        /** Reference to the Data.Chains table */
+        chain: number,
+        residues: ResidueLayer,
+        atoms: AtomLayer
+    }> { }
+
+    export interface Bonds extends Readonly<{
+        /**
+         * Where bonds for atom A start and end.
+         * Start at idx, end at idx + 1
+         */
+        offset: ArrayLike<number>,
+        neighbor: ArrayLike<number>,
+
+        order: ArrayLike<number>,
+        flags: ArrayLike<number>,
+
+        count: number
+    }> { }
+
+    export interface Conformation extends Readonly<{
+        positions: Data.Positions
+        spatialLookup: any, // TODO
+        boundingSphere: { readonly center: Vec3, readonly radius: number },
+        secodaryStructure: Data.SecondaryStructures,
+        bonds: Bonds
+    }> { }
+
+    export type OperatorKind =
+        | { kind: 'identity' }
+        | { kind: 'symmetry', id: string, hkl: Vec3 }
+        | { kind: 'assembly', index: number }
+
+    export interface Operator extends Readonly<{
+        kind: OperatorKind,
+        transform: Mat4,
+        inverse: Mat4
+    }> { }
+
+    export interface Lookup3D {
+        // TODO
+    }
+}
+
+export interface Model extends Readonly<{
+    index: number,
+
+    structure: Model.Structure,
+    conformation: Model.Conformation
+}> { }
+
+export namespace Model {
+    export interface Structure extends Readonly<{
+        entityData: Data.Entities,
+        chainData: Data.Chains,
+
+        operators: Unit.Operator[],
+        units: Unit.Structure[]
+    }> { }
+
+    export interface Conformation extends Readonly<{
+        units: Unit.Conformation[],
+        spatialLookup: Unit.Lookup3D
+    }> { }
+}
+
+export namespace Atom {
+    /**
+     * Represents a "packed reference" to an atom.
+     * This is because selections can then be represented
+     * a both number[] and Float64Array(), making it much
+     * more efficient than storing an array of objects.
+     */
+    export type Reference = number
+    export interface Location { unit: number, atom: number }
+
+    const { _uint32, _float64 } = (function() {
+        const data = new ArrayBuffer(8);
+        return { _uint32: new Uint32Array(data), _float64: new Float64Array(data) };
+    }());
+
+    export function emptyLocation(): Location { return { unit: 0, atom: 0 }; }
+
+    export function getRef(location: Location) {
+        _uint32[0] = location.unit;
+        _uint32[1] = location.atom;
+        return _float64[0];
+    }
+
+    export function getLocation(ref: Reference) {
+        return updateLocation(ref, emptyLocation());
+    }
+
+    export function updateLocation(ref: Reference, location: Location): Location {
+        _float64[0] = ref;
+        location.unit = _uint32[0];
+        location.atom = _uint32[1];
+        return location;
+    }
+}

src/structure/topology/secondary-structure.ts

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+/**
+ * Copyright (c) 2017 molio contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author Alexander Rose <alexander.rose@weirdbyte.de>
+ */
+
+const enum SSF {
+    None = 0x0,
+
+    // category
+    DoubleHelix = 0x1,
+    Helix = 0x2,
+    Beta = 0x4,
+    Turn = 0x8,
+
+    // category variant
+    LeftHanded = 0x10,  // helix
+    RightHanded = 0x20,
+
+    ClassicTurn = 0x40,  // turn
+    InverseTurn = 0x80,
+
+    // sub-category
+    HelixOther = 0x100,  // protein
+    Helix27 = 0x200,
+    Helix3Ten = 0x400,
+    HelixAlpha = 0x800,
+    HelixGamma = 0x1000,
