webgl 高级变换与动画基础

• 前言
  在前面文章提到过平移,旋转,缩放等变换操作虽然可以使用一个 4x4的矩阵表示,但是在写 webgl 的时候,手动计算每个矩阵很耗费时间.所以在网上找了一个简单的矩阵封装的库.有了这个简单的库,可以很简单的是实现平移,旋转,缩放已经一系列组合操作.矩阵库源码如下

// cuon-matrix.js (c) 2012 kanda and matsuda
/** 
 * This is a class treating 4x4 matrix.
 * This class contains the function that is equivalent to OpenGL matrix stack.
 * The matrix after conversion is calculated by multiplying a conversion matrix from the right.
 * The matrix is replaced by the calculated result.
 */

/**
 * Constructor of Matrix4
 * If opt_src is specified, new matrix is initialized by opt_src.
 * Otherwise, new matrix is initialized by identity matrix.
 * @param opt_src source matrix(option)
 */
var Matrix4 = function(opt_src) {
  var i, s, d;
  if (opt_src && typeof opt_src === 'object' && opt_src.hasOwnProperty('elements')) {
    s = opt_src.elements;
    d = new Float32Array(16);
    for (i = 0; i < 16; ++i) {
      d[i] = s[i];
    }
    this.elements = d;
  } else {
    this.elements = new Float32Array([1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]);
  }
};

/**
 * Set the identity matrix.
 * @return this
 */
Matrix4.prototype.setIdentity = function() {
  var e = this.elements;
  e[0] = 1;   e[4] = 0;   e[8]  = 0;   e[12] = 0;
  e[1] = 0;   e[5] = 1;   e[9]  = 0;   e[13] = 0;
  e[2] = 0;   e[6] = 0;   e[10] = 1;   e[14] = 0;
  e[3] = 0;   e[7] = 0;   e[11] = 0;   e[15] = 1;
  return this;
};

/**
 * Copy matrix.
 * @param src source matrix
 * @return this
 */
Matrix4.prototype.set = function(src) {
  var i, s, d;

  s = src.elements;
  d = this.elements;

  if (s === d) {
    return;
  }
    
  for (i = 0; i < 16; ++i) {
    d[i] = s[i];
  }

  return this;
};

/**
 * Multiply the matrix from the right.
 * @param other The multiply matrix
 * @return this
 */
Matrix4.prototype.concat = function(other) {
  var i, e, a, b, ai0, ai1, ai2, ai3;
  
  // Calculate e = a * b
  e = this.elements;
  a = this.elements;
  b = other.elements;
  
  // If e equals b, copy b to temporary matrix.
  if (e === b) {
    b = new Float32Array(16);
    for (i = 0; i < 16; ++i) {
      b[i] = e[i];
    }
  }
  
  for (i = 0; i < 4; i++) {
    ai0=a[i];  ai1=a[i+4];  ai2=a[i+8];  ai3=a[i+12];
    e[i]    = ai0 * b[0]  + ai1 * b[1]  + ai2 * b[2]  + ai3 * b[3];
    e[i+4]  = ai0 * b[4]  + ai1 * b[5]  + ai2 * b[6]  + ai3 * b[7];
    e[i+8]  = ai0 * b[8]  + ai1 * b[9]  + ai2 * b[10] + ai3 * b[11];
    e[i+12] = ai0 * b[12] + ai1 * b[13] + ai2 * b[14] + ai3 * b[15];
  }
  
  return this;
};
Matrix4.prototype.multiply = Matrix4.prototype.concat;

/**
 * Multiply the three-dimensional vector.
 * @param pos  The multiply vector
 * @return The result of multiplication(Float32Array)
 */
Matrix4.prototype.multiplyVector3 = function(pos) {
  var e = this.elements;
  var p = pos.elements;
  var v = new Vector3();
  var result = v.elements;

  result[0] = p[0] * e[0] + p[1] * e[4] + p[2] * e[ 8] + e[11];
  result[1] = p[0] * e[1] + p[1] * e[5] + p[2] * e[ 9] + e[12];
  result[2] = p[0] * e[2] + p[1] * e[6] + p[2] * e[10] + e[13];

  return v;
};

/**
 * Multiply the four-dimensional vector.
 * @param pos  The multiply vector
 * @return The result of multiplication(Float32Array)
 */
Matrix4.prototype.multiplyVector4 = function(pos) {
  var e = this.elements;
  var p = pos.elements;
  var v = new Vector4();
  var result = v.elements;

  result[0] = p[0] * e[0] + p[1] * e[4] + p[2] * e[ 8] + p[3] * e[12];
  result[1] = p[0] * e[1] + p[1] * e[5] + p[2] * e[ 9] + p[3] * e[13];
  result[2] = p[0] * e[2] + p[1] * e[6] + p[2] * e[10] + p[3] * e[14];
  result[3] = p[0] * e[3] + p[1] * e[7] + p[2] * e[11] + p[3] * e[15];

  return v;
};

