caseEditor/src/util/mt4.ts

type NumArr = number[];
export const identity = () => [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];

// 转置矩阵
export const transpose = (m: number[]) => {
  return [
    m[0],
    m[4],
    m[8],
    m[12],
    m[1],
    m[5],
    m[9],
    m[13],
    m[2],
    m[6],
    m[10],
    m[14],
    m[3],
    m[7],
    m[11],
    m[15],
  ];
};

export const orthographic = (
  left: number,
  right: number,
  bottom: number,
  top: number,
  near: number,
  far: number
) => {
  const dst = new Float32Array(16);

  dst[0] = 2 / (right - left);
  dst[1] = 0;
  dst[2] = 0;
  dst[3] = 0;
  dst[4] = 0;
  dst[5] = 2 / (top - bottom);
  dst[6] = 0;
  dst[7] = 0;
  dst[8] = 0;
  dst[9] = 0;
  dst[10] = 2 / (near - far);
  dst[11] = 0;
  dst[12] = (left + right) / (left - right);
  dst[13] = (bottom + top) / (bottom - top);
  dst[14] = (near + far) / (near - far);
  dst[15] = 1;

  return dst;
};

export const getFrustumArgumentsOnMatrix = (projectionMatrix: NumArr) => {
  const inverseProjectionMatrix = inverse(projectionMatrix);
  const ltn = positionTransform([-1, 1, -1], inverseProjectionMatrix);
  const rbn = positionTransform([1, -1, -1], inverseProjectionMatrix);
  const ccf = positionTransform([0, 0, 1], inverseProjectionMatrix);

  const [left, top, near] = ltn;
  const [right, bottom] = rbn;
  const far = ccf[2];

  return {
    left,
    top,
    right,
    bottom,
    near,
    far,
  };
};

export const frustum = (
  left: number,
  right: number,
  bottom: number,
  top: number,
  near: number,
  far: number
) => {
  const dst = new Float32Array(16);

  var dx = right - left;
  var dy = top - bottom;
  var dz = far - near;

  dst[0] = (2 * near) / dx;
  dst[1] = 0;
  dst[2] = 0;
  dst[3] = 0;
  dst[4] = 0;
  dst[5] = (2 * near) / dy;
  dst[6] = 0;
  dst[7] = 0;
  dst[8] = (left + right) / dx;
  dst[9] = (top + bottom) / dy;
  dst[10] = -(far + near) / dz;
  dst[11] = -1;
  dst[12] = 0;
  dst[13] = 0;
  dst[14] = (-2 * near * far) / dz;
  dst[15] = 0;

  return dst;
};

export const makeZToWMatrix = (fudgeFactor: number) => [
  1,
  0,
  0,
  0,
  0,
  1,
  0,
  0,
  0,
  0,
  1,
  fudgeFactor,
  0,
  0,
  0,
  1,
];

export const translate = (tx: number, ty: number, tz: number) => [
  1,
  0,
  0,
  0,
  0,
  1,
  0,
  0,
  0,
  0,
  1,
  0,
  tx,
  ty,
  tz,
  1,
];

export const rotateX = (angleInRadians: number) => {
  const s = Math.sin(angleInRadians);
  const c = Math.cos(angleInRadians);

  return [1, 0, 0, 0, 0, c, s, 0, 0, -s, c, 0, 0, 0, 0, 1];
};

export const rotateY = (angleInRadians: number) => {
  const s = Math.sin(angleInRadians);
  const c = Math.cos(angleInRadians);

  return [c, 0, -s, 0, 0, 1, 0, 0, s, 0, c, 0, 0, 0, 0, 1];
};

export const rotateZ = (angleInRadians: number) => {
  const s = Math.sin(angleInRadians);
  const c = Math.cos(angleInRadians);

  return [c, s, 0, 0, -s, c, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];
};

export const scale = (sx: number, sy: number, sz: number) => [
  sx,
  0,
  0,
  0,
  0,
  sy,
  0,
  0,
  0,
  0,
  sz,
  0,
  0,
  0,
  0,
  1,
];

// 正交
export const projection = (width: number, height: number, depth: number) => [
  2 / width,
  0,
  0,
  0,
  0,
  -2 / height,
  0,
  0,
  0,
  0,
  2 / depth,
  0,
  -1,
  1,
  0,
  1,
];

// 根据三维bound转化，正交形式
export const orthogonal = (
  left: number,
  right: number,
  top: number,
  bottom: number,
  near: number,
  far: number
) => [
  2 / (right - left),
  0,
  0,
  0,
  0,
  2 / (bottom - top),
  0,
  0,
  0,
  0,
  2 / (far - near),
  0,
  (left + right) / (left - right),
  (top + bottom) / (top - bottom),
  (far + near) / (near - far),
  1,
];

export const perspective = (
  l: number,
  r: number,
  t: number,
  b: number,
  n: number,
  f: number
) => [
  (2 * n) / (r - l),
  0,
  0,
  0,
  0,
  (2 * n) / (b - t),
  0,
  0,
  (l + r) / (l - r),
  (b + t) / (t - b),
  2 / (f - n),
  1,
  0,
  0,
  -(f + n) / (n - f),
  0,
];