+    HelixOmega = 0x2000,
+    HelixPi = 0x4000,
+    HelixPolyproline = 0x8000,
+
+    DoubleHelixOther = 0x10000,  // nucleic
+    DoubleHelixZ = 0x20000,
+    DoubleHelixA = 0x40000,
+    DoubleHelixB = 0x80000,
+
+    BetaOther = 0x100000,  // protein
+    BetaStrand = 0x200000,  // single strand
+    BetaSheet = 0x400000,  // multiple hydrogen bonded strands
+    BetaBarell = 0x800000,  // closed series of sheets
+
+    TurnOther = 0x1000000,  // protein
+    Turn1 = 0x2000000,
+    Turn2 = 0x4000000,
+    Turn3 = 0x8000000,
+
+    NA = 0x10000000,  // not applicable/available
+}
+export { SSF as SecondaryStructureFlag }
+
+export const SecondaryStructureMmcif: { [value: string]: number } = {
+    HELX_LH_27_P: SSF.Helix | SSF.LeftHanded | SSF.Helix27,  // left-handed 2-7 helix (protein)
+    HELX_LH_3T_P: SSF.Helix | SSF.LeftHanded | SSF.Helix3Ten,  // left-handed 3-10 helix (protein)
+    HELX_LH_AL_P: SSF.Helix | SSF.LeftHanded | SSF.HelixAlpha,  // left-handed alpha helix (protein)
+    HELX_LH_A_N: SSF.DoubleHelix | SSF.LeftHanded | SSF.DoubleHelixA,  // left-handed A helix (nucleic acid)
+    HELX_LH_B_N: SSF.DoubleHelix | SSF.LeftHanded | SSF.DoubleHelixB,  // left-handed B helix (nucleic acid)
+    HELX_LH_GA_P: SSF.Helix | SSF.LeftHanded | SSF.HelixGamma,  // left-handed gamma helix (protein)
+    HELX_LH_N: SSF.DoubleHelix | SSF.LeftHanded,  // left-handed helix with type not specified (nucleic acid)
+    HELX_LH_OM_P: SSF.Helix | SSF.LeftHanded | SSF.HelixOmega,  // left-handed omega helix (protein)
+    HELX_LH_OT_N: SSF.DoubleHelix | SSF.LeftHanded | SSF.DoubleHelixOther,  // left-handed helix with type that does not conform to an accepted category (nucleic acid)
+    HELX_LH_OT_P: SSF.Helix | SSF.LeftHanded | SSF.HelixOther,  // left-handed helix with type that does not conform to an accepted category (protein)
+    HELX_LH_P: SSF.Helix | SSF.LeftHanded,  // left-handed helix with type not specified (protein)
+    HELX_LH_PI_P: SSF.Helix | SSF.LeftHanded | SSF.HelixPi,  // left-handed pi helix (protein)
+    HELX_LH_PP_P: SSF.Helix | SSF.LeftHanded | SSF.HelixPolyproline,  // left-handed polyproline helix (protein)
+    HELX_LH_Z_N: SSF.DoubleHelix | SSF.LeftHanded | SSF.DoubleHelixZ,  // left-handed Z helix (nucleic acid)
+    HELX_N: SSF.DoubleHelix,  // helix with handedness and type not specified (nucleic acid)
+    HELX_OT_N: SSF.DoubleHelix,  // helix with handedness and type that do not conform to an accepted category (nucleic acid)
+    HELX_OT_P: SSF.Helix,  // helix with handedness and type that do not conform to an accepted category (protein)
+    HELX_P: SSF.Helix,  // helix with handedness and type not specified (protein)
+    HELX_RH_27_P: SSF.Helix | SSF.RightHanded | SSF.Helix27,  // right-handed 2-7 helix (protein)
+    HELX_RH_3T_P: SSF.Helix | SSF.RightHanded | SSF.Helix3Ten,  // right-handed 3-10 helix (protein)
+    HELX_RH_AL_P: SSF.Helix | SSF.RightHanded | SSF.HelixAlpha,  // right-handed alpha helix (protein)
+    HELX_RH_A_N: SSF.DoubleHelix | SSF.RightHanded | SSF.DoubleHelixA,  // right-handed A helix (nucleic acid)
+    HELX_RH_B_N: SSF.DoubleHelix | SSF.RightHanded | SSF.DoubleHelixB,  // right-handed B helix (nucleic acid)
+    HELX_RH_GA_P: SSF.Helix | SSF.RightHanded | SSF.HelixGamma,  // right-handed gamma helix (protein)
+    HELX_RH_N: SSF.DoubleHelix | SSF.RightHanded,  // right-handed helix with type not specified (nucleic acid)
