helpers.curve.ts

import {almostEquals, distanceBetweenPoints, sign} from './helpers.math.js';
import {_isPointInArea} from './helpers.canvas.js';
import type {ChartArea} from '../types/index.js';
import type {SplinePoint} from '../types/geometric.js';

const EPSILON = Number.EPSILON || 1e-14;

type OptionalSplinePoint = SplinePoint | false
const getPoint = (points: SplinePoint[], i: number): OptionalSplinePoint => i < points.length && !points[i].skip && points[i];
const getValueAxis = (indexAxis: 'x' | 'y') => indexAxis === 'x' ? 'y' : 'x';

export function splineCurve(
  firstPoint: SplinePoint,
  middlePoint: SplinePoint,
  afterPoint: SplinePoint,
  t: number
): {
    previous: SplinePoint
    next: SplinePoint
  } {
  // Props to Rob Spencer at scaled innovation for his post on splining between points
  // http://scaledinnovation.com/analytics/splines/aboutSplines.html

  // This function must also respect "skipped" points

  const previous = firstPoint.skip ? middlePoint : firstPoint;
  const current = middlePoint;
  const next = afterPoint.skip ? middlePoint : afterPoint;
  const d01 = distanceBetweenPoints(current, previous);
  const d12 = distanceBetweenPoints(next, current);

  let s01 = d01 / (d01 + d12);
  let s12 = d12 / (d01 + d12);

  // If all points are the same, s01 & s02 will be inf
  s01 = isNaN(s01) ? 0 : s01;
  s12 = isNaN(s12) ? 0 : s12;

  const fa = t * s01; // scaling factor for triangle Ta
  const fb = t * s12;

  return {
    previous: {
      x: current.x - fa * (next.x - previous.x),
      y: current.y - fa * (next.y - previous.y)
    },
    next: {
      x: current.x + fb * (next.x - previous.x),
      y: current.y + fb * (next.y - previous.y)
    }
  };
}

/**
 * Adjust tangents to ensure monotonic properties
 */
function monotoneAdjust(points: SplinePoint[], deltaK: number[], mK: number[]) {
  const pointsLen = points.length;

  let alphaK: number, betaK: number, tauK: number, squaredMagnitude: number, pointCurrent: OptionalSplinePoint;
  let pointAfter = getPoint(points, 0);
  for (let i = 0; i < pointsLen - 1; ++i) {
    pointCurrent = pointAfter;
    pointAfter = getPoint(points, i + 1);
    if (!pointCurrent || !pointAfter) {
      continue;
    }

    if (almostEquals(deltaK[i], 0, EPSILON)) {
      mK[i] = mK[i + 1] = 0;
      continue;
    }

    alphaK = mK[i] / deltaK[i];
    betaK = mK[i + 1] / deltaK[i];
    squaredMagnitude = Math.pow(alphaK, 2) + Math.pow(betaK, 2);
    if (squaredMagnitude <= 9) {
      continue;
    }

    tauK = 3 / Math.sqrt(squaredMagnitude);
    mK[i] = alphaK * tauK * deltaK[i];
    mK[i + 1] = betaK * tauK * deltaK[i];
  }
}

function monotoneCompute(points: SplinePoint[], mK: number[], indexAxis: 'x' | 'y' = 'x') {
  const valueAxis = getValueAxis(indexAxis);
  const pointsLen = points.length;
  let delta: number, pointBefore: OptionalSplinePoint, pointCurrent: OptionalSplinePoint;
  let pointAfter = getPoint(points, 0);

  for (let i = 0; i < pointsLen; ++i) {
    pointBefore = pointCurrent;
    pointCurrent = pointAfter;
    pointAfter = getPoint(points, i + 1);
    if (!pointCurrent) {
      continue;
    }

    const iPixel = pointCurrent[indexAxis];
    const vPixel = pointCurrent[valueAxis];
    if (pointBefore) {
      delta = (iPixel - pointBefore[indexAxis]) / 3;
      pointCurrent[`cp1${indexAxis}`] = iPixel - delta;
      pointCurrent[`cp1${valueAxis}`] = vPixel - delta * mK[i];
    }
    if (pointAfter) {
      delta = (pointAfter[indexAxis] - iPixel) / 3;
      pointCurrent[`cp2${indexAxis}`] = iPixel + delta;
      pointCurrent[`cp2${valueAxis}`] = vPixel + delta * mK[i];
    }
  }
}

