moved matrix class from utils to samples

utils/matrix/matrix4.dart

-// Copyright (c) 2011, the Dart project authors.  Please see the AUTHORS file
-// for details. All rights reserved. Use of this source code is governed by a
-// BSD-style license that can be found in the LICENSE file.
-
-// based on code from 
-// http://code.google.com/p/closure-library/source/browse/trunk/closure/goog/vec/mat4.js  
-
-/**
- * Thrown if you attempt to normalize a zero length vector.
- */
-class ZeroLengthVectorException implements Exception {
-  ZeroLengthVectorException() {}
-}
-
-/**
- * Thrown if you attempt to invert a singular matrix.  (A
- * singular matrix has no inverse.)
- */
-class SingularMatrixException implements Exception {
-  SingularMatrixException() {}
-}
-
-/**
- * 3 dimensional vector.
- */
-class Vector3 {
-  final double x;
-  final double y;
-  final double z;
-
-  // TODO - should be const, but cannot because of
-  // bug http://code.google.com/p/dart/issues/detail?id=777
-
-  // TODO - switch to initializing formal syntax once we have type
-  // checking for this.x style constructors.  See bug
-  // http://code.google.com/p/dart/issues/detail?id=464
-  Vector3(double x, double y, double z) : x = x, y = y, z = z;
-
-  double magnitude() => Math.sqrt(x*x + y*y + z*z);
-
-  Vector3 normalize() {
-    double len = magnitude();
-    if (len == 0.0) {
-      throw new ZeroLengthVectorException();
-    }
-    return new Vector3(x/len, y/len, z/len);
-  }
-
-  Vector3 operator negate() {
-    return new Vector3(-x, -y, -z);
-  }
-
-  Vector3 operator -(Vector3 other) {
-    return new Vector3(x - other.x, y - other.y, z - other.z);
-  }
-
-  Vector3 cross(Vector3 other) {
-    double xResult = y * other.z - z * other.y;
-    double yResult = z * other.x - x * other.z;
-    double zResult = x * other.y - y * other.x;
-    return new Vector3(xResult, yResult, zResult);
-  }
-
-  String toString() {
-    return "Vector3($x,$y,$z)";
-  }
-}
-
-/**
- * A 4x4 transformation matrix (for use with webgl)
- *
- * We label the elements of the matrix as follows:
- *
- *     m00 m01 m02 m03
- *     m10 m11 m12 m13
- *     m20 m21 m22 m23
- *     m30 m31 m32 m33
- *
- * These are stored in a 16 element [Float32Array], in column major
- * order, so they are ordered like this:
- *
- * [ m00,m10,m20,m30, m11,m21,m31,m41, m02,m12,m22,m32, m03,m13,m23,m33 ]
- *   0   1   2   3    4   5   6   7    8   9   10  11   12  13  14  15
- *
- * We use column major order because that is what WebGL APIs expect.
- *
- */
-class Matrix4 {
-  final Float32Array buf;
-
-  /**
-   * Constructs a new Matrix4 with all entries initialized
-   * to zero.
-   */
-  Matrix4() : buf = new Float32Array(16);
-
-  /**
-   * returns the index into [buf] for a given
-   * row and column.
-   */
-  static int rc(int row, int col) => row + col * 4;
-
-  double get m00() => buf[rc(0, 0)];
-  double get m01() => buf[rc(0, 1)];
-  double get m02() => buf[rc(0, 2)];
-  double get m03() => buf[rc(0, 3)];
-  double get m10() => buf[rc(1, 0)];
-  double get m11() => buf[rc(1, 1)];
-  double get m12() => buf[rc(1, 2)];
-  double get m13() => buf[rc(1, 3)];
-  double get m20() => buf[rc(2, 0)];
-  double get m21() => buf[rc(2, 1)];
-  double get m22() => buf[rc(2, 2)];
-  double get m23() => buf[rc(2, 3)];
-  double get m30() => buf[rc(3, 0)];
-  double get m31() => buf[rc(3, 1)];
-  double get m32() => buf[rc(3, 2)];
-  double get m33() => buf[rc(3, 3)];
-
-  void set m00(double m) { buf[rc(0, 0)] = m; }
-  void set m01(double m) { buf[rc(0, 1)] = m; }
-  void set m02(double m) { buf[rc(0, 2)] = m; }
-  void set m03(double m) { buf[rc(0, 3)] = m; }
-  void set m10(double m) { buf[rc(1, 0)] = m; }
-  void set m11(double m) { buf[rc(1, 1)] = m; }
-  void set m12(double m) { buf[rc(1, 2)] = m; }
-  void set m13(double m) { buf[rc(1, 3)] = m; }
-  void set m20(double m) { buf[rc(2, 0)] = m; }
-  void set m21(double m) { buf[rc(2, 1)] = m; }
-  void set m22(double m) { buf[rc(2, 2)] = m; }
-  void set m23(double m) { buf[rc(2, 3)] = m; }
-  void set m30(double m) { buf[rc(3, 0)] = m; }
-  void set m31(double m) { buf[rc(3, 1)] = m; }
-  void set m32(double m) { buf[rc(3, 2)] = m; }
-  void set m33(double m) { buf[rc(3, 3)] = m; }
-
-  String toString() {
-    List<String> rows = new List();
-    for (int row = 0; row < 4; row++) {
-      List<String> items = new List();
-      for (int col = 0; col < 4; col++) {
-        double v = buf[rc(row, col)];
-        if (v.abs() < 1e-16) {
-          v = 0.0;
-        }
-        String display;
-        try {
-          display = v.toStringAsPrecision(4);
-        } catch (Object e) {
-          // TODO - remove this once toStringAsPrecision is implemented in vm
-          display = v.toString();
-        }
-        items.add(display);
-      }
-      rows.add("| ${Strings.join(items, ", ")} |");
-    }
-    return "Matrix4:\n${Strings.join(rows, '\n')}";
-  }
-
-  /**
-   * Cosntructs a new Matrix4 that represents the identity transformation
-   * (all the diagonal entries are 1, and everything else is zero).