/**
 * Transpose the matrix.
 * @return this
 */
Matrix4.prototype.transpose = function() {
  var e, t;

  e = this.elements;

  t = e[ 1];  e[ 1] = e[ 4];  e[ 4] = t;
  t = e[ 2];  e[ 2] = e[ 8];  e[ 8] = t;
  t = e[ 3];  e[ 3] = e[12];  e[12] = t;
  t = e[ 6];  e[ 6] = e[ 9];  e[ 9] = t;
  t = e[ 7];  e[ 7] = e[13];  e[13] = t;
  t = e[11];  e[11] = e[14];  e[14] = t;

  return this;
};

/**
 * Calculate the inverse matrix of specified matrix, and set to this.
 * @param other The source matrix
 * @return this
 */
Matrix4.prototype.setInverseOf = function(other) {
  var i, s, d, inv, det;

  s = other.elements;
  d = this.elements;
  inv = new Float32Array(16);

  inv[0]  =   s[5]*s[10]*s[15] - s[5] *s[11]*s[14] - s[9] *s[6]*s[15]
            + s[9]*s[7] *s[14] + s[13]*s[6] *s[11] - s[13]*s[7]*s[10];
  inv[4]  = - s[4]*s[10]*s[15] + s[4] *s[11]*s[14] + s[8] *s[6]*s[15]
            - s[8]*s[7] *s[14] - s[12]*s[6] *s[11] + s[12]*s[7]*s[10];
  inv[8]  =   s[4]*s[9] *s[15] - s[4] *s[11]*s[13] - s[8] *s[5]*s[15]
            + s[8]*s[7] *s[13] + s[12]*s[5] *s[11] - s[12]*s[7]*s[9];
  inv[12] = - s[4]*s[9] *s[14] + s[4] *s[10]*s[13] + s[8] *s[5]*s[14]
            - s[8]*s[6] *s[13] - s[12]*s[5] *s[10] + s[12]*s[6]*s[9];

  inv[1]  = - s[1]*s[10]*s[15] + s[1] *s[11]*s[14] + s[9] *s[2]*s[15]
            - s[9]*s[3] *s[14] - s[13]*s[2] *s[11] + s[13]*s[3]*s[10];
  inv[5]  =   s[0]*s[10]*s[15] - s[0] *s[11]*s[14] - s[8] *s[2]*s[15]
            + s[8]*s[3] *s[14] + s[12]*s[2] *s[11] - s[12]*s[3]*s[10];
  inv[9]  = - s[0]*s[9] *s[15] + s[0] *s[11]*s[13] + s[8] *s[1]*s[15]
            - s[8]*s[3] *s[13] - s[12]*s[1] *s[11] + s[12]*s[3]*s[9];
  inv[13] =   s[0]*s[9] *s[14] - s[0] *s[10]*s[13] - s[8] *s[1]*s[14]
            + s[8]*s[2] *s[13] + s[12]*s[1] *s[10] - s[12]*s[2]*s[9];

  inv[2]  =   s[1]*s[6]*s[15] - s[1] *s[7]*s[14] - s[5] *s[2]*s[15]
            + s[5]*s[3]*s[14] + s[13]*s[2]*s[7]  - s[13]*s[3]*s[6];
  inv[6]  = - s[0]*s[6]*s[15] + s[0] *s[7]*s[14] + s[4] *s[2]*s[15]
            - s[4]*s[3]*s[14] - s[12]*s[2]*s[7]  + s[12]*s[3]*s[6];
  inv[10] =   s[0]*s[5]*s[15] - s[0] *s[7]*s[13] - s[4] *s[1]*s[15]
            + s[4]*s[3]*s[13] + s[12]*s[1]*s[7]  - s[12]*s[3]*s[5];
  inv[14] = - s[0]*s[5]*s[14] + s[0] *s[6]*s[13] + s[4] *s[1]*s[14]
            - s[4]*s[2]*s[13] - s[12]*s[1]*s[6]  + s[12]*s[2]*s[5];

