curve.js

var _vector = require("./vector");

var v2Create = _vector.create;
var v2DistSquare = _vector.distSquare;

/**
 * 曲线辅助模块
 * @module zrender/core/curve
 * @author pissang(https://www.github.com/pissang)
 */
var mathPow = Math.pow;
var mathSqrt = Math.sqrt;
var EPSILON = 1e-8;
var EPSILON_NUMERIC = 1e-4;
var THREE_SQRT = mathSqrt(3);
var ONE_THIRD = 1 / 3; // 临时变量

var _v0 = v2Create();

var _v1 = v2Create();

var _v2 = v2Create();

function isAroundZero(val) {
  return val > -EPSILON && val < EPSILON;
}

function isNotAroundZero(val) {
  return val > EPSILON || val < -EPSILON;
}
/**
 * 计算三次贝塞尔值
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} p3
 * @param  {number} t
 * @return {number}
 */


function cubicAt(p0, p1, p2, p3, t) {
  var onet = 1 - t;
  return onet * onet * (onet * p0 + 3 * t * p1) + t * t * (t * p3 + 3 * onet * p2);
}
/**
 * 计算三次贝塞尔导数值
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} p3
 * @param  {number} t
 * @return {number}
 */


function cubicDerivativeAt(p0, p1, p2, p3, t) {
  var onet = 1 - t;
  return 3 * (((p1 - p0) * onet + 2 * (p2 - p1) * t) * onet + (p3 - p2) * t * t);
}
/**
 * 计算三次贝塞尔方程根，使用盛金公式
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} p3
 * @param  {number} val
 * @param  {Array.<number>} roots
 * @return {number} 有效根数目
 */


function cubicRootAt(p0, p1, p2, p3, val, roots) {
  // Evaluate roots of cubic functions
  var a = p3 + 3 * (p1 - p2) - p0;
  var b = 3 * (p2 - p1 * 2 + p0);
  var c = 3 * (p1 - p0);
  var d = p0 - val;
  var A = b * b - 3 * a * c;
  var B = b * c - 9 * a * d;
  var C = c * c - 3 * b * d;
  var n = 0;

  if (isAroundZero(A) && isAroundZero(B)) {
    if (isAroundZero(b)) {
      roots[0] = 0;
    } else {
      var t1 = -c / b; //t1, t2, t3, b is not zero

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }
    }
  } else {
    var disc = B * B - 4 * A * C;

    if (isAroundZero(disc)) {
      var K = B / A;
      var t1 = -b / a + K; // t1, a is not zero

      var t2 = -K / 2; // t2, t3

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }

      if (t2 >= 0 && t2 <= 1) {
        roots[n++] = t2;
      }
    } else if (disc > 0) {
      var discSqrt = mathSqrt(disc);
      var Y1 = A * b + 1.5 * a * (-B + discSqrt);
      var Y2 = A * b + 1.5 * a * (-B - discSqrt);

      if (Y1 < 0) {
        Y1 = -mathPow(-Y1, ONE_THIRD);
      } else {
        Y1 = mathPow(Y1, ONE_THIRD);
      }

      if (Y2 < 0) {
        Y2 = -mathPow(-Y2, ONE_THIRD);
      } else {
        Y2 = mathPow(Y2, ONE_THIRD);
      }

      var t1 = (-b - (Y1 + Y2)) / (3 * a);

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }
    } else {
      var T = (2 * A * b - 3 * a * B) / (2 * mathSqrt(A * A * A));
      var theta = Math.acos(T) / 3;
      var ASqrt = mathSqrt(A);
      var tmp = Math.cos(theta);
      var t1 = (-b - 2 * ASqrt * tmp) / (3 * a);
      var t2 = (-b + ASqrt * (tmp + THREE_SQRT * Math.sin(theta))) / (3 * a);
      var t3 = (-b + ASqrt * (tmp - THREE_SQRT * Math.sin(theta))) / (3 * a);

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }

      if (t2 >= 0 && t2 <= 1) {
        roots[n++] = t2;
      }

      if (t3 >= 0 && t3 <= 1) {
        roots[n++] = t3;
      }
    }
  }

  return n;
}
/**
 * 计算三次贝塞尔方程极限值的位置
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} p3
 * @param  {Array.<number>} extrema
 * @return {number} 有效数目
 */


function cubicExtrema(p0, p1, p2, p3, extrema) {
  var b = 6 * p2 - 12 * p1 + 6 * p0;
  var a = 9 * p1 + 3 * p3 - 3 * p0 - 9 * p2;
  var c = 3 * p1 - 3 * p0;
  var n = 0;

