@kitware/vtk.js/Common/DataModel/CardinalSpline1D.js

Visualization Toolkit for the Web

import macro from '../../macros.js';
import vtkSpline1D from './Spline1D.js';
import { BoundaryCondition } from './Spline1D/Constants.js';

var VTK_EPSILON = 0.0001; // ----------------------------------------------------------------------------
// vtkCardinalSpline1D methods
// ----------------------------------------------------------------------------

function vtkCardinalSpline1D(publicAPI, model) {
  // Set our classname
  model.classHierarchy.push('vtkCardinalSpline1D'); // --------------------------------------------------------------------------

  publicAPI.computeCloseCoefficients = function (size, work, x, y) {
    if (!model.coefficients || model.coefficients.length !== 4 * size) {
      model.coefficients = new Float32Array(4 * size);
    }

    var N = size - 1;

    for (var k = 1; k < N; k++) {
      var _xlk = x[k] - x[k - 1];

      var _xlkp = x[k + 1] - x[k];

      model.coefficients[4 * k + 0] = _xlkp;
      model.coefficients[4 * k + 1] = 2 * (_xlkp + _xlk);
      model.coefficients[4 * k + 2] = _xlk;
      work[k] = 3.0 * (_xlkp * (y[k] - y[k - 1]) / _xlk + _xlk * (y[k + 1] - y[k]) / _xlkp);
    }

    var xlk = x[N] - x[N - 1];
    var xlkp = x[1] - x[0];
    model.coefficients[4 * N + 0] = xlkp;
    model.coefficients[4 * N + 1] = 2 * (xlkp + xlk);
    model.coefficients[4 * N + 2] = xlk;
    work[N] = 3 * (xlkp * (y[N] - y[N - 1]) / xlk + xlk * (y[1] - y[0]) / xlkp);
    var aN = model.coefficients[4 * N + 0];
    var bN = model.coefficients[4 * N + 1];
    var cN = model.coefficients[4 * N + 2];
    var dN = work[N]; // solve resulting set of equations.

    model.coefficients[4 * 0 + 2] = 0;
    work[0] = 0;
    model.coefficients[4 * 0 + 3] = 1;

    for (var _k = 1; _k <= N; _k++) {
      model.coefficients[4 * _k + 1] -= model.coefficients[4 * _k + 0] * model.coefficients[4 * (_k - 1) + 2];
      model.coefficients[4 * _k + 2] = model.coefficients[4 * _k + 2] / model.coefficients[4 * _k + 1];
      work[_k] = (work[_k] - model.coefficients[4 * _k + 0] * work[_k - 1]) / model.coefficients[4 * _k + 1];
      model.coefficients[4 * _k + 3] = -model.coefficients[4 * _k + 0] * model.coefficients[4 * (_k - 1) + 3] / model.coefficients[4 * _k + 1];
    }

    model.coefficients[4 * N + 0] = 1;
    model.coefficients[4 * N + 1] = 0;

    for (var _k2 = N - 1; _k2 > 0; _k2--) {
      model.coefficients[4 * _k2 + 0] = model.coefficients[4 * _k2 + 3] - model.coefficients[4 * _k2 + 2] * model.coefficients[4 * (_k2 + 1) + 0];
      model.coefficients[4 * _k2 + 1] = work[_k2] - model.coefficients[4 * _k2 + 2] * model.coefficients[4 * (_k2 + 1) + 1];
    }

    work[0] = (dN - cN * model.coefficients[4 * 1 + 1] - aN * model.coefficients[4 * (N - 1) + 1]) / (bN + cN * model.coefficients[4 * 1 + 0] + aN * model.coefficients[4 * (N - 1) + 0]);
    work[N] = work[0];

    for (var _k3 = 1; _k3 < N; _k3++) {
      work[_k3] = model.coefficients[4 * _k3 + 0] * work[N] + model.coefficients[4 * _k3 + 1];
    } // the column vector work now contains the first
    // derivative of the spline function at each joint.
    // compute the coefficients of the cubic between
    // each pair of joints.


