dc-sdk/modules/utils/PlotUtil.js

/**
 * @Author: Caven
 * @Date: 2020-08-21 18:05:39
 */

const TWO_PI = Math.PI * 2
const FITTING_COUNT = 100
const ZERO_TOLERANCE = 0.0001

class PlotUtil {
  /**
   * @param pnt1
   * @param pnt2
   * @returns {number}
   */
  static distance(pnt1, pnt2) {
    return Math.sqrt(
      Math.pow(pnt1[0] - pnt2[0], 2) + Math.pow(pnt1[1] - pnt2[1], 2)
    )
  }

  /**
   * @param points
   * @returns {number}
   */
  static wholeDistance(points) {
    let distance = 0
    for (let i = 0; i < points.length - 1; i++)
      distance += this.distance(points[i], points[i + 1])
    return distance
  }

  /**
   * @param points
   * @returns {number}
   */
  static getBaseLength(points) {
    return Math.pow(this.wholeDistance(points), 0.99)
  }

  /**
   * @param pnt1
   * @param pnt2
   * @returns {number[]}
   */
  static mid(pnt1, pnt2) {
    return [(pnt1[0] + pnt2[0]) / 2, (pnt1[1] + pnt2[1]) / 2]
  }

  /**
   * @param pnt1
   * @param pnt2
   * @param pnt3
   * @returns {[*, *]|[*, *]|[*, number]}
   */
  static getCircleCenterOfThreePoints(pnt1, pnt2, pnt3) {
    let pntA = [(pnt1[0] + pnt2[0]) / 2, (pnt1[1] + pnt2[1]) / 2]
    let pntB = [pntA[0] - pnt1[1] + pnt2[1], pntA[1] + pnt1[0] - pnt2[0]]
    let pntC = [(pnt1[0] + pnt3[0]) / 2, (pnt1[1] + pnt3[1]) / 2]
    let pntD = [pntC[0] - pnt1[1] + pnt3[1], pntC[1] + pnt1[0] - pnt3[0]]
    return this.getIntersectPoint(pntA, pntB, pntC, pntD)
  }

  /**
   * @param pntA
   * @param pntB
   * @param pntC
   * @param pntD
   * @returns {(*|number)[]|*[]}
   */
  static getIntersectPoint(pntA, pntB, pntC, pntD) {
    let x, y, f, e
    if (pntA[1] === pntB[1]) {
      f = (pntD[0] - pntC[0]) / (pntD[1] - pntC[1])
      x = f * (pntA[1] - pntC[1]) + pntC[0]
      y = pntA[1]
      return [x, y]
    }
    if (pntC[1] === pntD[1]) {
      e = (pntB[0] - pntA[0]) / (pntB[1] - pntA[1])
      x = e * (pntC[1] - pntA[1]) + pntA[0]
      y = pntC[1]
      return [x, y]
    }
    e = (pntB[0] - pntA[0]) / (pntB[1] - pntA[1])
    f = (pntD[0] - pntC[0]) / (pntD[1] - pntC[1])
    y = (e * pntA[1] - pntA[0] - f * pntC[1] + pntC[0]) / (e - f)
    x = e * y - e * pntA[1] + pntA[0]
    return [x, y]
  }

  /**
   * @param startPnt
   * @param endPnt
   * @returns {number}
   */
  static getAzimuth(startPnt, endPnt) {
    let azimuth
    let angle = Math.asin(
      Math.abs(endPnt[1] - startPnt[1]) / this.distance(startPnt, endPnt)
    )
    if (endPnt[1] >= startPnt[1] && endPnt[0] >= startPnt[0])
      azimuth = angle + Math.PI
    else if (endPnt[1] >= startPnt[1] && endPnt[0] < startPnt[0])
      azimuth = TWO_PI - angle
    else if (endPnt[1] < startPnt[1] && endPnt[0] < startPnt[0]) azimuth = angle
    else if (endPnt[1] < startPnt[1] && endPnt[0] >= startPnt[0])
      azimuth = Math.PI - angle
    return azimuth
  }