+    HELX_RH_OM_P: SSF.Helix | SSF.RightHanded | SSF.HelixOmega,  // right-handed omega helix (protein)
+    HELX_RH_OT_N: SSF.DoubleHelix | SSF.RightHanded | SSF.DoubleHelixOther,  // right-handed helix with type that does not conform to an accepted category (nucleic acid)
+    HELX_RH_OT_P: SSF.Helix | SSF.RightHanded | SSF.HelixOther,  // right-handed helix with type that does not conform to an accepted category (protein)
+    HELX_RH_P: SSF.Helix | SSF.RightHanded,  // right-handed helix with type not specified (protein)
+    HELX_RH_PI_P: SSF.Helix | SSF.RightHanded | SSF.HelixPi,  // right-handed pi helix (protein)
+    HELX_RH_PP_P: SSF.Helix | SSF.RightHanded | SSF.HelixPolyproline,  // right-handed polyproline helix (protein)
+    HELX_RH_Z_N: SSF.DoubleHelix | SSF.RightHanded | SSF.DoubleHelixZ,  // right-handed Z helix (nucleic acid)
+    STRN: SSF.Beta | SSF.BetaStrand,  // beta strand (protein)
+    TURN_OT_P: SSF.Turn | SSF.TurnOther,  // turn with type that does not conform to an accepted category (protein)
+    TURN_P: SSF.Turn,  // turn with type not specified (protein)
+    TURN_TY1P_P: SSF.Turn | SSF.InverseTurn | SSF.Turn1,  // type I prime turn (protein)
+    TURN_TY1_P: SSF.Turn | SSF.ClassicTurn | SSF.Turn1,  // type I turn (protein)
+    TURN_TY2P_P: SSF.Turn | SSF.InverseTurn | SSF.Turn2,  // type II prime turn (protein)
+    TURN_TY2_P: SSF.Turn | SSF.ClassicTurn | SSF.Turn2,  // type II turn (protein)
+    TURN_TY3P_P: SSF.Turn | SSF.InverseTurn | SSF.Turn3,  // type III prime turn (protein)
+    TURN_TY3_P: SSF.Turn | SSF.ClassicTurn | SSF.Turn3,  // type III turn (protein)
+}
+
+export const SecondaryStructurePdb: { [value: string]: number } = {
+    1: SSF.Helix | SSF.RightHanded | SSF.HelixAlpha,  // Right-handed alpha (default)
+    2: SSF.Helix | SSF.RightHanded | SSF.HelixOmega,  // Right-handed omega
+    3: SSF.Helix | SSF.RightHanded | SSF.HelixPi,  // Right-handed pi
+    4: SSF.Helix | SSF.RightHanded | SSF.HelixGamma,  // Right-handed gamma
+    5: SSF.Helix | SSF.RightHanded | SSF.Helix3Ten,  // Right-handed 310
+    6: SSF.Helix | SSF.LeftHanded | SSF.HelixAlpha,  // Left-handed alpha
+    7: SSF.Helix | SSF.LeftHanded | SSF.HelixOmega,  // Left-handed omega
+    8: SSF.Helix | SSF.LeftHanded | SSF.HelixGamma,  // Left-handed gamma
+    9: SSF.Helix | SSF.Helix27,  // 27 ribbon/helix
+    10: SSF.Helix | SSF.HelixPolyproline,  // Polyproline
+}
+
+export const SecondaryStructureStride: { [value: string]: number } = {
+    H: SSF.Helix | SSF.HelixAlpha,  // Alpha helix
+    G: SSF.Helix | SSF.Helix3Ten,  // 3-10 helix
+    I: SSF.Helix | SSF.HelixPi,  // PI-helix
+    E: SSF.Beta | SSF.BetaSheet,  // Extended conformation
+    B: SSF.Beta | SSF.BetaStrand,  // Isolated bridge
+    b: SSF.Beta | SSF.BetaStrand,  // Isolated bridge
+    T: SSF.Turn,  // Turn
+    C: SSF.NA,  // Coil (none of the above)
+}
+
+export const SecondaryStructureDssp: { [value: string]: number } = {
+    H: SSF.Helix | SSF.HelixAlpha,  // alpha-helix
+    B: SSF.Beta | SSF.BetaStrand,  // residue in isolated beta-bridge
+    E: SSF.Beta | SSF.BetaSheet,  // extended strand, participates in beta ladder
+    G: SSF.Helix | SSF.Helix3Ten,  // 3-helix (310 helix)
+    I: SSF.Helix | SSF.HelixPi,  // 5 helix (pi-helix)
+    T: SSF.Turn,  // hydrogen bonded turn
+    S: SSF.Turn,  // bend
+}

src/utils/linear-algebra.ts

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+/**
+ * Copyright (c) 2017 molio contributors, licensed under MIT, See LICENSE file for more info.
