--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/light9/web/lib/sylvester.d.ts	Wed May 17 18:53:10 2023 -0700
@@ -0,0 +1,825 @@
+// Type definitions for sylvester 0.1.3
+// Project: https://github.com/jcoglan/sylvester
+// Definitions by: Stephane Alie <https://github.com/StephaneAlie>
+// Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
+
+// === Sylvester ===
+// Vector and Matrix mathematics modules for JavaScript
+// Copyright (c) 2007 James Coglan
+
+declare module Sylvester {
+    interface VectorStatic {
+        /**
+         * Constructor function.
+         */
+        create(elements: Vector|Array<number>): Vector;
+
+        i: Vector;
+        j: Vector;
+        k: Vector;
+
+        /**
+         * Random vector of size n.
+         *
+         * @param {number} n The vector size.
+         */
+        Random(n: number): Vector;
+
+        /**
+         * Vector filled with zeros.
+         *
+         * @param {number} n The vector size.
+         */
+        Zero(n: number): Vector;
+    }
+    interface MatrixStatic {
+        /**
+         * Constructor function.
+         *
+         * @param {Array<number>|Array<Array<number>>|Vector|Matrix} elements The elements.
+         */
+        create(elements: Array<number>|Array<Array<number>>|Vector | Matrix): Matrix;
+
+        /**
+         * Identity matrix of size n.
+         *
+         * @param {number} n The size.
+         */
+        I(n: number): Matrix;
+
+        /**
+         * Diagonal matrix - all off-diagonal elements are zero
+         *
+         * @param {any} elements The elements.
+         */
+        Diagonal(elements: Array<number>|Array<Array<number>>|Vector | Matrix): Matrix;
+
+        /**
+         * Rotation matrix about some axis. If no axis is supplied, assume we're after a 2D transform.
+         *
+         * @param {number} theta The angle in radians.
+         * @param {Vector} a [Optional] The axis.
+         */
+        Rotation(theta: number, a?: Vector): Matrix;
+
+        RotationX(t: number): Matrix;
+        RotationY(t: number): Matrix;
+        RotationZ(t: number): Matrix;
+
+        /**
+         * Random matrix of n rows, m columns.
+         *
+         * @param {number} n The number of rows.
+         * @param {number} m The number of columns.
+         */
+        Random(n: number, m: number): Matrix;
+
+        /**
+         * Matrix filled with zeros.
+         *
+         * @param {number} n The number of rows.
+         * @param {number} m The number of columns.
+         */
+        Zero(n: number, m: number): Matrix;
+    }
+
+    interface LineStatic {
+        /**
+         * Constructor function.
+         *
+         * @param Array<number>|Vector anchor The anchor vector.
+         * @param Array<number>|Vector direction The direction vector.
+         */
+        create(anchor: Array<number>|Vector, direction: Array<number>|Vector): Line;
+
+        X: Line;
+        Y: Line;
+        Z: Line;
+    }
+    interface PlaneStatic {
+        /**
+         * Constructor function.
+         */
+        create(anchor: Array<number>|Vector, normal: Array<number>|Vector): Plane;
+
+        /**
+         * Constructor function.
+         */
+        create(anchor: Array<number>|Vector, v1: Array<number>|Vector, v2: Array<number>|Vector): Plane;
+
+        XY: Plane;
+        YZ: Plane;
+        ZX: Plane;
+        YX: Plane;
+    }
+}
+
+interface Vector {
+    /**
+     * Gets an array containing the vector's elements.
+     */
+    elements: Array<number>;
+
+    /**
+     * Returns element i of the vector.
+     */
+    e(i: number): number;
+
+    /**
+     * Returns the number of elements the vector has.
+     */
+    dimensions(): number;
+
+    /**
+     * Returns the modulus ('length') of the vector.
+     */
+    modulus(): number;
+
+    /**
+     * Returns true if the vector is equal to the argument.
+     *
+     * @param {Vector|Array<number>} vector The vector to compare equality.
+     */
+    eql(vector: Vector|Array<number>): boolean;
+
+    /**
+     * Returns a copy of the vector.