-   */
-  static Matrix4 identity() {
-    Matrix4 m = new Matrix4();
-    m.m00 = 1.0;
-    m.m11 = 1.0;
-    m.m22 = 1.0;
-    m.m33 = 1.0;
-    return m;
-  }
-
-  /**
-   * Constructs a new Matrix4 that represents a rotation around an axis.
-   *
-   * [degrees] number of degrees to rotate
-   * [axis] direction of axis of rotation (must not be zero length)
-   */
-  static Matrix4 rotation(double degrees, Vector3 axis) {
-    double radians = degrees / 180.0 * Math.PI;
-    axis = axis.normalize();
-
-    double x = axis.x;
-    double y = axis.y;
-    double z = axis.z;
-    double s = Math.sin(radians);
-    double c = Math.cos(radians);
-    double t = 1 - c;
-
-    Matrix4 m = new Matrix4();
-    m.m00 = x * x * t + c;
-    m.m10 = x * y * t + z * s;
-    m.m20 = x * z * t - y * s;
-
-    m.m01 = x * y * t - z * s;
-    m.m11 = y * y * t + c;
-    m.m21 = y * z * t + x * s;
-
-    m.m02 = x * z * t + y * s;
-    m.m12 = y * z * t - x * s;
-    m.m22 = z * z * t + c;
-
-    m.m33 = 1.0;
-    return m;
-  }
-
-  /**
-   * Constructs a new Matrix4 that represents a translation.
-   *
-   * [v] vector representing which direction to move and how much to move
-   */
-  static Matrix4 translation(Vector3 v) {
-    Matrix4 m = identity();
-    m.m03 = v.x;
-    m.m13 = v.y;
-    m.m23 = v.z;
-    return m;
-  }
-
-  /**
-   * returns the transpose of this matrix
-   */
-  Matrix4 transpose() {
-    Matrix4 m = new Matrix4();
-    for (int row = 0; row < 4; row++) {
-      for (int col = 0; col < 4; col++) {
-        m.buf[rc(col, row)] = this.buf[rc(row, col)];
-      }
-    }
-    return m;
-  }
-
-  /**
-   * Returns result of multiplication of this matrix
-   * by another matrix.
-   *
-   * In this equation:
-   *
-   * C = A * B
-   *
-   * C is the result of multiplying A * B.
-   * A is this matrix
-   * B is another matrix
-   *
-   */
-  Matrix4 operator *(Matrix4 matrixB) {
-    Matrix4 matrixC = new Matrix4();
-    Float32Array bufA = this.buf;
-    Float32Array bufB = matrixB.buf;
-    Float32Array bufC = matrixC.buf;
-    for (int row = 0; row < 4; row++) {
-      for (int col = 0; col < 4; col++) {
-        for (int i = 0; i < 4; i++) {
-          bufC[rc(row, col)] += bufA[rc(row, i)] * bufB[rc(i, col)];
-        }
-      }
-    }
-    return matrixC;
-  }
-
-  /**
-   * Constructs a 4x4 matrix matrix so that the eye is 'looking at' a
-   * given center point.  (What this means is that the returned matrix can be
-   * used transform points from world coordinates to a new coordinate system
-   * where the eye is at the origin, and the negative z-axis of the new
-   * coordinate system goes from the eye towards the center point.)
-   *
-   * [eye] position of the eye (i.e. camera origin).
-   * [center] point to aim the camera at.