  inv[3]  = - s[1]*s[6]*s[11] + s[1]*s[7]*s[10] + s[5]*s[2]*s[11]
            - s[5]*s[3]*s[10] - s[9]*s[2]*s[7]  + s[9]*s[3]*s[6];
  inv[7]  =   s[0]*s[6]*s[11] - s[0]*s[7]*s[10] - s[4]*s[2]*s[11]
            + s[4]*s[3]*s[10] + s[8]*s[2]*s[7]  - s[8]*s[3]*s[6];
  inv[11] = - s[0]*s[5]*s[11] + s[0]*s[7]*s[9]  + s[4]*s[1]*s[11]
            - s[4]*s[3]*s[9]  - s[8]*s[1]*s[7]  + s[8]*s[3]*s[5];
  inv[15] =   s[0]*s[5]*s[10] - s[0]*s[6]*s[9]  - s[4]*s[1]*s[10]
            + s[4]*s[2]*s[9]  + s[8]*s[1]*s[6]  - s[8]*s[2]*s[5];

  det = s[0]*inv[0] + s[1]*inv[4] + s[2]*inv[8] + s[3]*inv[12];
  if (det === 0) {
    return this;
  }

  det = 1 / det;
  for (i = 0; i < 16; i++) {
    d[i] = inv[i] * det;
  }

  return this;
};

/**
 * Calculate the inverse matrix of this, and set to this.
 * @return this
 */
Matrix4.prototype.invert = function() {
  return this.setInverseOf(this);
};

/**
 * Set the orthographic projection matrix.
 * @param left The coordinate of the left of clipping plane.
 * @param right The coordinate of the right of clipping plane.
 * @param bottom The coordinate of the bottom of clipping plane.
 * @param top The coordinate of the top top clipping plane.
 * @param near The distances to the nearer depth clipping plane. This value is minus if the plane is to be behind the viewer.
 * @param far The distances to the farther depth clipping plane. This value is minus if the plane is to be behind the viewer.
 * @return this
 */
Matrix4.prototype.setOrtho = function(left, right, bottom, top, near, far) {
  var e, rw, rh, rd;

  if (left === right || bottom === top || near === far) {
    throw 'null frustum';
  }

  rw = 1 / (right - left);
  rh = 1 / (top - bottom);
  rd = 1 / (far - near);

  e = this.elements;

  e[0]  = 2 * rw;
  e[1]  = 0;
  e[2]  = 0;
  e[3]  = 0;

  e[4]  = 0;
  e[5]  = 2 * rh;
  e[6]  = 0;
  e[7]  = 0;

  e[8]  = 0;
  e[9]  = 0;
  e[10] = -2 * rd;
  e[11] = 0;

  e[12] = -(right + left) * rw;
  e[13] = -(top + bottom) * rh;
  e[14] = -(far + near) * rd;
  e[15] = 1;

  return this;
};

/**
 * Multiply the orthographic projection matrix from the right.
 * @param left The coordinate of the left of clipping plane.
 * @param right The coordinate of the right of clipping plane.
 * @param bottom The coordinate of the bottom of clipping plane.
 * @param top The coordinate of the top top clipping plane.
 * @param near The distances to the nearer depth clipping plane. This value is minus if the plane is to be behind the viewer.
 * @param far The distances to the farther depth clipping plane. This value is minus if the plane is to be behind the viewer.
 * @return this
 */
Matrix4.prototype.ortho = function(left, right, bottom, top, near, far) {
  return this.concat(new Matrix4().setOrtho(left, right, bottom, top, near, far));
};

/**
 * Set the perspective projection matrix.
 * @param left The coordinate of the left of clipping plane.
 * @param right The coordinate of the right of clipping plane.
 * @param bottom The coordinate of the bottom of clipping plane.
 * @param top The coordinate of the top top clipping plane.
 * @param near The distances to the nearer depth clipping plane. This value must be plus value.
 * @param far The distances to the farther depth clipping plane. This value must be plus value.
 * @return this
 */
Matrix4.prototype.setFrustum = function(left, right, bottom, top, near, far) {
  var e, rw, rh, rd;

  if (left === right || top === bottom || near === far) {
    throw 'null frustum';
  }
  if (near <= 0) {
    throw 'near <= 0';
  }
  if (far <= 0) {
    throw 'far <= 0';
  }

  rw = 1 / (right - left);
  rh = 1 / (top - bottom);
  rd = 1 / (far - near);

  e = this.elements;

  e[ 0] = 2 * near * rw;
  e[ 1] = 0;
  e[ 2] = 0;
  e[ 3] = 0;

  e[ 4] = 0;
  e[ 5] = 2 * near * rh;
  e[ 6] = 0;
  e[ 7] = 0;

  e[ 8] = (right + left) * rw;
  e[ 9] = (top + bottom) * rh;
  e[10] = -(far + near) * rd;
  e[11] = -1;

  e[12] = 0;
  e[13] = 0;
  e[14] = -2 * near * far * rd;
  e[15] = 0;

  return this;
};