+     */
+    dup(): Vector;
+
+    /**
+     * Maps the vector to another vector according to the given function.
+     *
+     * @param {Function} fn The function to apply to each element (x, i) => {}.
+     */
+    map(fn: (x: number, i: number) => any): Vector;
+
+    /**
+     * Calls the iterator for each element of the vector in turn.
+     *
+     * @param {Function} fn The function to apply to each element (x, i) => {}.
+     */
+    each(fn: (x: number, i: number) => any): void;
+
+    /**
+     * Returns a new vector created by normalizing the receiver.
+     */
+    toUnitVector(): Vector;
+
+    /**
+     * Returns the angle between the vector and the argument (also a vector).
+     *
+     * @param {Vector} vector The other vector to calculate the angle.
+     */
+    angleFrom(vector: Vector): number;
+
+    /**
+     * Returns true if the vector is parallel to the argument.
+     *
+     * @param {Vector} vector The other vector.
+     */
+    isParallelTo(vector: Vector): boolean;
+
+    /**
+     * Returns true if the vector is antiparallel to the argument.
+     *
+     * @param {Vector} vector The other vector.
+     */
+    isAntiparallelTo(vector: Vector): boolean;
+
+    /**
+     * Returns true iff the vector is perpendicular to the argument.
+     *
+     * @param {Vector} vector The other vector.
+     */
+    isPerpendicularTo(vector: Vector): boolean;
+
+    /**
+     * Returns the result of adding the argument to the vector.
+     *
+     * @param {Vector|Array<number>} vector The vector.
+     */
+    add(vector: Vector|Array<number>): Vector;
+
+    /**
+     * Returns the result of subtracting the argument from the vector.
+     *
+     * @param {Vector|Array<number>} vector The vector.
+     */
+    subtract(vector: Vector|Array<number>): Vector;
+
+    /**
+     * Returns the result of multiplying the elements of the vector by the argument.
+     *
+     * @param {number} k The value by which to multiply the vector.
+     */
+    multiply(k: number): Vector;
+
+    /**
+     * Returns the result of multiplying the elements of the vector by the argument (Alias for multiply(k)).
+     *
+     * @param {number} k The value by which to multiply the vector.
+     */
+    x(k: number): Vector;
+
+    /**
+     * Returns the scalar product of the vector with the argument. Both vectors must have equal dimensionality.
+     *
+     * @param: {Vector|Array<number>} vector The other vector.
+     */
+    dot(vector: Vector|Array<number>): number;
+
+    /**
+     * Returns the vector product of the vector with the argument. Both vectors must have dimensionality 3.
+     *
+     * @param {Vector|Array<number>} vector The other vector.
+     */
+    cross(vector: Vector|Array<number>): Vector;
+
+    /**
+     * Returns the (absolute) largest element of the vector.
+     */
+    max(): number;
+
+    /**
+     * Returns the index of the first match found.
+     *
+     * @param {number} x The value.
+     */
+    indexOf(x: number): number;
+
+    /**
+     * Returns a diagonal matrix with the vector's elements as its diagonal elements.
+     */
+    toDiagonalMatrix(): Matrix;
+
+    /**
+     * Returns the result of rounding the elements of the vector.
+     */
+    round(): Vector;
+
+    /**
+     * Returns a copy of the vector with elements set to the given value if they differ from
+     * it by less than Sylvester.precision.
+     *
+     * @param {number} x The value to snap to.
+     */
+    snapTo(x: number): Vector;
+
+    /**
+     * Returns the vector's distance from the argument, when considered as a point in space.
+     *
+     * @param {Vector|Line|Plane} obj The object to calculate the distance.
+     */
+    distanceFrom(obj: Vector|Line|Plane): number;
+
+    /**
+     * Returns true if the vector is point on the given line.
+     *
+     * @param {Line} line The line.
+     */
+    liesOn(line: Line): boolean;
+
+    /**
+     * Return true if the vector is a point in the given plane.
+     *
+     * @param {Plane} plane The plane.