    for (var _k4 = 0; _k4 < N; _k4++) {
      var b = x[_k4 + 1] - x[_k4];
      model.coefficients[4 * _k4 + 0] = y[_k4];
      model.coefficients[4 * _k4 + 1] = work[_k4];
      model.coefficients[4 * _k4 + 2] = 3 * (y[_k4 + 1] - y[_k4]) / (b * b) - (work[_k4 + 1] + 2 * work[_k4]) / b;
      model.coefficients[4 * _k4 + 3] = 2 * (y[_k4] - y[_k4 + 1]) / (b * b * b) + (work[_k4 + 1] + work[_k4]) / (b * b);
    } // the coefficients of a fictitious nth cubic
    // are the same as the coefficients in the first interval


    model.coefficients[4 * N + 0] = y[N];
    model.coefficients[4 * N + 1] = work[N];
    model.coefficients[4 * N + 2] = model.coefficients[4 * 0 + 2];
    model.coefficients[4 * N + 3] = model.coefficients[4 * 0 + 3];
  }; // --------------------------------------------------------------------------


  publicAPI.computeOpenCoefficients = function (size, work, x, y) {
    var options = arguments.length > 4 && arguments[4] !== undefined ? arguments[4] : {};

    if (!model.coefficients || model.coefficients.length !== 4 * size) {
      model.coefficients = new Float32Array(4 * size);
    }

    var N = size - 1; // develop constraint at leftmost point.

    switch (options.leftConstraint) {
      case BoundaryCondition.DERIVATIVE:
        // desired slope at leftmost point is leftValue.
        model.coefficients[4 * 0 + 1] = 1.0;
        model.coefficients[4 * 0 + 2] = 0.0;
        work[0] = options.leftValue;
        break;

      case BoundaryCondition.SECOND_DERIVATIVE:
        // desired second derivative at leftmost point is leftValue.
        model.coefficients[4 * 0 + 1] = 2.0;
        model.coefficients[4 * 0 + 2] = 1.0;
        work[0] = 3.0 * ((y[1] - y[0]) / (x[1] - x[0])) - 0.5 * (x[1] - x[0]) * options.leftValue;
        break;

      case BoundaryCondition.SECOND_DERIVATIVE_INTERIOR_POINT:
        // desired second derivative at leftmost point is
        // leftValue times second derivative at first interior point.
        model.coefficients[4 * 0 + 1] = 2.0;

        if (Math.abs(options.leftValue + 2) > VTK_EPSILON) {
          model.coefficients[4 * 0 + 2] = 4.0 * ((0.5 + options.leftValue) / (2.0 + options.leftValue));
          work[0] = 6.0 * ((1.0 + options.leftValue) / (2.0 + options.leftValue)) * ((y[1] - y[0]) / (x[1] - x[0]));
        } else {
          model.coefficients[4 * 0 + 2] = 0;
          work[0] = 0;
        }

        break;

      case BoundaryCondition.DEFAULT:
      default:
        // desired slope at leftmost point is derivative from two points
        model.coefficients[4 * 0 + 1] = 1.0;
        model.coefficients[4 * 0 + 2] = 0.0;
        work[0] = y[2] - y[0];
        break;
    }

    for (var k = 1; k < N; k++) {
      var xlk = x[k] - x[k - 1];
      var xlkp = x[k + 1] - x[k];
      model.coefficients[4 * k + 0] = xlkp;
      model.coefficients[4 * k + 1] = 2 * (xlkp + xlk);
      model.coefficients[4 * k + 2] = xlk;
      work[k] = 3.0 * (xlkp * (y[k] - y[k - 1]) / xlk + xlk * (y[k + 1] - y[k]) / xlkp);
    } // develop constraint at rightmost point.


    switch (options.rightConstraint) {
      case BoundaryCondition.DERIVATIVE:
        // desired slope at rightmost point is rightValue
        model.coefficients[4 * N + 0] = 0.0;
        model.coefficients[4 * N + 1] = 1.0;
        work[N] = options.rightValue;
        break;

      case BoundaryCondition.SECOND_DERIVATIVE:
        // desired second derivative at rightmost point is rightValue.
        model.coefficients[4 * N + 0] = 1.0;
        model.coefficients[4 * N + 1] = 2.0;
        work[N] = 3.0 * ((y[N] - y[N - 1]) / (x[N] - x[N - 1])) + 0.5 * (x[N] - x[N - 1]) * options.rightValue;
        break;

