KochanekSpline1D

Introduction

vtkKochanekSpline1D provides methods for creating a Kochanek interpolating
spline object from given parameters, and allows for the calculation of the
spline value and derivative at any given point inside the spline intervals.

Methods

computeCloseCoefficients

Argument	Type	Required	Description
size	Number	Yes
work	Float32Array	Yes
x	Array.	Yes
y	Array.	Yes

computeOpenCoefficients

Argument	Type	Required	Description
size	Number	Yes
work	Float32Array	Yes
x	Array.	Yes
y	Array.	Yes
options	Object	Yes
options.leftConstraint	BoundaryCondition	Yes
options.leftValue	Number	Yes
options.rightConstraint	BoundaryCondition	Yes
options.rightValue	Number	Yes

extend

Method used to decorate a given object (publicAPI+model) with vtkKochanekSpline1D characteristics.

Argument	Type	Required	Description
publicAPI		Yes	object on which methods will be bounds (public)
model		Yes	object on which data structure will be bounds (protected)
initialValues	IKochanekSpline1DInitialValues	No	(default: {})

getValue

Argument	Type	Required	Description
intervalIndex	Number	Yes
t	Number	Yes

newInstance

Method used to create a new instance of vtkKochanekSpline1D.

Argument	Type	Required	Description
initialValues	IKochanekSpline1DInitialValues	No	for pre-setting some of its content

Source

index.d.ts

import vtkSpline1D, {
  ISpline1DInitialValues,
  BoundaryCondition,
} from '../Spline1D';

export interface IKochanekSpline1DInitialValues extends ISpline1DInitialValues {
  tension?: number;
  bias?: number;
  continuity?: number;
}

export interface vtkKochanekSpline1D extends vtkSpline1D {
  /**
   *
   * @param {Number} size
   * @param {Float32Array} work
   * @param {Number[]} x
   * @param {Number[]} y
   */
  computeCloseCoefficients(
    size: number,
    work: Float32Array,
    x: number[],
    y: number[]
  ): void;

  /**
   *
   * @param {Number} size
   * @param {Float32Array} work
   * @param {Number[]} x
   * @param {Number[]} y
   * @param {Object} options
   * @param {BoundaryCondition} options.leftConstraint
   * @param {Number} options.leftValue
   * @param {BoundaryCondition} options.rightConstraint
   * @param {Number} options.rightValue
   */
  computeOpenCoefficients(
    size: number,
    work: Float32Array,
    x: number[],
    y: number[],
    options: {
      leftConstraint: BoundaryCondition;
      leftValue: number;
      rightConstraint: BoundaryCondition;
      rightValue: Number;
    }
  ): void;

  /**
   *
   * @param {Number} intervalIndex
   * @param {Number} t
   */
  getValue(intervalIndex: number, t: number): number;
}

/**
 * Method used to decorate a given object (publicAPI+model) with vtkKochanekSpline1D characteristics.
 *
 * @param publicAPI object on which methods will be bounds (public)
 * @param model object on which data structure will be bounds (protected)
 * @param {IKochanekSpline1DInitialValues} [initialValues] (default: {})
 */
export function extend(
  publicAPI: object,
  model: object,
  initialValues?: IKochanekSpline1DInitialValues
): void;

/**
 * Method used to create a new instance of vtkKochanekSpline1D.
 * @param {IKochanekSpline1DInitialValues} [initialValues] for pre-setting some of its content
 */
export function newInstance(
  initialValues?: IKochanekSpline1DInitialValues
): vtkKochanekSpline1D;

/**
 * vtkKochanekSpline1D provides methods for creating a Kochanek interpolating
 * spline object from given parameters, and allows for the calculation of the
 * spline value and derivative at any given point inside the spline intervals.
 */

export declare const vtkKochanekSpline1D: {
  newInstance: typeof newInstance;
  extend: typeof extend;
};
export default vtkKochanekSpline1D;

index.js

import macro from 'vtk.js/Sources/macros';
import vtkSpline1D from 'vtk.js/Sources/Common/DataModel/Spline1D';

import { BoundaryCondition } from 'vtk.js/Sources/Common/DataModel/Spline1D/Constants';

const VTK_EPSILON = 0.0001;

// ----------------------------------------------------------------------------
// vtkKochanekSpline1D methods
// ----------------------------------------------------------------------------

function vtkKochanekSpline1D(publicAPI, model) {
  // Set our classname
  model.classHierarchy.push('vtkKochanekSpline1D');