+ *
+ * @author David Sehnal <david.sehnal@gmail.com>
+ */
+
+/*
+ * This code has been modified from https://github.com/toji/gl-matrix/, 
+ * copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ */
+
+export type Mat4 = number[]
+export type Vec3 = number[]
+export type Vec4 = number[]
+
+const enum EPSILON { Value = 0.000001 }
+
+export function Mat4() {
+    return Mat4.zero();
+}
+
+/**
+ * Stores a 4x4 matrix in a column major (j * 4 + i indexing) format.
+ */
+export namespace Mat4 {
+    export function zero(): number[] {
+        // force double backing array by 0.1.
+        const ret = [0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
+        ret[0] = 0.0;
+        return ret;
+    }
+
+    export function identity(): number[] {
+        let out = zero();
+        out[0] = 1;
+        out[1] = 0;
+        out[2] = 0;
+        out[3] = 0;
+        out[4] = 0;
+        out[5] = 1;
+        out[6] = 0;
+        out[7] = 0;
+        out[8] = 0;
+        out[9] = 0;
+        out[10] = 1;
+        out[11] = 0;
+        out[12] = 0;
+        out[13] = 0;
+        out[14] = 0;
+        out[15] = 1;
+        return out;
+    }
+
+    export function fromIdentity(mat: number[]): number[] {
+        mat[0] = 1;
+        mat[1] = 0;
+        mat[2] = 0;
+        mat[3] = 0;
+        mat[4] = 0;
+        mat[5] = 1;
+        mat[6] = 0;
+        mat[7] = 0;
+        mat[8] = 0;
+        mat[9] = 0;
+        mat[10] = 1;
+        mat[11] = 0;
+        mat[12] = 0;
+        mat[13] = 0;
+        mat[14] = 0;
+        mat[15] = 1;
+        return mat;
+    }
+
+    export function ofRows(rows: number[][]): number[] {
+        let out = zero(), i: number, j: number, r: number[];
+        for (i = 0; i < 4; i++) {
+            r = rows[i];
+            for (j = 0; j < 4; j++) {
+                out[4 * j + i] = r[j];
+            }
+        }
+        return out;
+    }
+
+    export function areEqual(a: number[], b: number[], eps: number) {
+        for (let i = 0; i < 16; i++) {
+            if (Math.abs(a[i] - b[i]) > eps) {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    export function setValue(a: number[], i: number, j: number, value: number) {
+        a[4 * j + i] = value;
+    }
+
+    export function copy(out: number[], a: number[]) {
+        out[0] = a[0];
+        out[1] = a[1];
+        out[2] = a[2];
+        out[3] = a[3];
+        out[4] = a[4];
+        out[5] = a[5];
+        out[6] = a[6];
+        out[7] = a[7];
+        out[8] = a[8];
+        out[9] = a[9];
+        out[10] = a[10];
+        out[11] = a[11];
+        out[12] = a[12];
+        out[13] = a[13];
+        out[14] = a[14];
+        out[15] = a[15];
+        return out;
+    }
+
+    export function clone(a: number[]) {
+        return Mat4.copy(Mat4.zero(), a);
+    }
+
+    export function invert(out: number[], a: number[]) {
+        let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
+            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
+            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
+            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
+
+            b00 = a00 * a11 - a01 * a10,
+            b01 = a00 * a12 - a02 * a10,
+            b02 = a00 * a13 - a03 * a10,
+            b03 = a01 * a12 - a02 * a11,
+            b04 = a01 * a13 - a03 * a11,
+            b05 = a02 * a13 - a03 * a12,
+            b06 = a20 * a31 - a21 * a30,
+            b07 = a20 * a32 - a22 * a30,
+            b08 = a20 * a33 - a23 * a30,
+            b09 = a21 * a32 - a22 * a31,
+            b10 = a21 * a33 - a23 * a31,
+            b11 = a22 * a33 - a23 * a32,
+
+            // Calculate the determinant
+            det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
+
+        if (!det) {
+            return null;
+        }
+        det = 1.0 / det;
+
+        out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
+        out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
+        out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
+        out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
+        out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
+        out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