      case BoundaryCondition.SECOND_DERIVATIVE_INTERIOR_POINT:
        // desired second derivative at rightmost point is
        // rightValue times second derivative at last interior point.
        model.coefficients[4 * N + 1] = 2.0;

        if (Math.abs(options.rightValue + 2) > VTK_EPSILON) {
          model.coefficients[4 * N + 0] = 4.0 * ((0.5 + options.rightValue) / (2.0 + options.rightValue));
          work[N] = 6.0 * ((1.0 + options.rightValue) / (2.0 + options.rightValue)) * ((y[N] - y[size - 2]) / (x[N] - x[size - 2]));
        } else {
          model.coefficients[4 * N + 0] = 0;
          work[N] = 0;
        }

        break;

      case BoundaryCondition.DEFAULT:
      default:
        // desired slope at rightmost point is derivative from two points
        model.coefficients[4 * N + 0] = 0.0;
        model.coefficients[4 * N + 1] = 1.0;
        work[N] = y[N] - y[N - 2];
        break;
    } // solve resulting set of equations.


    model.coefficients[4 * 0 + 2] /= model.coefficients[4 * 0 + 1];
    work[0] /= model.coefficients[4 * N + 1];
    model.coefficients[4 * N + 3] = 1;

    for (var _k5 = 1; _k5 <= N; _k5++) {
      model.coefficients[4 * _k5 + 1] -= model.coefficients[4 * _k5 + 0] * model.coefficients[4 * (_k5 - 1) + 2];
      model.coefficients[4 * _k5 + 2] /= model.coefficients[4 * _k5 + 1];
      work[_k5] = (work[_k5] - model.coefficients[4 * _k5 + 0] * work[_k5 - 1]) / model.coefficients[4 * _k5 + 1];
    }

    for (var _k6 = N - 1; _k6 >= 0; _k6--) {
      work[_k6] -= model.coefficients[4 * _k6 + 2] * work[_k6 + 1];
    } // the column vector work now contains the first
    // derivative of the spline function at each joint.
    // compute the coefficients of the cubic between
    // each pair of joints.


    for (var _k7 = 0; _k7 < N; _k7++) {
      var b = x[_k7 + 1] - x[_k7];
      model.coefficients[4 * _k7 + 0] = y[_k7];
      model.coefficients[4 * _k7 + 1] = work[_k7];
      model.coefficients[4 * _k7 + 2] = 3 * (y[_k7 + 1] - y[_k7]) / (b * b) - (work[_k7 + 1] + 2 * work[_k7]) / b;
      model.coefficients[4 * _k7 + 3] = 2 * (y[_k7] - y[_k7 + 1]) / (b * b * b) + (work[_k7 + 1] + work[_k7]) / (b * b);
    } // the coefficients of a fictitious nth cubic
    // are the same as the coefficients in the first interval


    model.coefficients[4 * N + 0] = y[N];
    model.coefficients[4 * N + 1] = work[N];
    model.coefficients[4 * N + 2] = model.coefficients[4 * 0 + 2];
    model.coefficients[4 * N + 3] = model.coefficients[4 * 0 + 3];
  }; // --------------------------------------------------------------------------


  publicAPI.getValue = function (intervalIndex, t) {
    var t2 = t * t;
    var t3 = t * t * t;
    return model.coefficients[4 * intervalIndex + 3] * t3 + model.coefficients[4 * intervalIndex + 2] * t2 + model.coefficients[4 * intervalIndex + 1] * t + model.coefficients[4 * intervalIndex + 0];
  };
} // ----------------------------------------------------------------------------
// Object factory
// ----------------------------------------------------------------------------


var DEFAULT_VALUES = {}; // ----------------------------------------------------------------------------

function extend(publicAPI, model) {
  var initialValues = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : {};
  Object.assign(model, DEFAULT_VALUES, initialValues);
  vtkSpline1D.extend(publicAPI, model, initialValues); // Build VTK API

  macro.obj(publicAPI, model);
  vtkCardinalSpline1D(publicAPI, model);
} // ----------------------------------------------------------------------------

var newInstance = macro.newInstance(extend, 'vtkCardinalSpline1D'); // ----------------------------------------------------------------------------

var vtkCardinalSpline1D$1 = {
  newInstance: newInstance,
  extend: extend
};

export { vtkCardinalSpline1D$1 as default, extend, newInstance };