  if (isAroundZero(a)) {
    if (isNotAroundZero(b)) {
      var t1 = -c / b;

      if (t1 >= 0 && t1 <= 1) {
        extrema[n++] = t1;
      }
    }
  } else {
    var disc = b * b - 4 * a * c;

    if (isAroundZero(disc)) {
      extrema[0] = -b / (2 * a);
    } else if (disc > 0) {
      var discSqrt = mathSqrt(disc);
      var t1 = (-b + discSqrt) / (2 * a);
      var t2 = (-b - discSqrt) / (2 * a);

      if (t1 >= 0 && t1 <= 1) {
        extrema[n++] = t1;
      }

      if (t2 >= 0 && t2 <= 1) {
        extrema[n++] = t2;
      }
    }
  }

  return n;
}
/**
 * 细分三次贝塞尔曲线
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} p3
 * @param  {number} t
 * @param  {Array.<number>} out
 */


function cubicSubdivide(p0, p1, p2, p3, t, out) {
  var p01 = (p1 - p0) * t + p0;
  var p12 = (p2 - p1) * t + p1;
  var p23 = (p3 - p2) * t + p2;
  var p012 = (p12 - p01) * t + p01;
  var p123 = (p23 - p12) * t + p12;
  var p0123 = (p123 - p012) * t + p012; // Seg0

  out[0] = p0;
  out[1] = p01;
  out[2] = p012;
  out[3] = p0123; // Seg1

  out[4] = p0123;
  out[5] = p123;
  out[6] = p23;
  out[7] = p3;
}
/**
 * 投射点到三次贝塞尔曲线上，返回投射距离。
 * 投射点有可能会有一个或者多个，这里只返回其中距离最短的一个。
 * @param {number} x0
 * @param {number} y0
 * @param {number} x1
 * @param {number} y1
 * @param {number} x2
 * @param {number} y2
 * @param {number} x3
 * @param {number} y3
 * @param {number} x
 * @param {number} y
 * @param {Array.<number>} [out] 投射点
 * @return {number}
 */


function cubicProjectPoint(x0, y0, x1, y1, x2, y2, x3, y3, x, y, out) {
  // http://pomax.github.io/bezierinfo/#projections
  var t;
  var interval = 0.005;
  var d = Infinity;
  var prev;
  var next;
  var d1;
  var d2;
  _v0[0] = x;
  _v0[1] = y; // 先粗略估计一下可能的最小距离的 t 值
  // PENDING

  for (var _t = 0; _t < 1; _t += 0.05) {
    _v1[0] = cubicAt(x0, x1, x2, x3, _t);
    _v1[1] = cubicAt(y0, y1, y2, y3, _t);
    d1 = v2DistSquare(_v0, _v1);

    if (d1 < d) {
      t = _t;
      d = d1;
    }
  }

  d = Infinity; // At most 32 iteration

  for (var i = 0; i < 32; i++) {
    if (interval < EPSILON_NUMERIC) {
      break;
    }

    prev = t - interval;
    next = t + interval; // t - interval

    _v1[0] = cubicAt(x0, x1, x2, x3, prev);
    _v1[1] = cubicAt(y0, y1, y2, y3, prev);
    d1 = v2DistSquare(_v1, _v0);

    if (prev >= 0 && d1 < d) {
      t = prev;
      d = d1;
    } else {
      // t + interval
      _v2[0] = cubicAt(x0, x1, x2, x3, next);
      _v2[1] = cubicAt(y0, y1, y2, y3, next);
      d2 = v2DistSquare(_v2, _v0);

      if (next <= 1 && d2 < d) {
        t = next;
        d = d2;
      } else {
        interval *= 0.5;
      }
    }
  } // t


  if (out) {
    out[0] = cubicAt(x0, x1, x2, x3, t);
    out[1] = cubicAt(y0, y1, y2, y3, t);
  } // console.log(interval, i);


  return mathSqrt(d);
}
/**
 * 计算二次方贝塞尔值
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} t
 * @return {number}
 */


function quadraticAt(p0, p1, p2, t) {
  var onet = 1 - t;
  return onet * (onet * p0 + 2 * t * p1) + t * t * p2;
}
/**
 * 计算二次方贝塞尔导数值
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} t
 * @return {number}
 */


function quadraticDerivativeAt(p0, p1, p2, t) {
  return 2 * ((1 - t) * (p1 - p0) + t * (p2 - p1));
}
/**
 * 计算二次方贝塞尔方程根
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} t
 * @param  {Array.<number>} roots
 * @return {number} 有效根数目
 */


function quadraticRootAt(p0, p1, p2, val, roots) {
  var a = p0 - 2 * p1 + p2;
  var b = 2 * (p1 - p0);
  var c = p0 - val;
  var n = 0;

  if (isAroundZero(a)) {
    if (isNotAroundZero(b)) {
      var t1 = -c / b;