/**
 * Multiply the perspective projection matrix from the right.
 * @param left The coordinate of the left of clipping plane.
 * @param right The coordinate of the right of clipping plane.
 * @param bottom The coordinate of the bottom of clipping plane.
 * @param top The coordinate of the top top clipping plane.
 * @param near The distances to the nearer depth clipping plane. This value must be plus value.
 * @param far The distances to the farther depth clipping plane. This value must be plus value.
 * @return this
 */
Matrix4.prototype.frustum = function(left, right, bottom, top, near, far) {
  return this.concat(new Matrix4().setFrustum(left, right, bottom, top, near, far));
};

/**
 * Set the perspective projection matrix by fovy and aspect.
 * @param fovy The angle between the upper and lower sides of the frustum.
 * @param aspect The aspect ratio of the frustum. (width/height)
 * @param near The distances to the nearer depth clipping plane. This value must be plus value.
 * @param far The distances to the farther depth clipping plane. This value must be plus value.
 * @return this
 */
Matrix4.prototype.setPerspective = function(fovy, aspect, near, far) {
  var e, rd, s, ct;

  if (near === far || aspect === 0) {
    throw 'null frustum';
  }
  if (near <= 0) {
    throw 'near <= 0';
  }
  if (far <= 0) {
    throw 'far <= 0';
  }

  fovy = Math.PI * fovy / 180 / 2;
  s = Math.sin(fovy);
  if (s === 0) {
    throw 'null frustum';
  }

  rd = 1 / (far - near);
  ct = Math.cos(fovy) / s;

  e = this.elements;

  e[0]  = ct / aspect;
  e[1]  = 0;
  e[2]  = 0;
  e[3]  = 0;

  e[4]  = 0;
  e[5]  = ct;
  e[6]  = 0;
  e[7]  = 0;

  e[8]  = 0;
  e[9]  = 0;
  e[10] = -(far + near) * rd;
  e[11] = -1;

  e[12] = 0;
  e[13] = 0;
  e[14] = -2 * near * far * rd;
  e[15] = 0;

  return this;
};

/**
 * Multiply the perspective projection matrix from the right.
 * @param fovy The angle between the upper and lower sides of the frustum.
 * @param aspect The aspect ratio of the frustum. (width/height)
 * @param near The distances to the nearer depth clipping plane. This value must be plus value.
 * @param far The distances to the farther depth clipping plane. This value must be plus value.
 * @return this
 */
Matrix4.prototype.perspective = function(fovy, aspect, near, far) {
  return this.concat(new Matrix4().setPerspective(fovy, aspect, near, far));
};

/**
 * Set the matrix for scaling.
 * @param x The scale factor along the X axis
 * @param y The scale factor along the Y axis
 * @param z The scale factor along the Z axis
 * @return this
 */
Matrix4.prototype.setScale = function(x, y, z) {
  var e = this.elements;
  e[0] = x;  e[4] = 0;  e[8]  = 0;  e[12] = 0;
  e[1] = 0;  e[5] = y;  e[9]  = 0;  e[13] = 0;
  e[2] = 0;  e[6] = 0;  e[10] = z;  e[14] = 0;
  e[3] = 0;  e[7] = 0;  e[11] = 0;  e[15] = 1;
  return this;
};

/**
 * Multiply the matrix for scaling from the right.
 * @param x The scale factor along the X axis
 * @param y The scale factor along the Y axis
 * @param z The scale factor along the Z axis
 * @return this
 */
Matrix4.prototype.scale = function(x, y, z) {
  var e = this.elements;
  e[0] *= x;  e[4] *= y;  e[8]  *= z;
  e[1] *= x;  e[5] *= y;  e[9]  *= z;
  e[2] *= x;  e[6] *= y;  e[10] *= z;
  e[3] *= x;  e[7] *= y;  e[11] *= z;
  return this;
};

/**
 * Set the matrix for translation.
 * @param x The X value of a translation.
 * @param y The Y value of a translation.
 * @param z The Z value of a translation.
 * @return this
 */
Matrix4.prototype.setTranslate = function(x, y, z) {
  var e = this.elements;
  e[0] = 1;  e[4] = 0;  e[8]  = 0;  e[12] = x;
  e[1] = 0;  e[5] = 1;  e[9]  = 0;  e[13] = y;
  e[2] = 0;  e[6] = 0;  e[10] = 1;  e[14] = z;
  e[3] = 0;  e[7] = 0;  e[11] = 0;  e[15] = 1;
  return this;
};