  // --------------------------------------------------------------------------

  publicAPI.computeCloseCoefficients = (size, work, x, y) => {
    if (!model.coefficients || model.coefficients.length !== 4 * size) {
      model.coefficients = new Float32Array(4 * size);
    }
    const N = size - 1;

    for (let i = 1; i < N; i++) {
      const cs = y[i] - y[i - 1];
      const cd = y[i + 1] - y[i];

      let ds =
        cs * ((1 - model.tension) * (1 - model.continuity) * (1 + model.bias)) +
        cd * ((1 - model.tension) * (1 + model.continuity) * (1 - model.bias));

      let dd =
        cs * ((1 - model.tension) * (1 + model.continuity) * (1 + model.bias)) +
        cd * ((1 - model.tension) * (1 - model.continuity) * (1 - model.bias));

      // adjust deriviatives for non uniform spacing between nodes
      const n1 = x[i + 1] - x[i];
      const n0 = x[i] - x[i - 1];

      ds *= n0 / (n0 + n1);
      dd *= n1 / (n0 + n1);

      model.coefficients[4 * i + 0] = y[i];
      model.coefficients[4 * i + 1] = dd;
      model.coefficients[4 * i + 2] = ds;
    }

    // Calculate the deriviatives at the end points
    model.coefficients[4 * 0 + 0] = y[0];
    model.coefficients[4 * N + 0] = y[N];
    model.coefficients[4 * N + 1] = 0;
    model.coefficients[4 * N + 2] = 0;
    model.coefficients[4 * N + 3] = 0;

    // The curve is continuous and closed at P0=Pn
    const cs = y[N] - y[N - 1];
    const cd = y[1] - y[0];

    let ds =
      cs * ((1 - model.tension) * (1 - model.continuity) * (1 + model.bias)) +
      cd * ((1 - model.tension) * (1 + model.continuity) * (1 - model.bias));

    let dd =
      cs * ((1 - model.tension) * (1 + model.continuity) * (1 + model.bias)) +
      cd * ((1 - model.tension) * (1 - model.continuity) * (1 - model.bias));

    // adjust deriviatives for non uniform spacing between nodes
    const n1 = x[1] - x[0];
    const n0 = x[N] - x[N - 1];

    ds *= n0 / (n0 + n1);
    dd *= n1 / (n0 + n1);

    model.coefficients[4 * 0 + 1] = dd;
    model.coefficients[4 * 0 + 2] = ds;
    model.coefficients[4 * N + 1] = dd;
    model.coefficients[4 * N + 2] = ds;

    for (let i = 0; i < N; i++) {
      //
      // c0    = P ;    c1    = DD ;
      //   i      i       i       i
      //
      // c1    = P   ;  c2    = DS   ;
      //   i+1    i+1     i+1     i+1
      //
      // c2  = -3P  + 3P    - 2DD  - DS   ;
      //   i      i     i+1      i     i+1
      //
      // c3  =  2P  - 2P    +  DD  + DS   ;
      //   i      i     i+1      i     i+1
      //
      model.coefficients[4 * i + 2] =
        -3 * y[i] +
        3 * y[i + 1] +
        -2 * model.coefficients[4 * i + 1] +
        -1 * model.coefficients[4 * (i + 1) + 2];
      model.coefficients[4 * i + 3] =
        2 * y[i] +
        -2 * y[i + 1] +
        1 * model.coefficients[4 * i + 1] +
        1 * model.coefficients[4 * (i + 1) + 2];
    }
  };

  // --------------------------------------------------------------------------

  publicAPI.computeOpenCoefficients = (size, work, x, y, options = {}) => {
    if (!model.coefficients || model.coefficients.length !== 4 * size) {
      model.coefficients = new Float32Array(4 * size);
    }
    const N = size - 1;

    for (let i = 1; i < N; i++) {
      const cs = y[i] - y[i - 1];
      const cd = y[i + 1] - y[i];

      let ds =
        cs * ((1 - model.tension) * (1 - model.continuity) * (1 + model.bias)) +
        cd * ((1 - model.tension) * (1 + model.continuity) * (1 - model.bias));

      let dd =
        cs * ((1 - model.tension) * (1 + model.continuity) * (1 + model.bias)) +
        cd * ((1 - model.tension) * (1 - model.continuity) * (1 - model.bias));

      // adjust deriviatives for non uniform spacing between nodes
      const n1 = x[i + 1] - x[i];
      const n0 = x[i] - x[i - 1];

      ds *= n0 / (n0 + n1);
      dd *= n1 / (n0 + n1);

      model.coefficients[4 * i + 0] = y[i];
      model.coefficients[4 * i + 1] = dd;
      model.coefficients[4 * i + 2] = ds;
    }