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }
    }
  } else {
    var disc = b * b - 4 * a * c;

    if (isAroundZero(disc)) {
      var t1 = -b / (2 * a);

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }
    } else if (disc > 0) {
      var discSqrt = mathSqrt(disc);
      var t1 = (-b + discSqrt) / (2 * a);
      var t2 = (-b - discSqrt) / (2 * a);

      if (t1 >= 0 && t1 <= 1) {
        roots[n++] = t1;
      }

      if (t2 >= 0 && t2 <= 1) {
        roots[n++] = t2;
      }
    }
  }

  return n;
}
/**
 * 计算二次贝塞尔方程极限值
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @return {number}
 */


function quadraticExtremum(p0, p1, p2) {
  var divider = p0 + p2 - 2 * p1;

  if (divider === 0) {
    // p1 is center of p0 and p2
    return 0.5;
  } else {
    return (p0 - p1) / divider;
  }
}
/**
 * 细分二次贝塞尔曲线
 * @memberOf module:zrender/core/curve
 * @param  {number} p0
 * @param  {number} p1
 * @param  {number} p2
 * @param  {number} t
 * @param  {Array.<number>} out
 */


function quadraticSubdivide(p0, p1, p2, t, out) {
  var p01 = (p1 - p0) * t + p0;
  var p12 = (p2 - p1) * t + p1;
  var p012 = (p12 - p01) * t + p01; // Seg0

  out[0] = p0;
  out[1] = p01;
  out[2] = p012; // Seg1

  out[3] = p012;
  out[4] = p12;
  out[5] = p2;
}
/**
 * 投射点到二次贝塞尔曲线上，返回投射距离。
 * 投射点有可能会有一个或者多个，这里只返回其中距离最短的一个。
 * @param {number} x0
 * @param {number} y0
 * @param {number} x1
 * @param {number} y1
 * @param {number} x2
 * @param {number} y2
 * @param {number} x
 * @param {number} y
 * @param {Array.<number>} out 投射点
 * @return {number}
 */


function quadraticProjectPoint(x0, y0, x1, y1, x2, y2, x, y, out) {
  // http://pomax.github.io/bezierinfo/#projections
  var t;
  var interval = 0.005;
  var d = Infinity;
  _v0[0] = x;
  _v0[1] = y; // 先粗略估计一下可能的最小距离的 t 值
  // PENDING

  for (var _t = 0; _t < 1; _t += 0.05) {
    _v1[0] = quadraticAt(x0, x1, x2, _t);
    _v1[1] = quadraticAt(y0, y1, y2, _t);
    var d1 = v2DistSquare(_v0, _v1);

    if (d1 < d) {
      t = _t;
      d = d1;
    }
  }

  d = Infinity; // At most 32 iteration

  for (var i = 0; i < 32; i++) {
    if (interval < EPSILON_NUMERIC) {
      break;
    }

    var prev = t - interval;
    var next = t + interval; // t - interval

    _v1[0] = quadraticAt(x0, x1, x2, prev);
    _v1[1] = quadraticAt(y0, y1, y2, prev);
    var d1 = v2DistSquare(_v1, _v0);

    if (prev >= 0 && d1 < d) {
      t = prev;
      d = d1;
    } else {
      // t + interval
      _v2[0] = quadraticAt(x0, x1, x2, next);
      _v2[1] = quadraticAt(y0, y1, y2, next);
      var d2 = v2DistSquare(_v2, _v0);

      if (next <= 1 && d2 < d) {
        t = next;
        d = d2;
      } else {
        interval *= 0.5;
      }
    }
  } // t


  if (out) {
    out[0] = quadraticAt(x0, x1, x2, t);
    out[1] = quadraticAt(y0, y1, y2, t);
  } // console.log(interval, i);


  return mathSqrt(d);
}

exports.cubicAt = cubicAt;
exports.cubicDerivativeAt = cubicDerivativeAt;
exports.cubicRootAt = cubicRootAt;
exports.cubicExtrema = cubicExtrema;
exports.cubicSubdivide = cubicSubdivide;
exports.cubicProjectPoint = cubicProjectPoint;
exports.quadraticAt = quadraticAt;
exports.quadraticDerivativeAt = quadraticDerivativeAt;
exports.quadraticRootAt = quadraticRootAt;
exports.quadraticExtremum = quadraticExtremum;
exports.quadraticSubdivide = quadraticSubdivide;
exports.quadraticProjectPoint = quadraticProjectPoint;