// 正中间投影 l r 和 t b对称
export const straightPerspective = (w: number, h: number, n: number, f: number) => {
  return [
    (2 * n) / w,
    0,
    0,
    0,
    0,
    (-2 * n) / h,
    0,
    0,
    0,
    0,
    2 / (f - n),
    1,
    0,
    0,
    -(f + n) / (n - f),
    0,
  ];
};

/**
 * @param fieldOfViewInRadians 可视角度
 * @param aspect w / h 比例
 * @param near 近面
 * @param far 远面
 */
export const straightPerspective1 = (
  fieldOfViewInRadians: number,
  aspect: number,
  near: number,
  far: number
) => {
  // const a = Math.atan((Math.PI  - fieldOfViewInRadians) / 2)

  // return [
  //   a/aspect, 0, 0,           0,
  //   0,  -a, 0,           0,
  //   0,   0, 1/(far-near),     1,
  //   0,   0, -(near)/(far-near), 0
  // ]
  var f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewInRadians);
  var rangeInv = 1.0 / (near - far);

  return [
    f / aspect,
    0,
    0,
    0,
    0,
    f,
    0,
    0,
    0,
    0,
    (near + far) * rangeInv,
    -1,
    0,
    0,
    near * far * rangeInv * 2,
    0,
  ];
};

export const multiply = (...matrixs: NumArr[]): NumArr => {
  if (matrixs.length === 1) {
    return matrixs[0];
  }

  const radio = 4;
  const count = radio * radio;
  const result: number[] = [];

  for (let i = 0; i < count; i++) {
    const row = Math.floor(i / radio);
    const column = i % radio;

    let currentResult = 0;
    for (let offset = 0; offset < radio; offset++) {
      const rowIndex = row * radio + offset;
      const columnIndex = column + offset * radio;
      currentResult += matrixs[1][rowIndex] * matrixs[0][columnIndex];
    }
    result[i] = currentResult;
  }

  if (matrixs.length === 2) {
    return result;
  } else {
    return multiply(result, ...matrixs.slice(2));
  }
};

export const positionTransform = (pos: NumArr, matrix: number[]) => {
  const radio = 4;
  const w =
    pos[0] * matrix[3] +
    pos[1] * matrix[radio + 3] +
    pos[2] * matrix[radio * 2 + 3] +
    matrix[radio * 3 + 3];
  return [
    (pos[0] * matrix[0] +
      pos[1] * matrix[radio] +
      pos[2] * matrix[radio * 2] +
      matrix[radio * 3]) /
      w,
    (pos[0] * matrix[1] +
      pos[1] * matrix[radio + 1] +
      pos[2] * matrix[radio * 2 + 1] +
      matrix[radio * 3 + 1]) /
      w,
    (pos[0] * matrix[2] +
      pos[1] * matrix[radio + 2] +
      pos[2] * matrix[radio * 2 + 2] +
      matrix[radio * 3 + 2]) /
      w,
  ];
};

export const addVectors = (a: NumArr, b: NumArr, v: NumArr = []) => {
  v[0] = a[0] + b[0];
  v[1] = a[1] + b[1];
  v[2] = a[2] + b[2];
  return v;
};

export const subtractVectors = (a: NumArr, b: NumArr) => [
  a[0] - b[0],
  a[1] - b[1],
  a[2] - b[2],
];

export const scaleVector = (a: NumArr, b: number) => [a[0] * b, a[1] * b, a[2] * b];

export const normalVector = (v: NumArr, cv: NumArr = []) => {
  const [x, y, z] = v;
  const len = Math.sqrt(x * x + y * y + z * z);
  if (len > 0) {
    cv[0] = x / len;
    cv[1] = y / len;
    cv[2] = z / len;
  } else {
    cv[0] = 0;
    cv[1] = 0;
    cv[2] = 0;
  }
  return cv;
};

// 向量叉乘，叉乘结果向量必然同事垂直两个向量
export const cross = (a: NumArr, b: NumArr) => [
  a[1] * b[2] - a[2] * b[1],
  a[2] * b[0] - a[0] * b[2],
  a[0] * b[1] - a[1] * b[0],
];