  /**
   * @param pntA
   * @param pntB
   * @param pntC
   * @returns {number}
   */
  static getAngleOfThreePoints(pntA, pntB, pntC) {
    let angle = this.getAzimuth(pntB, pntA) - this.getAzimuth(pntB, pntC)
    return angle < 0 ? angle + TWO_PI : angle
  }

  /**
   * @param pnt1
   * @param pnt2
   * @param pnt3
   * @returns {boolean}
   */
  static isClockWise(pnt1, pnt2, pnt3) {
    return (
      (pnt3[1] - pnt1[1]) * (pnt2[0] - pnt1[0]) >
      (pnt2[1] - pnt1[1]) * (pnt3[0] - pnt1[0])
    )
  }

  /**
   * @param t
   * @param startPnt
   * @param endPnt
   * @returns {*[]}
   */
  static getPointOnLine(t, startPnt, endPnt) {
    let x = startPnt[0] + t * (endPnt[0] - startPnt[0])
    let y = startPnt[1] + t * (endPnt[1] - startPnt[1])
    return [x, y]
  }

  /**
   * @param t
   * @param startPnt
   * @param cPnt1
   * @param cPnt2
   * @param endPnt
   * @returns {number[]}
   */
  static getCubicValue(t, startPnt, cPnt1, cPnt2, endPnt) {
    t = Math.max(Math.min(t, 1), 0)
    let tp = 1 - t
    let t2 = t * t
    let t3 = t2 * t
    let tp2 = tp * tp
    let tp3 = tp2 * tp
    let x =
      tp3 * startPnt[0] +
      3 * tp2 * t * cPnt1[0] +
      3 * tp * t2 * cPnt2[0] +
      t3 * endPnt[0]
    let y =
      tp3 * startPnt[1] +
      3 * tp2 * t * cPnt1[1] +
      3 * tp * t2 * cPnt2[1] +
      t3 * endPnt[1]
    return [x, y]
  }

  /**
   * @param startPnt
   * @param endPnt
   * @param angle
   * @param distance
   * @param clockWise
   * @returns {*[]}
   */
  static getThirdPoint(startPnt, endPnt, angle, distance, clockWise) {
    let azimuth = this.getAzimuth(startPnt, endPnt)
    let alpha = clockWise ? azimuth + angle : azimuth - angle
    let dx = distance * Math.cos(alpha)
    let dy = distance * Math.sin(alpha)
    return [endPnt[0] + dx, endPnt[1] + dy]
  }

  /**
   * @param center
   * @param radius
   * @param startAngle
   * @param endAngle
   * @returns {[]}
   */
  static getArcPoints(center, radius, startAngle, endAngle) {
    let x,
      y,
      pnts = []
    let angleDiff = endAngle - startAngle
    angleDiff = angleDiff < 0 ? angleDiff + TWO_PI : angleDiff
    for (let i = 0; i <= FITTING_COUNT; i++) {
      let angle = startAngle + (angleDiff * i) / FITTING_COUNT
      x = center[0] + radius * Math.cos(angle)
      y = center[1] + radius * Math.sin(angle)
      pnts.push([x, y])
    }
    return pnts
  }

  /**
   * @param t
   * @param pnt1
   * @param pnt2
   * @param pnt3
   * @returns {*[][]}
   */
  static getBisectorNormals(t, pnt1, pnt2, pnt3) {
    let normal = this.getNormal(pnt1, pnt2, pnt3)
    let dist = Math.sqrt(normal[0] * normal[0] + normal[1] * normal[1])
    let uX = normal[0] / dist
    let uY = normal[1] / dist
    let d1 = this.distance(pnt1, pnt2)
    let d2 = this.distance(pnt2, pnt3)
    let dt, x, y, bisectorNormalLeft, bisectorNormalRight
    if (dist > ZERO_TOLERANCE) {
      if (this.isClockWise(pnt1, pnt2, pnt3)) {
        dt = t * d1
        x = pnt2[0] - dt * uY
        y = pnt2[1] + dt * uX
        bisectorNormalRight = [x, y]
        dt = t * d2
        x = pnt2[0] + dt * uY
        y = pnt2[1] - dt * uX
        bisectorNormalLeft = [x, y]
      } else {
        dt = t * d1
        x = pnt2[0] + dt * uY
        y = pnt2[1] - dt * uX
        bisectorNormalRight = [x, y]
        dt = t * d2
        x = pnt2[0] - dt * uY
        y = pnt2[1] + dt * uX
        bisectorNormalLeft = [x, y]
      }
    } else {
      x = pnt2[0] + t * (pnt1[0] - pnt2[0])
      y = pnt2[1] + t * (pnt1[1] - pnt2[1])
      bisectorNormalRight = [x, y]
      x = pnt2[0] + t * (pnt3[0] - pnt2[0])
      y = pnt2[1] + t * (pnt3[1] - pnt2[1])
      bisectorNormalLeft = [x, y]
    }
    return [bisectorNormalRight, bisectorNormalLeft]
  }