/**
 * Multiply the matrix for translation from the right.
 * @param x The X value of a translation.
 * @param y The Y value of a translation.
 * @param z The Z value of a translation.
 * @return this
 */
Matrix4.prototype.translate = function(x, y, z) {
  var e = this.elements;
  e[12] += e[0] * x + e[4] * y + e[8]  * z;
  e[13] += e[1] * x + e[5] * y + e[9]  * z;
  e[14] += e[2] * x + e[6] * y + e[10] * z;
  e[15] += e[3] * x + e[7] * y + e[11] * z;
  return this;
};

/**
 * Set the matrix for rotation.
 * The vector of rotation axis may not be normalized.
 * @param angle The angle of rotation (degrees)
 * @param x The X coordinate of vector of rotation axis.
 * @param y The Y coordinate of vector of rotation axis.
 * @param z The Z coordinate of vector of rotation axis.
 * @return this
 */
Matrix4.prototype.setRotate = function(angle, x, y, z) {
  var e, s, c, len, rlen, nc, xy, yz, zx, xs, ys, zs;

  angle = Math.PI * angle / 180;
  e = this.elements;

  s = Math.sin(angle);
  c = Math.cos(angle);

  if (0 !== x && 0 === y && 0 === z) {
    // Rotation around X axis
    if (x < 0) {
      s = -s;
    }
    e[0] = 1;  e[4] = 0;  e[ 8] = 0;  e[12] = 0;
    e[1] = 0;  e[5] = c;  e[ 9] =-s;  e[13] = 0;
    e[2] = 0;  e[6] = s;  e[10] = c;  e[14] = 0;
    e[3] = 0;  e[7] = 0;  e[11] = 0;  e[15] = 1;
  } else if (0 === x && 0 !== y && 0 === z) {
    // Rotation around Y axis
    if (y < 0) {
      s = -s;
    }
    e[0] = c;  e[4] = 0;  e[ 8] = s;  e[12] = 0;
    e[1] = 0;  e[5] = 1;  e[ 9] = 0;  e[13] = 0;
    e[2] =-s;  e[6] = 0;  e[10] = c;  e[14] = 0;
    e[3] = 0;  e[7] = 0;  e[11] = 0;  e[15] = 1;
  } else if (0 === x && 0 === y && 0 !== z) {
    // Rotation around Z axis
    if (z < 0) {
      s = -s;
    }
    e[0] = c;  e[4] =-s;  e[ 8] = 0;  e[12] = 0;
    e[1] = s;  e[5] = c;  e[ 9] = 0;  e[13] = 0;
    e[2] = 0;  e[6] = 0;  e[10] = 1;  e[14] = 0;
    e[3] = 0;  e[7] = 0;  e[11] = 0;  e[15] = 1;
  } else {
    // Rotation around another axis
    len = Math.sqrt(x*x + y*y + z*z);
    if (len !== 1) {
      rlen = 1 / len;
      x *= rlen;
      y *= rlen;
      z *= rlen;
    }
    nc = 1 - c;
    xy = x * y;
    yz = y * z;
    zx = z * x;
    xs = x * s;
    ys = y * s;
    zs = z * s;

    e[ 0] = x*x*nc +  c;
    e[ 1] = xy *nc + zs;
    e[ 2] = zx *nc - ys;
    e[ 3] = 0;

    e[ 4] = xy *nc - zs;
    e[ 5] = y*y*nc +  c;
    e[ 6] = yz *nc + xs;
    e[ 7] = 0;

    e[ 8] = zx *nc + ys;
    e[ 9] = yz *nc - xs;
    e[10] = z*z*nc +  c;
    e[11] = 0;

    e[12] = 0;
    e[13] = 0;
    e[14] = 0;
    e[15] = 1;
  }

  return this;
};

/**
 * Multiply the matrix for rotation from the right.
 * The vector of rotation axis may not be normalized.
 * @param angle The angle of rotation (degrees)
 * @param x The X coordinate of vector of rotation axis.
 * @param y The Y coordinate of vector of rotation axis.
 * @param z The Z coordinate of vector of rotation axis.
 * @return this
 */
Matrix4.prototype.rotate = function(angle, x, y, z) {
  return this.concat(new Matrix4().setRotate(angle, x, y, z));
};