+        out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
+        out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
+        out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
+        out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
+        out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
+        out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
+        out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
+        out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
+        out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
+        out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
+
+        return out;
+    }
+
+    export function mul(out: number[], a: number[], b: number[]) {
+        let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
+            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
+            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
+            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
+
+        // Cache only the current line of the second matrix
+        let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
+        out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
+        out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
+        out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
+        out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
+
+        b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
+        out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
+        out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
+        out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
+        out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
+
+        b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
+        out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
+        out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
+        out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
+        out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
+
+        b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
+        out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
+        out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
+        out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
+        out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
+        return out;
+    }
+
+    export function mul3(out: number[], a: number[], b: number[], c: number[]) {
+        return mul(out, mul(out, a, b), c);
+    }
+
+    export function translate(out: number[], a: number[], v: number[]) {
+        let x = v[0], y = v[1], z = v[2],
+            a00: number, a01: number, a02: number, a03: number,
+            a10: number, a11: number, a12: number, a13: number,
+            a20: number, a21: number, a22: number, a23: number;
+
+        if (a === out) {
+            out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
+            out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
+            out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
+            out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
+        } else {
+            a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
+            a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
+            a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
+
+            out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03;
+            out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13;
+            out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23;
+
+            out[12] = a00 * x + a10 * y + a20 * z + a[12];
+            out[13] = a01 * x + a11 * y + a21 * z + a[13];
+            out[14] = a02 * x + a12 * y + a22 * z + a[14];
+            out[15] = a03 * x + a13 * y + a23 * z + a[15];
+        }
+
+        return out;
+    }
+
+    export function fromTranslation(out: number[], v: number[]) {
+        out[0] = 1;
+        out[1] = 0;
+        out[2] = 0;
+        out[3] = 0;
+        out[4] = 0;
+        out[5] = 1;
+        out[6] = 0;
+        out[7] = 0;
+        out[8] = 0;
+        out[9] = 0;
+        out[10] = 1;
+        out[11] = 0;
+        out[12] = v[0];
+        out[13] = v[1];