// 对准一个目标（实际上是制作一个矩阵，将target扭转到cameraPosition）
export const lookAt = (cameraPosition: number[], target: number[], up: number[]) => {
  // camera是正对-z轴的 所以需要反向
  const zAxis = normalVector(subtractVectors(cameraPosition, target));
  // 相对于zAxis做出x朝向，注意顺序不能反，因为三维有两个垂直朝向，通过叉乘通过顺序确认
  const xAxis = normalVector(cross(up, zAxis));
  const yAxis = normalVector(cross(zAxis, xAxis));

  return [...xAxis, 0, ...yAxis, 0, ...zAxis, 0, ...cameraPosition, 1];
};

export const dot = (v1: NumArr, v2: NumArr) =>
  v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];

export const inverse = (m: NumArr) => {
  var m00 = m[0 * 4 + 0];
  var m01 = m[0 * 4 + 1];
  var m02 = m[0 * 4 + 2];
  var m03 = m[0 * 4 + 3];
  var m10 = m[1 * 4 + 0];
  var m11 = m[1 * 4 + 1];
  var m12 = m[1 * 4 + 2];
  var m13 = m[1 * 4 + 3];
  var m20 = m[2 * 4 + 0];
  var m21 = m[2 * 4 + 1];
  var m22 = m[2 * 4 + 2];
  var m23 = m[2 * 4 + 3];
  var m30 = m[3 * 4 + 0];
  var m31 = m[3 * 4 + 1];
  var m32 = m[3 * 4 + 2];
  var m33 = m[3 * 4 + 3];
  var tmp_0 = m22 * m33;
  var tmp_1 = m32 * m23;
  var tmp_2 = m12 * m33;
  var tmp_3 = m32 * m13;
  var tmp_4 = m12 * m23;
  var tmp_5 = m22 * m13;
  var tmp_6 = m02 * m33;
  var tmp_7 = m32 * m03;
  var tmp_8 = m02 * m23;
  var tmp_9 = m22 * m03;
  var tmp_10 = m02 * m13;
  var tmp_11 = m12 * m03;
  var tmp_12 = m20 * m31;
  var tmp_13 = m30 * m21;
  var tmp_14 = m10 * m31;
  var tmp_15 = m30 * m11;
  var tmp_16 = m10 * m21;
  var tmp_17 = m20 * m11;
  var tmp_18 = m00 * m31;
  var tmp_19 = m30 * m01;
  var tmp_20 = m00 * m21;
  var tmp_21 = m20 * m01;
  var tmp_22 = m00 * m11;
  var tmp_23 = m10 * m01;

  var t0 =
    tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31 - (tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);
  var t1 =
    tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31 - (tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);
  var t2 =
    tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31 - (tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);
  var t3 =
    tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21 - (tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);

  var d = 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);

  return [
    d * t0,
    d * t1,
    d * t2,
    d * t3,
    d *
      (tmp_1 * m10 +
        tmp_2 * m20 +
        tmp_5 * m30 -
        (tmp_0 * m10 + tmp_3 * m20 + tmp_4 * m30)),
    d *
      (tmp_0 * m00 +
        tmp_7 * m20 +
        tmp_8 * m30 -
        (tmp_1 * m00 + tmp_6 * m20 + tmp_9 * m30)),
    d *
      (tmp_3 * m00 +
        tmp_6 * m10 +
        tmp_11 * m30 -
        (tmp_2 * m00 + tmp_7 * m10 + tmp_10 * m30)),
    d *
      (tmp_4 * m00 +
        tmp_9 * m10 +
        tmp_10 * m20 -
        (tmp_5 * m00 + tmp_8 * m10 + tmp_11 * m20)),
    d *
      (tmp_12 * m13 +
        tmp_15 * m23 +
        tmp_16 * m33 -
        (tmp_13 * m13 + tmp_14 * m23 + tmp_17 * m33)),
    d *
      (tmp_13 * m03 +
        tmp_18 * m23 +
        tmp_21 * m33 -
        (tmp_12 * m03 + tmp_19 * m23 + tmp_20 * m33)),
    d *
      (tmp_14 * m03 +
        tmp_19 * m13 +
        tmp_22 * m33 -
        (tmp_15 * m03 + tmp_18 * m13 + tmp_23 * m33)),
    d *
      (tmp_17 * m03 +
        tmp_20 * m13 +
        tmp_23 * m23 -
        (tmp_16 * m03 + tmp_21 * m13 + tmp_22 * m23)),
    d *
      (tmp_14 * m22 +
        tmp_17 * m32 +
        tmp_13 * m12 -
        (tmp_16 * m32 + tmp_12 * m12 + tmp_15 * m22)),
    d *
      (tmp_20 * m32 +
        tmp_12 * m02 +
        tmp_19 * m22 -
        (tmp_18 * m22 + tmp_21 * m32 + tmp_13 * m02)),
    d *
      (tmp_18 * m12 +
        tmp_23 * m32 +
        tmp_15 * m02 -
        (tmp_22 * m32 + tmp_14 * m02 + tmp_19 * m12)),
    d *
      (tmp_22 * m22 +
        tmp_16 * m02 +
        tmp_21 * m12 -
        (tmp_20 * m12 + tmp_23 * m22 + tmp_17 * m02)),
  ];
};