/**
 * Set the viewing matrix.
 * @param eyeX, eyeY, eyeZ The position of the eye point.
 * @param centerX, centerY, centerZ The position of the reference point.
 * @param upX, upY, upZ The direction of the up vector.
 * @return this
 */
Matrix4.prototype.setLookAt = function(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ) {
  var e, fx, fy, fz, rlf, sx, sy, sz, rls, ux, uy, uz;

  fx = centerX - eyeX;
  fy = centerY - eyeY;
  fz = centerZ - eyeZ;

  // Normalize f.
  rlf = 1 / Math.sqrt(fx*fx + fy*fy + fz*fz);
  fx *= rlf;
  fy *= rlf;
  fz *= rlf;

  // Calculate cross product of f and up.
  sx = fy * upZ - fz * upY;
  sy = fz * upX - fx * upZ;
  sz = fx * upY - fy * upX;

  // Normalize s.
  rls = 1 / Math.sqrt(sx*sx + sy*sy + sz*sz);
  sx *= rls;
  sy *= rls;
  sz *= rls;

  // Calculate cross product of s and f.
  ux = sy * fz - sz * fy;
  uy = sz * fx - sx * fz;
  uz = sx * fy - sy * fx;

  // Set to this.
  e = this.elements;
  e[0] = sx;
  e[1] = ux;
  e[2] = -fx;
  e[3] = 0;

  e[4] = sy;
  e[5] = uy;
  e[6] = -fy;
  e[7] = 0;

  e[8] = sz;
  e[9] = uz;
  e[10] = -fz;
  e[11] = 0;

  e[12] = 0;
  e[13] = 0;
  e[14] = 0;
  e[15] = 1;

  // Translate.
  return this.translate(-eyeX, -eyeY, -eyeZ);
};

/**
 * Multiply the viewing matrix from the right.
 * @param eyeX, eyeY, eyeZ The position of the eye point.
 * @param centerX, centerY, centerZ The position of the reference point.
 * @param upX, upY, upZ The direction of the up vector.
 * @return this
 */
Matrix4.prototype.lookAt = function(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ) {
  return this.concat(new Matrix4().setLookAt(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ));
};

/**
 * Multiply the matrix for project vertex to plane from the right.
 * @param plane The array[A, B, C, D] of the equation of plane "Ax + By + Cz + D = 0".
 * @param light The array which stored coordinates of the light. if light[3]=0, treated as parallel light.
 * @return this
 */
Matrix4.prototype.dropShadow = function(plane, light) {
  var mat = new Matrix4();
  var e = mat.elements;

  var dot = plane[0] * light[0] + plane[1] * light[1] + plane[2] * light[2] + plane[3] * light[3];

  e[ 0] = dot - light[0] * plane[0];
  e[ 1] =     - light[1] * plane[0];
  e[ 2] =     - light[2] * plane[0];
  e[ 3] =     - light[3] * plane[0];

  e[ 4] =     - light[0] * plane[1];
  e[ 5] = dot - light[1] * plane[1];
  e[ 6] =     - light[2] * plane[1];
  e[ 7] =     - light[3] * plane[1];

  e[ 8] =     - light[0] * plane[2];
  e[ 9] =     - light[1] * plane[2];
  e[10] = dot - light[2] * plane[2];
  e[11] =     - light[3] * plane[2];

  e[12] =     - light[0] * plane[3];
  e[13] =     - light[1] * plane[3];
  e[14] =     - light[2] * plane[3];
  e[15] = dot - light[3] * plane[3];

  return this.concat(mat);
}

/**
 * Multiply the matrix for project vertex to plane from the right.(Projected by parallel light.)
 * @param normX, normY, normZ The normal vector of the plane.(Not necessary to be normalized.)
 * @param planeX, planeY, planeZ The coordinate of arbitrary points on a plane.
 * @param lightX, lightY, lightZ The vector of the direction of light.(Not necessary to be normalized.)
 * @return this
 */
Matrix4.prototype.dropShadowDirectionally = function(normX, normY, normZ, planeX, planeY, planeZ, lightX, lightY, lightZ) {
  var a = planeX * normX + planeY * normY + planeZ * normZ;
  return this.dropShadow([normX, normY, normZ, -a], [lightX, lightY, lightZ, 0]);
};

/**
 * Constructor of Vector3
 * If opt_src is specified, new vector is initialized by opt_src.
 * @param opt_src source vector(option)
 */
var Vector3 = function(opt_src) {
  var v = new Float32Array(3);
  if (opt_src && typeof opt_src === 'object') {
    v[0] = opt_src[0]; v[1] = opt_src[1]; v[2] = opt_src[2];
  } 
  this.elements = v;
}