/**
 * This function calculates Bézier control points in a similar way than |splineCurve|,
 * but preserves monotonicity of the provided data and ensures no local extremums are added
 * between the dataset discrete points due to the interpolation.
 * See : https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
 */
export function splineCurveMonotone(points: SplinePoint[], indexAxis: 'x' | 'y' = 'x') {
  const valueAxis = getValueAxis(indexAxis);
  const pointsLen = points.length;
  const deltaK: number[] = Array(pointsLen).fill(0);
  const mK: number[] = Array(pointsLen);

  // Calculate slopes (deltaK) and initialize tangents (mK)
  let i, pointBefore: OptionalSplinePoint, pointCurrent: OptionalSplinePoint;
  let pointAfter = getPoint(points, 0);

  for (i = 0; i < pointsLen; ++i) {
    pointBefore = pointCurrent;
    pointCurrent = pointAfter;
    pointAfter = getPoint(points, i + 1);
    if (!pointCurrent) {
      continue;
    }

    if (pointAfter) {
      const slopeDelta = pointAfter[indexAxis] - pointCurrent[indexAxis];

      // In the case of two points that appear at the same x pixel, slopeDeltaX is 0
      deltaK[i] = slopeDelta !== 0 ? (pointAfter[valueAxis] - pointCurrent[valueAxis]) / slopeDelta : 0;
    }
    mK[i] = !pointBefore ? deltaK[i]
      : !pointAfter ? deltaK[i - 1]
        : (sign(deltaK[i - 1]) !== sign(deltaK[i])) ? 0
          : (deltaK[i - 1] + deltaK[i]) / 2;
  }

  monotoneAdjust(points, deltaK, mK);

  monotoneCompute(points, mK, indexAxis);
}

function capControlPoint(pt: number, min: number, max: number) {
  return Math.max(Math.min(pt, max), min);
}

function capBezierPoints(points: SplinePoint[], area: ChartArea) {
  let i, ilen, point, inArea, inAreaPrev;
  let inAreaNext = _isPointInArea(points[0], area);
  for (i = 0, ilen = points.length; i < ilen; ++i) {
    inAreaPrev = inArea;
    inArea = inAreaNext;
    inAreaNext = i < ilen - 1 && _isPointInArea(points[i + 1], area);
    if (!inArea) {
      continue;
    }
    point = points[i];
    if (inAreaPrev) {
      point.cp1x = capControlPoint(point.cp1x, area.left, area.right);
      point.cp1y = capControlPoint(point.cp1y, area.top, area.bottom);
    }
    if (inAreaNext) {
      point.cp2x = capControlPoint(point.cp2x, area.left, area.right);
      point.cp2y = capControlPoint(point.cp2y, area.top, area.bottom);
    }
  }
}

/**
 * @private
 */
export function _updateBezierControlPoints(
  points: SplinePoint[],
  options,
  area: ChartArea,
  loop: boolean,
  indexAxis: 'x' | 'y'
) {
  let i: number, ilen: number, point: SplinePoint, controlPoints: ReturnType<typeof splineCurve>;

  // Only consider points that are drawn in case the spanGaps option is used
  if (options.spanGaps) {
    points = points.filter((pt) => !pt.skip);
  }

  if (options.cubicInterpolationMode === 'monotone') {
    splineCurveMonotone(points, indexAxis);
  } else {
    let prev = loop ? points[points.length - 1] : points[0];
    for (i = 0, ilen = points.length; i < ilen; ++i) {
      point = points[i];
      controlPoints = splineCurve(
        prev,
        point,
        points[Math.min(i + 1, ilen - (loop ? 0 : 1)) % ilen],
        options.tension
      );
      point.cp1x = controlPoints.previous.x;
      point.cp1y = controlPoints.previous.y;
      point.cp2x = controlPoints.next.x;
      point.cp2y = controlPoints.next.y;
      prev = point;
    }
  }

  if (options.capBezierPoints) {
    capBezierPoints(points, area);
  }
}