  /**
   * @param pnt1
   * @param pnt2
   * @param pnt3
   * @returns {number[]}
   */
  static getNormal(pnt1, pnt2, pnt3) {
    let dX1 = pnt1[0] - pnt2[0]
    let dY1 = pnt1[1] - pnt2[1]
    let d1 = Math.sqrt(dX1 * dX1 + dY1 * dY1)
    dX1 /= d1
    dY1 /= d1

    let dX2 = pnt3[0] - pnt2[0]
    let dY2 = pnt3[1] - pnt2[1]
    let d2 = Math.sqrt(dX2 * dX2 + dY2 * dY2)
    dX2 /= d2
    dY2 /= d2

    let uX = dX1 + dX2
    let uY = dY1 + dY2
    return [uX, uY]
  }

  /**
   * @param t
   * @param controlPoints
   * @returns {[]}
   */
  static getCurvePoints(t, controlPoints) {
    let leftControl = this.getLeftMostControlPoint(t, controlPoints)
    let normals = [leftControl]
    let pnt1, pnt2, pnt3, normalPoints
    for (let i = 0; i < controlPoints.length - 2; i++) {
      pnt1 = controlPoints[i]
      pnt2 = controlPoints[i + 1]
      pnt3 = controlPoints[i + 2]
      normalPoints = this.getBisectorNormals(t, pnt1, pnt2, pnt3)
      normals = normals.concat(normalPoints)
    }
    let rightControl = this.getRightMostControlPoint(t, controlPoints)
    normals.push(rightControl)
    let points = []
    for (let i = 0; i < controlPoints.length - 1; i++) {
      pnt1 = controlPoints[i]
      pnt2 = controlPoints[i + 1]
      points.push(pnt1)
      for (let t = 0; t < FITTING_COUNT; t++) {
        let pnt = this.getCubicValue(
          t / FITTING_COUNT,
          pnt1,
          normals[i * 2],
          normals[i * 2 + 1],
          pnt2
        )
        points.push(pnt)
      }
      points.push(pnt2)
    }
    return points
  }

  /**
   * @param t
   * @param controlPoints
   * @returns {number[]}
   */
  static getLeftMostControlPoint(t, controlPoints) {
    let pnt1 = controlPoints[0]
    let pnt2 = controlPoints[1]
    let pnt3 = controlPoints[2]
    let pnts = this.getBisectorNormals(0, pnt1, pnt2, pnt3)
    let normalRight = pnts[0]
    let normal = this.getNormal(pnt1, pnt2, pnt3)
    let dist = Math.sqrt(normal[0] * normal[0] + normal[1] * normal[1])
    let controlX, controlY
    if (dist > ZERO_TOLERANCE) {
      let mid = this.mid(pnt1, pnt2)
      let pX = pnt1[0] - mid[0]
      let pY = pnt1[1] - mid[1]
      let d1 = this.distance(pnt1, pnt2)
      // normal at midpoint
      let n = 2.0 / d1
      let nX = -n * pY
      let nY = n * pX
      // upper triangle of symmetric transform matrix
      let a11 = nX * nX - nY * nY
      let a12 = 2 * nX * nY
      let a22 = nY * nY - nX * nX
      let dX = normalRight[0] - mid[0]
      let dY = normalRight[1] - mid[1]
      // coordinates of reflected vector
      controlX = mid[0] + a11 * dX + a12 * dY
      controlY = mid[1] + a12 * dX + a22 * dY
    } else {
      controlX = pnt1[0] + t * (pnt2[0] - pnt1[0])
      controlY = pnt1[1] + t * (pnt2[1] - pnt1[1])
    }
    return [controlX, controlY]
  }