+     */
+    liesIn(plane: Plane): boolean;
+
+    /**
+     * Rotates the vector about the given object. The object should be a point if the vector is 2D,
+     * and a line if it is 3D. Be careful with line directions!
+     *
+     * @param {number|Matrix} t The angle in radians or in rotation matrix.
+     * @param {Vector|Line} obj The rotation axis.
+     */
+    rotate(t: number|Matrix, obj: Vector|Line): Vector;
+
+    /**
+     * Returns the result of reflecting the point in the given point, line or plane.
+     *
+     * @param {Vector|Line|Plane} obj The object.
+     */
+    reflectionIn(obj: Vector|Line|Plane): Vector;
+
+    /**
+     * Utility to make sure vectors are 3D. If they are 2D, a zero z-component is added.
+     */
+    to3D(): Vector;
+
+    /**
+     * Returns a string representation of the vector.
+     */
+    inspect(): string;
+
+    /**
+     * Set vector's elements from an array.
+     *
+     * @param {Vector|Array<number>} els The elements.
+     */
+    setElements(els: Vector|Array<number>): Vector;
+}
+
+interface Matrix {
+    /**
+     * Gets a nested array containing the matrix's elements.
+     */
+    elements: Array<Array<number>>;
+    /**
+     * Returns element (i,j) of the matrix.
+     *
+     * @param {number} i The row index.
+     * @param {number} j The column index.
+     */
+    e(i: number, j: number): any;
+
+    /**
+     * Returns row k of the matrix as a vector.
+     *
+     * @param {number} i The row index.
+     */
+    row(i: number): Vector;
+
+    /**
+     * Returns column k of the matrix as a vector.
+     *
+     * @param {number} j The column index.
+     */
+    col(j: number): Vector;
+
+    /**
+     * Returns the number of rows/columns the matrix has.
+     *
+     * @return {any} An object { rows: , cols: }.
+     */
+    dimensions(): any;
+
+    /**
+     * Returns the number of rows in the matrix.
+     */
+    rows(): number;
+
+    /**
+     * Returns the number of columns in the matrix.
+     */
+    cols(): number;
+
+    /**
+     * Returns true if the matrix is equal to the argument. You can supply a vector as the argument,
+     * in which case the receiver must be a one-column matrix equal to the vector.
+     *
+     * @param {Vector|Matrix} matrix The argument to compare.
+     */
+    eql(matrix: Vector|Matrix): boolean;
+
+    /**
+     * Returns a copy of the matrix.
+     */
+    dup(): Matrix;
+
+    /**
+     * Maps the matrix to another matrix (of the same dimensions) according to the given function.
+     *
+     * @param {Function} fn The function.
+     */
+    map(fn: (x: number, i: number, j: number) => any): Matrix;
+
+    /**
+     * Returns true iff the argument has the same dimensions as the matrix.
+     *
+     * @param {Matrix} matrix The other matrix.
+     */
+    isSameSizeAs(matrix: Matrix): boolean;
+
+    /**
+     * Returns the result of adding the argument to the matrix.
+     *
+     * @param {Matrix} matrix The matrix to add.
+     */
+    add(matrix: Matrix): Matrix;
+
+    /**
+     * Returns the result of subtracting the argument from the matrix.
+     *
+     * @param {Matrix} matrix The matrix to substract.
+     */
+    subtract(matrix: Matrix): Matrix;
+
+    /**
+     * Returns true iff the matrix can multiply the argument from the left.
+     *
+     * @param {Matrix} matrix The matrix.
+     */
+    canMultiplyFromLeft(matrix: Matrix): boolean;
+
+    /**
+     * Returns the result of multiplying the matrix from the right by the argument. If the argument is a scalar
+     * then just multiply all the elements. If the argument is a vector, a vector is returned, which saves you
+     * having to remember calling col(1) on the result.
+     *
+     * @param {number|Matrix} matrix The multiplier.
+     */
+    multiply(matrix: number|Matrix): Matrix;
+
+    /**
+     * Returns the result of multiplying the matrix from the right by the argument. If the argument is a scalar
+     * then just multiply all the elements. If the argument is a vector, a vector is returned, which saves you
+     * having to remember calling col(1) on the result.