+        out[14] = v[2];
+        out[15] = 1;
+        return out;
+    }
+
+    export function rotate(out: number[], a: number[], rad: number, axis: number[]) {
+        let x = axis[0], y = axis[1], z = axis[2],
+            len = Math.sqrt(x * x + y * y + z * z),
+            s, c, t,
+            a00, a01, a02, a03,
+            a10, a11, a12, a13,
+            a20, a21, a22, a23,
+            b00, b01, b02,
+            b10, b11, b12,
+            b20, b21, b22;
+
+        if (Math.abs(len) < EPSILON.Value) { return null; }
+
+        len = 1 / len;
+        x *= len;
+        y *= len;
+        z *= len;
+
+        s = Math.sin(rad);
+        c = Math.cos(rad);
+        t = 1 - c;
+
+        a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
+        a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
+        a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
+
+        // Construct the elements of the rotation matrix
+        b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s;
+        b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s;
+        b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c;
+
+        // Perform rotation-specific matrix multiplication
+        out[0] = a00 * b00 + a10 * b01 + a20 * b02;
+        out[1] = a01 * b00 + a11 * b01 + a21 * b02;
+        out[2] = a02 * b00 + a12 * b01 + a22 * b02;
+        out[3] = a03 * b00 + a13 * b01 + a23 * b02;
+        out[4] = a00 * b10 + a10 * b11 + a20 * b12;
+        out[5] = a01 * b10 + a11 * b11 + a21 * b12;
+        out[6] = a02 * b10 + a12 * b11 + a22 * b12;
+        out[7] = a03 * b10 + a13 * b11 + a23 * b12;
+        out[8] = a00 * b20 + a10 * b21 + a20 * b22;
+        out[9] = a01 * b20 + a11 * b21 + a21 * b22;
+        out[10] = a02 * b20 + a12 * b21 + a22 * b22;
+        out[11] = a03 * b20 + a13 * b21 + a23 * b22;
+
+        if (a !== out) { // If the source and destination differ, copy the unchanged last row
+            out[12] = a[12];
+            out[13] = a[13];
+            out[14] = a[14];
+            out[15] = a[15];
+        }
+        return out;
+    }
+
+    export function fromRotation(out: number[], rad: number, axis: number[]) {
+        let x = axis[0], y = axis[1], z = axis[2],
+            len = Math.sqrt(x * x + y * y + z * z),
+            s, c, t;
+
+        if (Math.abs(len) < EPSILON.Value) { return fromIdentity(out); }
+
+        len = 1 / len;
+        x *= len;
+        y *= len;
+        z *= len;
+
+        s = Math.sin(rad);
+        c = Math.cos(rad);
+        t = 1 - c;
+
+        // Perform rotation-specific matrix multiplication
+        out[0] = x * x * t + c;
+        out[1] = y * x * t + z * s;
+        out[2] = z * x * t - y * s;
+        out[3] = 0;
+        out[4] = x * y * t - z * s;
+        out[5] = y * y * t + c;
+        out[6] = z * y * t + x * s;
+        out[7] = 0;
+        out[8] = x * z * t + y * s;
+        out[9] = y * z * t - x * s;
+        out[10] = z * z * t + c;
+        out[11] = 0;
+        out[12] = 0;
+        out[13] = 0;
+        out[14] = 0;
+        out[15] = 1;
+        return out;
+    }
+
+    export function scale(out: number[], a: number[], v: number[]) {
+        let x = v[0], y = v[1], z = v[2];
+
+        out[0] = a[0] * x;
+        out[1] = a[1] * x;
+        out[2] = a[2] * x;
+        out[3] = a[3] * x;
+        out[4] = a[4] * y;
+        out[5] = a[5] * y;
+        out[6] = a[6] * y;
+        out[7] = a[7] * y;
+        out[8] = a[8] * z;
+        out[9] = a[9] * z;
+        out[10] = a[10] * z;
+        out[11] = a[11] * z;
+        out[12] = a[12];
+        out[13] = a[13];
+        out[14] = a[14];
+        out[15] = a[15];
+        return out;
+    }
+
+    export function fromScaling(out: number[], v: number[]) {
+        out[0] = v[0];
+        out[1] = 0;
+        out[2] = 0;
+        out[3] = 0;
+        out[4] = 0;
+        out[5] = v[1];
+        out[6] = 0;
+        out[7] = 0;
+        out[8] = 0;
+        out[9] = 0;
+        out[10] = v[2];
+        out[11] = 0;
+        out[12] = 0;
+        out[13] = 0;
+        out[14] = 0;
+        out[15] = 1;
+        return out;
+    }
+
+    export function makeTable(m: number[]) {
+        let ret = '';
+        for (let i = 0; i < 4; i++) {