  /**
   * @param t
   * @param controlPoints
   * @returns {number[]}
   */
  static getRightMostControlPoint(t, controlPoints) {
    let count = controlPoints.length
    let pnt1 = controlPoints[count - 3]
    let pnt2 = controlPoints[count - 2]
    let pnt3 = controlPoints[count - 1]
    let pnts = this.getBisectorNormals(0, pnt1, pnt2, pnt3)
    let normalLeft = pnts[1]
    let normal = this.getNormal(pnt1, pnt2, pnt3)
    let dist = Math.sqrt(normal[0] * normal[0] + normal[1] * normal[1])
    let controlX, controlY
    if (dist > ZERO_TOLERANCE) {
      let mid = this.mid(pnt2, pnt3)
      let pX = pnt3[0] - mid[0]
      let pY = pnt3[1] - mid[1]

      let d1 = this.distance(pnt2, pnt3)
      // normal at midpoint
      let n = 2.0 / d1
      let nX = -n * pY
      let nY = n * pX

      // upper triangle of symmetric transform matrix
      let a11 = nX * nX - nY * nY
      let a12 = 2 * nX * nY
      let a22 = nY * nY - nX * nX

      let dX = normalLeft[0] - mid[0]
      let dY = normalLeft[1] - mid[1]

      // coordinates of reflected vector
      controlX = mid[0] + a11 * dX + a12 * dY
      controlY = mid[1] + a12 * dX + a22 * dY
    } else {
      controlX = pnt3[0] + t * (pnt2[0] - pnt3[0])
      controlY = pnt3[1] + t * (pnt2[1] - pnt3[1])
    }
    return [controlX, controlY]
  }

  /**
   * @param points
   * @returns {[]|*}
   */
  static getBezierPoints(points) {
    if (points.length <= 2) return points
    let bezierPoints = []
    let n = points.length - 1
    for (let t = 0; t <= 1; t += 0.01) {
      let x = 0
      let y = 0
      for (let index = 0; index <= n; index++) {
        let factor = this.getBinomialFactor(n, index)
        let a = Math.pow(t, index)
        let b = Math.pow(1 - t, n - index)
        x += factor * a * b * points[index][0]
        y += factor * a * b * points[index][1]
      }
      bezierPoints.push([x, y])
    }
    bezierPoints.push(points[n])
    return bezierPoints
  }

  /**
   *
   * @param n
   * @param index
   * @returns {number}
   */
  static getBinomialFactor(n, index) {
    return (
      this.getFactorial(n) /
      (this.getFactorial(index) * this.getFactorial(n - index))
    )
  }

  /**
   * @param n
   * @returns {number}
   */
  static getFactorial(n) {
    if (n <= 1) return 1
    if (n === 2) return 2
    if (n === 3) return 6
    if (n === 4) return 24
    if (n === 5) return 120
    let result = 1
    for (let i = 1; i <= n; i++) result *= i
    return result
  }

  /**
   * @param points
   * @returns {[]|*}
   */
  static getQBSplinePoints(points) {
    if (points.length <= 2) return points
    let n = 2
    let bSplinePoints = []
    let m = points.length - n - 1
    bSplinePoints.push(points[0])
    for (let i = 0; i <= m; i++) {
      for (let t = 0; t <= 1; t += 0.05) {
        let x = 0
        let y = 0
        for (let k = 0; k <= n; k++) {
          let factor = this.getQuadricBSplineFactor(k, t)
          x += factor * points[i + k][0]
          y += factor * points[i + k][1]
        }
        bSplinePoints.push([x, y])
      }
    }
    bSplinePoints.push(points[points.length - 1])
    return bSplinePoints
  }

  /**
   * @param k
   * @param t
   * @returns {number}
   */
  static getQuadricBSplineFactor(k, t) {
    if (k === 0) return Math.pow(t - 1, 2) / 2
    if (k === 1) return (-2 * Math.pow(t, 2) + 2 * t + 1) / 2
    if (k === 2) return Math.pow(t, 2) / 2
    return 0
  }
}

export default PlotUtil