+     *
+     * @param {Vector} vector The multiplier.
+     */
+    multiply(vector: Vector): Vector;
+
+    x(matrix: number|Matrix): Matrix;
+
+    x(vector: Vector): Vector;
+
+    /**
+     * Returns a submatrix taken from the matrix. Argument order is: start row, start col, nrows, ncols.
+     * Element selection wraps if the required index is outside the matrix's bounds, so you could use
+     * this to perform row/column cycling or copy-augmenting.
+     *
+     * @param {number} a Starting row index.
+     * @param {number} b Starting column index.
+     * @param {number} c Number of rows.
+     * @param {number} d Number of columns.
+     */
+    minor(a: number, b: number, c: number, d: number): Matrix;
+
+    /**
+     * Returns the transpose of the matrix.
+     */
+    transpose(): Matrix;
+
+    /**
+     * Returns true if the matrix is square.
+     */
+    isSquare(): boolean;
+
+    /**
+     * Returns the (absolute) largest element of the matrix.
+     */
+    max(): number;
+
+    /**
+     * Returns the indeces of the first match found by reading row-by-row from left to right.
+     *
+     * @param {number} x The value.
+     *
+     * @return {any} The element indeces i.e: { row:1, col:1 }
+     */
+    indexOf(x: number): any;
+
+    /**
+     * If the matrix is square, returns the diagonal elements as a vector; otherwise, returns null.
+     */
+    diagonal(): Vector;
+
+    /**
+     * Make the matrix upper (right) triangular by Gaussian elimination. This method only adds multiples
+     * of rows to other rows. No rows are scaled up or switched, and the determinant is preserved.
+     */
+    toRightTriangular(): Matrix;
+    toUpperTriangular(): Matrix;
+
+    /**
+     * Returns the determinant for square matrices.
+     */
+    determinant(): number;
+    det(): number;
+
+    /**
+     * Returns true if the matrix is singular.
+     */
+    isSingular(): boolean;
+
+    /**
+     * Returns the trace for square matrices.
+     */
+    trace(): number;
+    tr(): number;
+
+    /**
+     * Returns the rank of the matrix.
+     */
+    rank(): number;
+    rk(): number;
+
+    /**
+     * Returns the result of attaching the given argument to the right-hand side of the matrix.
+     *
+     * @param {Matrix|Vector} matrix The matrix or vector.
+     */
+    augment(matrix: Matrix|Vector): Matrix;
+
+    /**
+     * Returns the inverse (if one exists) using Gauss-Jordan.
+     */
+    inverse(): Matrix;
+    inv(): Matrix;
+
+    /**
+     * Returns the result of rounding all the elements.
+     */
+    round(): Matrix;
+
+    /**
+     * Returns a copy of the matrix with elements set to the given value if they differ from it
+     * by less than Sylvester.precision.
+     *
+     * @param {number} x The value.
+     */
+    snapTo(x: number): Matrix;
+
+    /**
+     * Returns a string representation of the matrix.
+     */
+    inspect(): string;
+
+    /**
+     * Set the matrix's elements from an array. If the argument passed is a vector, the resulting matrix
+     * will be a single column.
+     *
+     * @param {Array<number>|Array<Array<number>>|Vector|Matrix} matrix The elements.
+     */
+    setElements(matrix: Array<number>|Array<Array<number>>|Vector|Matrix): Matrix;
+}
+
+interface Line {
+    /**
+     * Gets the 3D vector corresponding to a point on the line.
+     */
+    anchor: Vector;
+
+    /**
+     * Gets a normalized 3D vector representing the line's direction.
+     */
+    direction: Vector;
+
+    /**
+     * Returns true if the argument occupies the same space as the line.
+     *
+     * @param {Line} line The other line.
+     */
+    eql(line: Line): boolean;
+
+    /**
+     * Returns a copy of the line.
+     */
+    dup(): Line;
+
+    /**
+     * Returns the result of translating the line by the given vector/array.
+     *
+     * @param {Vector|Array<number>} vector The translation vector.