-   * [up] vector that identifies the up direction of the camera
-   */
-  static Matrix4 lookAt(Vector3 eye, Vector3 center, Vector3 up) {
-    // Compute the z basis vector.  (The z-axis negative direction is
-    // from eye to center point.)
-    Vector3 zBasis = (eye - center).normalize();
-
-    // Compute x basis.  (The positive x-axis points right.)
-    Vector3 xBasis = up.cross(zBasis).normalize();
-
-    // Compute the y basis.  (The positive y-axis points approximately the same
-    // direction as the supplied [up] direction, and is perpendicular to z and
-    // x.)
-    Vector3 yBasis = zBasis.cross(xBasis);
-
-    // We now have an orthonormal basis.
-    Matrix4 b = new Matrix4();
-    b.m00 = xBasis.x; b.m01 = xBasis.y; b.m02 = xBasis.z;
-    b.m10 = yBasis.x; b.m11 = yBasis.y; b.m12 = yBasis.z;
-    b.m20 = zBasis.x; b.m21 = zBasis.y; b.m22 = zBasis.z;
-    b.m33 = 1.0;
-
-    // Before switching to the new basis, first translate by the negation
-    // of the eye point.  (This will put the eye at the origin of the
-    // new coordinate system.)
-    return b * Matrix4.translation(-eye);
-  }
-
-  /**
-   * Makse a 4x4 matrix perspective projection matrix given a field of view and
-   * aspect ratio.
-   *
-   * [fovyDegrees] field of view (in degrees) of the y-axis
-   * [aspectRatio] width to height aspect ratio.
-   * [zNear] distance to the near clipping plane.
-   * [zFar] distance to the far clipping plane.
-   */
-  static Matrix4 perspective(double fovyDegrees, double aspectRatio,
-      double zNear, double zFar) {
-    double yTop = Math.tan(fovyDegrees * Math.PI / 180.0 / 2.0) * zNear;
-    double xRight = aspectRatio * yTop;
-    double zDepth = zFar - zNear;
-
-    Matrix4 m = new Matrix4();
-    m.m00 = zNear / xRight;
-    m.m11 = zNear / yTop;
-    m.m22 = -(zFar + zNear) / zDepth;
-    m.m23 = -(2 * zNear * zFar) / zDepth;
-    m.m32 = -1;
-    return m;
-  }
-
-  /**
-   * Returns the inverse of this matrix.
-   */
-  Matrix4 inverse() {
-    double a0 = m00 * m11 - m10 * m01;
-    double a1 = m00 * m21 - m20 * m01;
-    double a2 = m00 * m31 - m30 * m01;
-    double a3 = m10 * m21 - m20 * m11;
-    double a4 = m10 * m31 - m30 * m11;
-    double a5 = m20 * m31 - m30 * m21;
-
-    double b0 = m02 * m13 - m12 * m03;
-    double b1 = m02 * m23 - m22 * m03;
-    double b2 = m02 * m33 - m32 * m03;
-    double b3 = m12 * m23 - m22 * m13;
-    double b4 = m12 * m33 - m32 * m13;
-    double b5 = m22 * m33 - m32 * m23;
-
-    // compute determinant
-    double det = a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0;
-    if (det == 0) {
-      throw new SingularMatrixException();
-    }
-
-    Matrix4 m = new Matrix4();
-    m.m00 = (m11 * b5 - m21 * b4 + m31 * b3) / det;
-    m.m10 = (-m10 * b5 + m20 * b4 - m30 * b3) / det;
-    m.m20 = (m13 * a5 - m23 * a4 + m33 * a3) / det;
-    m.m30 = (-m12 * a5 + m22 * a4 - m32 * a3) / det;
-
-    m.m01 = (-m01 * b5 + m21 * b2 - m31 * b1) / det;
-    m.m11 = (m00 * b5 - m20 * b2 + m30 * b1) / det;
-    m.m21 = (-m03 * a5 + m23 * a2 - m33 * a1) / det;
-    m.m31 = (m02 * a5 - m22 * a2 + m32 * a1) / det;
-
-    m.m02 = (m01 * b4 - m11 * b2 + m31 * b0) / det;
-    m.m12 = (-m00 * b4 + m10 * b2 - m30 * b0) / det;
-    m.m22 = (m03 * a4 - m13 * a2 + m33 * a0) / det;
-    m.m32 = (-m02 * a4 + m12 * a2 - m32 * a0) / det;
-
-    m.m03 = (-m01 * b3 + m11 * b1 - m21 * b0) / det;
-    m.m13 = (m00 * b3 - m10 * b1 + m20 * b0) / det;
-    m.m23 = (-m03 * a3 + m13 * a1 - m23 * a0) / det;
-    m.m33 = (m02 * a3 - m12 * a1 + m22 * a0) / det;
-
-    return m;
-  }
-}