/**
  * Normalize.
  * @return this
  */
Vector3.prototype.normalize = function() {
  var v = this.elements;
  var c = v[0], d = v[1], e = v[2], g = Math.sqrt(c*c+d*d+e*e);
  if(g){
    if(g == 1)
        return this;
   } else {
     v[0] = 0; v[1] = 0; v[2] = 0;
     return this;
   }
   g = 1/g;
   v[0] = c*g; v[1] = d*g; v[2] = e*g;
   return this;
};

/**
 * Constructor of Vector4
 * If opt_src is specified, new vector is initialized by opt_src.
 * @param opt_src source vector(option)
 */
var Vector4 = function(opt_src) {
  var v = new Float32Array(4);
  if (opt_src && typeof opt_src === 'object') {
    v[0] = opt_src[0]; v[1] = opt_src[1]; v[2] = opt_src[2]; v[3] = opt_src[3];
  } 
  this.elements = v;
}

Matrix4 对象所支持的方法和属性如下表所示

复合变换

复合变换是指进行多次的平移或者旋转或者缩放操作.下面已一次平移加上一次缩放为例子.

• 第一次平移:
  <平移后的坐标> = <平移矩阵> x <原始坐标>
• 第二次旋转:
  <平移旋转后的坐标> = <旋转坐标> *<平移后的坐标>
• 把这两步等式合并起来
  <平移旋转后的坐标> = <旋转坐标> x(<平移坐标> *<原始坐标>)
  等式也可以写成
  <平移后的坐标> = (<旋转坐标>x(<平移坐标>)) x<原始坐标>
  将这些变换全部复合成一个等效的变换,就得到; 模型变换,相应的,模型变换的矩阵称为模型矩阵.

示例

下面的例子标识先平移后旋转的代码

<!DOCTYPE html>
<html>
    <head>
        <meta charset="utf-8">
        <title></title>
    </head>
    <body onload="main()">
        <canvas id="webgl" width="400" height="400"></canvas>
    </body>
    <script id="vertextShader" type="x-shader/x-vertex">
        attribute vec4 a_Position;
        uniform mat4 u_xformMatrix;
        void main () {
            gl_Position = u_xformMatrix*a_Position;
        }
    </script>
    <script id="fragmentShader" type="x-shader/x-fragment">
        //  全局设置浮点数的精确度,其他类型都有默认的精度类型,浮点数需要单独的设置
        // precision mediump float;
        // uniform vec4 u_FragColor;
        void main () {
            gl_FragColor = vec4(1.0,0.0,0.0,1.0);
        }
    </script>
    <script src="./jsm/util.js"></script>
    <script src="tool/cuon-matrix.js"></script>
    <script>
        let tx=0.0,ty=0.0,tz=0.0
        let angle = 0.0;
        function main () {
            const canvas = document.getElementById('webgl')
            const gl = canvas.getContext('webgl')
            const vertextShader  = document.getElementById('vertextShader').innerText
            const fragmentShader = document.getElementById('fragmentShader').innerText
            if (!initShaders(gl,vertextShader,fragmentShader)) return
            if (!gl) return
            const a_Position = gl.getAttribLocation(gl.program,'a_Position')
            const u_xformMatrix = gl.getUniformLocation(gl.program,'u_xformMatrix')
            if (a_Position < 0 ) return
            angleChange(gl,u_xformMatrix)
            const vertexs = [0.0,0.0,0.2,0.0,0.0,0.2]
            //  创建缓冲区域
            const buffer = gl.createBuffer()
            //  绑定缓冲区域
            gl.bindBuffer(gl.ARRAY_BUFFER,buffer)
            //  向缓冲区域写入数据
            gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(vertexs),gl.STATIC_DRAW)
            //  将缓冲对象分配给 attribute 对象
            gl.vertexAttribPointer(a_Position,2,gl.FLOAT,false,0,0)
            // 开启链接 attribute 变量
            gl.enableVertexAttribArray(a_Position)
            gl.clearColor(0.0,0.0,0.0,1.0)
            render(gl)
            // canvas.onmousedown = function (e) {
            //  click(gl,u_xformMatrix)
            // }
        }
        function render (gl) {
            // 颜色深度清空
            gl.clear(gl.COLOR_BUFFER_BIT) 
            //  开始绘制
            gl.drawArrays(gl.TRIANGLES,0,3)
        }
        function angleChange(gl,u_xformMatrix) {
            let ANGLE = 60.0
            let TX = 0.1
            let modeMatrix  =  new Matrix4()
            modeMatrix.setRotate(ANGLE,0,0,1)
            modeMatrix.translate(TX,0,0)
            gl.uniformMatrix4fv(u_xformMatrix,false,modeMatrix.elements)
        }
        function click(gl,u_xformMatrix) {
            angle+=60
            angleChange(gl,u_xformMatrix)
            render(gl)
        } 
    </script>
</html>