+     */
+    translate(vector: Vector|Array<number>): Line;
+
+    /**
+     * Returns true if the line is parallel to the argument. Here, 'parallel to' means that the argument's
+     * direction is either parallel or antiparallel to the line's own direction. A line is parallel to a
+     * plane if the two do not have a unique intersection.
+     *
+     * @param {Line|Plane} obj The object.
+     */
+    isParallelTo(obj: Line|Plane): boolean;
+
+    /**
+     * Returns the line's perpendicular distance from the argument, which can be a point, a line or a plane.
+     *
+     * @param {Vector|Line|Plane} obj The object.
+     */
+    distanceFrom(obj: Vector|Line|Plane): number;
+
+    /**
+     * Returns true if the argument is a point on the line.
+     *
+     * @param {Vector} point The point.
+     */
+    contains(point: Vector): boolean;
+
+    /**
+     * Returns true if the line lies in the given plane.
+     *
+     * @param {Plane} plane The plane.
+     */
+    liesIn(plane: Plane): boolean;
+
+    /**
+     * Returns true if the line has a unique point of intersection with the argument.
+     *
+     * @param {Line|Plane} obj The object.
+     */
+    intersects(obj: Line|Plane): boolean;
+
+    /**
+     * Returns the unique intersection point with the argument, if one exists.
+     *
+     * @param {Line|Plane} obj The object.
+     */
+    intersectionWith(obj: Line|Plane): Vector;
+
+    /**
+     * Returns the point on the line that is closest to the given point or line.
+     *
+     * @param {Vector|Line} obj The object.
+     */
+    pointClosestTo(obj: Vector|Line): Vector;
+
+    /**
+     * Returns a copy of the line rotated by t radians about the given line. Works by finding the argument's
+     * closest point to this line's anchor point (call this C) and rotating the anchor about C. Also rotates
+     * the line's direction about the argument's. Be careful with this - the rotation axis' direction
+     * affects the outcome!
+     *
+     * @param {number} t The angle in radians.
+     * @param {Vector|Line} axis The axis.
+     */
+    rotate(t: number, axis: Vector|Line): Line;
+
+    /**
+     * Returns the line's reflection in the given point or line.
+     *
+     * @param {Vector|Line|Plane} obj The object.
+     */
+    reflectionIn(obj: Vector|Line|Plane): Line;
+
+    /**
+     * Set the line's anchor point and direction.
+     *
+     * @param {Array<number>|Vector} anchor The anchor vector.
+     * @param {Array<number>|Vector} direction The direction vector.
+     */
+    setVectors(anchor: Array<number>|Vector, direction: Array<number>|Vector): Line;
+}
+
+interface Plane {
+    /**
+     * Gets the 3D vector corresponding to a point in the plane.
+     */
+    anchor: Vector;
+
+    /**
+     * Gets a normalized 3D vector perpendicular to the plane.
+     */
+    normal: Vector;
+
+    /**
+     * Returns true if the plane occupies the same space as the argument.
+     *
+     * @param {Plane} plane The other plane.
+     */
+    eql(plane: Plane): boolean;
+
+    /**
+     * Returns a copy of the plane.
+     */
+    dup(): Plane;
+
+    /**
+     * Returns the result of translating the plane by the given vector.
+     *
+     * @param {Array<number>|Vector} vector The translation vector.
+     */
+    translate(vector: Array<number>|Vector): Plane;
+
+    /**
+     * Returns true if the plane is parallel to the argument. Will return true if the planes are equal,
+     * or if you give a line and it lies in the plane.
+     *
+     * @param {Line|Plane} obj The object.
+     */
+    isParallelTo(obj: Line|Plane): boolean;
+
+    /**
+     * Returns true if the receiver is perpendicular to the argument.
+     *
+     * @param {Plane} plane The other plane.
+     */
+    isPerpendicularTo(plane: Plane): boolean;
+
+    /**
+     * Returns the plane's distance from the given object (point, line or plane).
+     *
+     * @parm {Vector|Line|Plane} obj The object.