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

    // Calculate the deriviatives at the end points

    switch (options.leftConstraint) {
      // desired slope at leftmost point is leftValue
      case BoundaryCondition.DERIVATIVE:
        model.coefficients[4 * 0 + 1] = options.leftValue;
        break;
      case BoundaryCondition.SECOND_DERIVATIVE:
        // desired second derivative at leftmost point is leftValue
        model.coefficients[4 * 0 + 1] =
          (6 * (y[1] - y[0]) -
            2 * model.coefficients[4 * 1 + 2] -
            options.leftValue) /
          4;
        break;
      case BoundaryCondition.SECOND_DERIVATIVE_INTERIOR_POINT:
        // desired second derivative at leftmost point is leftValue
        // times second derivative at first interior point
        if (Math.abs(options.leftValue + 2) > VTK_EPSILON) {
          model.coefficients[4 * 0 + 1] =
            (3 * (1 + options.leftValue) * (y[1] - y[0]) -
              (1 + 2 * options.leftValue) * model.coefficients[4 * 1 + 2]) /
            (2 + options.leftValue);
        } else {
          model.coefficients[4 * 0 + 1] = 0.0;
        }
        break;
      case BoundaryCondition.DEFAULT:
      default:
        // desired slope at leftmost point is derivative from two points
        model.coefficients[4 * 0 + 1] = y[2] - y[0];
        break;
    }
    switch (options.rightConstraint) {
      case BoundaryCondition.DERIVATIVE:
        // desired slope at rightmost point is leftValue
        model.coefficients[4 * N + 2] = options.leftValue;
        break;

      case BoundaryCondition.SECOND_DERIVATIVE:
        // desired second derivative at rightmost point is leftValue
        model.coefficients[4 * N + 2] =
          (6 * (y[N] - y[N - 1]) -
            2 * model.coefficients[4 * (N - 1) + 1] +
            options.leftValue) /
          4.0;
        break;

      case BoundaryCondition.SECOND_DERIVATIVE_INTERIOR_POINT:
        // desired second derivative at rightmost point is leftValue
        // times second derivative at last interior point
        if (Math.abs(options.leftValue + 2) > VTK_EPSILON) {
          model.coefficients[4 * N + 2] =
            (3 * (1 + options.leftValue) * (y[N] - y[N - 1]) -
              (1 + 2 * options.leftValue) *
                model.coefficients[4 * (N - 1) + 1]) /
            (2 + options.leftValue);
        } else {
          model.coefficients[4 * N + 2] = 0.0;
        }
        break;
      case BoundaryCondition.DEFAULT:
      default:
        // desired slope at rightmost point is rightValue
        model.coefficients[4 * N + 2] = y[N] - y[N - 2];
        break;
    }

    for (let i = 0; i < N; i++) {
      //
      // c0    = P ;    c1    = DD ;
      //   i      i       i       i
      //
      // c1    = P   ;  c2    = DS   ;
      //   i+1    i+1     i+1     i+1
      //
      // c2  = -3P  + 3P    - 2DD  - DS   ;
      //   i      i     i+1      i     i+1
      //
      // c3  =  2P  - 2P    +  DD  + DS   ;
      //   i      i     i+1      i     i+1
      //
      model.coefficients[4 * i + 2] =
        -3 * y[i] +
        3 * y[i + 1] +
        -2 * model.coefficients[4 * i + 1] +
        -1 * model.coefficients[4 * (i + 1) + 2];
      model.coefficients[4 * i + 3] =
        2 * y[i] +
        -2 * y[i + 1] +
        1 * model.coefficients[4 * i + 1] +
        1 * model.coefficients[4 * (i + 1) + 2];
    }
  };

  // --------------------------------------------------------------------------

  publicAPI.getValue = (intervalIndex, t) => {
    const t2 = t * t;
    const 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
// ----------------------------------------------------------------------------

const DEFAULT_VALUES = {
  tension: 0,
  bias: 0,
  continuity: 0,
};

// ----------------------------------------------------------------------------

export function extend(publicAPI, model, initialValues = {}) {
  Object.assign(model, DEFAULT_VALUES, initialValues);

  vtkSpline1D.extend(publicAPI, model, initialValues);

  // Build VTK API
  macro.obj(publicAPI, model);
  vtkKochanekSpline1D(publicAPI, model);
}

// ----------------------------------------------------------------------------

export const newInstance = macro.newInstance(extend, 'vtkKochanekSpline1D');

// ----------------------------------------------------------------------------

export default { newInstance, extend };