基础动画

所谓的动画其实就是在不同的时间刻度上显示不同的位置或者样式.比如为了让一个三角形转动起来,需要做的是:不断擦除和重绘三角形,并且每次在重绘的时候轻微的改变其角度.在绘制动画的时候一般使用系统的requestAnimationFrame方法.
下面这个示例演示三角形角度的变化

<!DOCTYPE html>
<html>
    <head>
        <meta charset="utf-8">
        <title></title>
    </head>
    <body onload="main()">
        <canvas id="webgl" width="400" height="400"></canvas>
    </body>
    <script id="vertextShader" type="x-shader/x-vertex">
        attribute vec4 a_Position;
        uniform mat4 u_xformMatrix;
        void main () {
            gl_Position = u_xformMatrix*a_Position;
        }
    </script>
    <script id="fragmentShader" type="x-shader/x-fragment">
        //  全局设置浮点数的精确度,其他类型都有默认的精度类型,浮点数需要单独的设置
        // precision mediump float;
        // uniform vec4 u_FragColor;
        void main () {
            gl_FragColor = vec4(1.0,0.0,0.0,1.0);
        }
    </script>
    <script src="./jsm/util.js"></script>
    <script src="tool/cuon-matrix.js"></script>
    <script>
        let tx=0.0,ty=0.0,tz=0.0
        let angle = 0.0;
        let ANGLE_STEP = 45.0;
        function main () {
            const canvas = document.getElementById('webgl')
            const gl = canvas.getContext('webgl')
            const vertextShader  = document.getElementById('vertextShader').innerText
            const fragmentShader = document.getElementById('fragmentShader').innerText
            if (!initShaders(gl,vertextShader,fragmentShader)) return
            if (!gl) return
            const a_Position = gl.getAttribLocation(gl.program,'a_Position')
            const u_xformMatrix = gl.getUniformLocation(gl.program,'u_xformMatrix')
            if (a_Position < 0 ) return
            const vertexs = [0.0,0.0,0.2,0.0,0.0,0.2]
            //  创建缓冲区域
            const buffer = gl.createBuffer()
            //  绑定缓冲区域
            gl.bindBuffer(gl.ARRAY_BUFFER,buffer)
            //  向缓冲区域写入数据
            gl.bufferData(gl.ARRAY_BUFFER,new Float32Array(vertexs),gl.STATIC_DRAW)
            //  将缓冲对象分配给 attribute 对象
            gl.vertexAttribPointer(a_Position,2,gl.FLOAT,false,0,0)
            // 开启链接 attribute 变量
            gl.enableVertexAttribArray(a_Position)
            gl.clearColor(0.0,0.0,0.0,1.0)
            let currentAngle = 0.0
            let modeMatrix  = new Matrix4()
            let tick = function() {
                currentAngle = animate(currentAngle)
                draw(gl,3,currentAngle,modeMatrix,u_xformMatrix)
                requestAnimationFrame(tick)
            }
            tick()
            // render(gl)
        }
        function draw(gl,n,angle,model,u_xformMatrix) {
            model.setRotate(angle,0,0,1)
            gl.uniformMatrix4fv(u_xformMatrix,false,model.elements)
            gl.clear(gl.COLOR_BUFFER_BIT) 
            gl.drawArrays(gl.TRIANGLES,0,n)
        }
        let g_last  = Date.now()
        function animate(angle) {
            let now = Date.now()
            let elapsed =  now -g_last
            g_last = now
            //  根据上次调用的时间,更新当前旋转的角度
            var newAngle = angle +(ANGLE_STEP*elapsed)/1000;
            return newAngle %=360
        }
        // function render (gl) {
        //  // 颜色深度清空
        //  gl.clear(gl.COLOR_BUFFER_BIT) 
        //  //  开始绘制
        //  gl.drawArrays(gl.TRIANGLES,0,3)
        // }
        // function changeMatrixal(gl,u_xformMatrix) {
        //  let ANGLE = 60.0
        //  let TX = 0.1
        //  let modeMatrix  =  new Matrix4()
        //  modeMatrix.setRotate(ANGLE,0,0,1)
        //  modeMatrix.translate(TX,0,0)
        //  gl.uniformMatrix4fv(u_xformMatrix,false,modeMatrix.elements)
        // }

    </script>
</html>