+            for (let j = 0; j < 4; j++) {
+                ret += m[4 * j + i].toString();
+                if (j < 3) ret += ' ';
+            }
+            if (i < 3) ret += '\n';
+        }
+        return ret;
+    }
+
+    export function determinant(a: number[]) {
+        let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
+            a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
+            a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
+            a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
+
+            b00 = a00 * a11 - a01 * a10,
+            b01 = a00 * a12 - a02 * a10,
+            b02 = a00 * a13 - a03 * a10,
+            b03 = a01 * a12 - a02 * a11,
+            b04 = a01 * a13 - a03 * a11,
+            b05 = a02 * a13 - a03 * a12,
+            b06 = a20 * a31 - a21 * a30,
+            b07 = a20 * a32 - a22 * a30,
+            b08 = a20 * a33 - a23 * a30,
+            b09 = a21 * a32 - a22 * a31,
+            b10 = a21 * a33 - a23 * a31,
+            b11 = a22 * a33 - a23 * a32;
+
+        // Calculate the determinant
+        return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
+    }
+}
+
+export function Vec3(x?: number, y?: number, z?: number) {
+    return Vec3.fromValues(x || 0, y || 0, z || 0);
+}
+
+export namespace Vec3 {
+    export function zero() {
+        let out = [0.1, 0.0, 0.0];
+        out[0] = 0;
+        return out;
+    }
+
+    export function clone(a: number[]) {
+        let out = zero();
+        out[0] = a[0];
+        out[1] = a[1];
+        out[2] = a[2];
+        return out;
+    }
+
+    export function fromObj(v: { x: number, y: number, z: number }) {
+        return fromValues(v.x, v.y, v.z);
+    }
+
+    export function toObj(v: number[]) {
+        return { x: v[0], y: v[1], z: v[2] };
+    }
+
+    export function fromValues(x: number, y: number, z: number) {
+        let out = zero();
+        out[0] = x;
+        out[1] = y;
+        out[2] = z;
+        return out;
+    }
+
+    export function set(out: number[], x: number, y: number, z: number) {
+        out[0] = x;
+        out[1] = y;
+        out[2] = z;
+        return out;
+    }
+
+    export function copy(out: number[], a: number[]) {
+        out[0] = a[0];
+        out[1] = a[1];
+        out[2] = a[2];
+        return out;
+    }
+
+    export function add(out: number[], a: number[], b: number[]) {
+        out[0] = a[0] + b[0];
+        out[1] = a[1] + b[1];
+        out[2] = a[2] + b[2];
+        return out;
+    }
+
+    export function sub(out: number[], a: number[], b: number[]) {
+        out[0] = a[0] - b[0];
+        out[1] = a[1] - b[1];
+        out[2] = a[2] - b[2];
+        return out;
+    }
+
+    export function scale(out: number[], a: number[], b: number) {
+        out[0] = a[0] * b;
+        out[1] = a[1] * b;
+        out[2] = a[2] * b;
+        return out;
+    }
+
+    export function scaleAndAdd(out: number[], a: number[], b: number[], scale: number) {
+        out[0] = a[0] + (b[0] * scale);
+        out[1] = a[1] + (b[1] * scale);
+        out[2] = a[2] + (b[2] * scale);
+        return out;
+    }
+
+    export function distance(a: number[], b: number[]) {
+        let x = b[0] - a[0],
+            y = b[1] - a[1],
+            z = b[2] - a[2];
+        return Math.sqrt(x * x + y * y + z * z);
+    }
+
+    export function squaredDistance(a: number[], b: number[]) {
+        let x = b[0] - a[0],
+            y = b[1] - a[1],
+            z = b[2] - a[2];
+        return x * x + y * y + z * z;
+    }
+
+    export function magnitude(a: number[]) {
+        let x = a[0],
+            y = a[1],
+            z = a[2];
+        return Math.sqrt(x * x + y * y + z * z);
+    }
+
+    export function squaredMagnitude(a: number[]) {
+        let x = a[0],
+            y = a[1],
+            z = a[2];
+        return x * x + y * y + z * z;
+    }
+
+    export function normalize(out: number[], a: number[]) {
+        let x = a[0],
+            y = a[1],
+            z = a[2];
+        let len = x * x + y * y + z * z;
+        if (len > 0) {
+            len = 1 / Math.sqrt(len);
+            out[0] = a[0] * len;
+            out[1] = a[1] * len;
+            out[2] = a[2] * len;
+        }
+        return out;