+     */
+    distanceFrom(obj: Vector|Line|Plane): number;
+
+    /**
+     * Returns true if the plane contains the given point or line.
+     *
+     * @param {Vector|Line} obj The object.
+     */
+    contains(obj: Vector|Line): boolean;
+
+    /**
+     * Returns true if the plane has a unique point/line of intersection with the argument.
+     *
+     * @param {Line|Plane} obj The object.
+     */
+    intersects(obj: Line|Plane): boolean;
+
+    /**
+     * Returns the unique intersection with the argument, if one exists.
+     *
+     * @param {Line} line The line.
+     */
+    intersectionWith(line: Line): Vector;
+
+    /**
+     * Returns the unique intersection with the argument, if one exists.
+     *
+     * @param {Plane} plane The plane.
+     */
+    intersectionWith(plane: Plane): Line;
+
+    /**
+     * Returns the point in the plane closest to the given point.
+     *
+     * @param {Vector} point The point.
+     */
+    pointClosestTo(point: Vector): Vector;
+
+    /**
+     * Returns a copy of the plane, rotated by t radians about the given line. See notes on Line#rotate.
+     *
+     * @param {number} t The angle in radians.
+     * @param {Line} axis The line axis.
+     */
+    rotate(t: number, axis: Line): Plane;
+
+    /**
+     * Returns the reflection of the plane in the given point, line or plane.
+     *
+     * @param {Vector|Line|Plane} obj The object.
+     */
+    reflectionIn(obj: Vector|Line|Plane): Plane;
+
+    /**
+     * Sets the anchor point and normal to the plane. Normal vector is normalised before storage.
+     *
+     * @param {Array<number>|Vector} anchor The anchor vector.
+     * @param {Array<number>|Vector} normal The normal vector.
+     */
+    setVectors(anchor: Array<number>|Vector, normal: Array<number>|Vector): Plane;
+
+    /**
+     * Sets the anchor point and normal to the plane. The normal is calculated by assuming the three points
+     * should lie in the same plane. Normal vector is normalised before storage.
+     *
+     * @param {Array<number>|Vector} anchor The anchor vector.
+     * @param {Array<number>|Vector} v1 The first direction vector.
+     * @param {Array<number>|Vector} v2 The second direction vector.
+     */
+    setVectors(anchor: Array<number>|Vector, v1: Array<number>|Vector, v2: Array<number>|Vector): Plane;
+}
+
+declare module Sylvester {
+    export var version: string;
+    export var precision: number;
+}
+
+declare var Vector: Sylvester.VectorStatic;
+declare var Matrix: Sylvester.MatrixStatic;
+declare var Line: Sylvester.LineStatic;
+declare var Plane: Sylvester.PlaneStatic;
+
+/**
+* Constructor function.
+*
+* @param {Vector|Array<number} elements The elements.
+*/
+declare function $V(elements: Vector|Array<number>): Vector;
+
+/**
+* Constructor function.
+*
+* @param {Array<number>|Array<Array<number>>|Vector|Matrix} elements The elements.
+*/
+declare function $M(elements: Array<number>|Array<Array<number>>|Vector | Matrix): Matrix;
+
+/**
+* Constructor function.
+*
+* @param Array<number>|Vector anchor The anchor vector.
+* @param Array<number>|Vector direction The direction vector.
+*/
+declare function $L(anchor: Array<number>|Vector, direction: Array<number>|Vector): Line;
+
+/**
+* Constructor function.
+*
+* @param {Array<number>|Vector} anchor The anchor vector.
+* @param {Array<number>|Vector} normal The normal vector.
+*/
+declare function $P(anchor: Array<number>|Vector, normal: Array<number>|Vector): Plane;
+
+/**
+ * Constructor function.
+ *
+ * @param {Array<number>|Vector} anchor The anchor vector.
+ * @param {Array<number>|Vector} v1 The first direction vector.
+ * @param {Array<number>|Vecotr} v2 The second direction vector.
+ */
+declare function $P(anchor: Array<number>|Vector, v1: Array<number>|Vector, v2: Array<number>|Vector): Plane;