+    }
+
+    export function dot(a: number[], b: number[]) {
+        return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
+    }
+
+    export function cross(out: number[], a: number[], b: number[]) {
+        let ax = a[0], ay = a[1], az = a[2],
+            bx = b[0], by = b[1], bz = b[2];
+
+        out[0] = ay * bz - az * by;
+        out[1] = az * bx - ax * bz;
+        out[2] = ax * by - ay * bx;
+        return out;
+    }
+
+    export function lerp(out: number[], a: number[], b: number[], t: number) {
+        let ax = a[0],
+            ay = a[1],
+            az = a[2];
+        out[0] = ax + t * (b[0] - ax);
+        out[1] = ay + t * (b[1] - ay);
+        out[2] = az + t * (b[2] - az);
+        return out;
+    }
+
+    export function transformMat4(out: number[], a: number[], m: number[]) {
+        let x = a[0], y = a[1], z = a[2],
+            w = m[3] * x + m[7] * y + m[11] * z + m[15];
+        w = w || 1.0;
+        out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;
+        out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;
+        out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;
+        return out;
+    }
+
+    const angleTempA = zero(), angleTempB = zero();
+    export function angle(a: number[], b: number[]) {
+        copy(angleTempA, a);
+        copy(angleTempB, b);
+
+        normalize(angleTempA, angleTempA);
+        normalize(angleTempB, angleTempB);
+
+        let cosine = dot(angleTempA, angleTempB);
+
+        if (cosine > 1.0) {
+            return 0;
+        }
+        else if (cosine < -1.0) {
+            return Math.PI;
+        } else {
+            return Math.acos(cosine);
+        }
+    }
+
+    const rotTemp = zero();
+    export function makeRotation(mat: Mat4, a: Vec3, b: Vec3): Mat4 {
+        const by = angle(a, b);
+        if (Math.abs(by) < 0.0001) return Mat4.fromIdentity(mat);
+        const axis = cross(rotTemp, a, b);
+        return Mat4.fromRotation(mat, by, axis);
+    }
+}
+
+export function Vec4(x?: number, y?: number, z?: number, w?: number) {
+    return Vec4.fromValues(x || 0, y || 0, z || 0, w || 0);
+}
+
+export namespace Vec4 {
+    export function zero(): number[] {
+        // force double backing array by 0.1.
+        const ret = [0.1, 0, 0, 0];
+        ret[0] = 0.0;
+        return ret;
+    }
+
+    export function clone(a: number[]) {
+        let out = zero();
+        out[0] = a[0];
+        out[1] = a[1];
+        out[2] = a[2];
+        out[3] = a[3];
+        return out;
+    }
+
+    export function fromValues(x: number, y: number, z: number, w: number) {
+        let out = zero();
+        out[0] = x;
+        out[1] = y;
+        out[2] = z;
+        out[3] = w;
+        return out;
+    }
+
+    export function set(out: number[], x: number, y: number, z: number, w: number) {
+        out[0] = x;
+        out[1] = y;
+        out[2] = z;
+        out[3] = w;
+        return out;
+    }
+
+    export function distance(a: number[], b: number[]) {
+        let x = b[0] - a[0],
+            y = b[1] - a[1],
+            z = b[2] - a[2],
+            w = b[3] - a[3];
+        return Math.sqrt(x * x + y * y + z * z + w * w);
+    }
+
+    export function squaredDistance(a: number[], b: number[]) {
+        let x = b[0] - a[0],
+            y = b[1] - a[1],
+            z = b[2] - a[2],
+            w = b[3] - a[3];
+        return x * x + y * y + z * z + w * w;
+    }
+
+    export function norm(a: number[]) {
+        let x = a[0],
+            y = a[1],
+            z = a[2],
+            w = a[3];
+        return Math.sqrt(x * x + y * y + z * z + w * w);
+    }
+
+    export function squaredNorm(a: number[]) {
+        let x = a[0],
+            y = a[1],
+            z = a[2],
+            w = a[3];
+        return x * x + y * y + z * z + w * w;
+    }
+
+    export function transform(out: number[], a: number[], m: number[]) {
+        let x = a[0], y = a[1], z = a[2], w = a[3];
+        out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w;
+        out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w;
+        out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;
+        out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
+        return out;
+    }
+}