@kitware/vtk.js
Version:
Visualization Toolkit for the Web
239 lines (212 loc) • 10.5 kB
JavaScript
import { m as macro } from '../../macros2.js';
import vtkSpline1D from './Spline1D.js';
import { BoundaryCondition } from './Spline1D/Constants.js';
const VTK_EPSILON = 0.0001;
// ----------------------------------------------------------------------------
// vtkCardinalSpline1D methods
// ----------------------------------------------------------------------------
function vtkCardinalSpline1D(publicAPI, model) {
// Set our classname
model.classHierarchy.push('vtkCardinalSpline1D');
// --------------------------------------------------------------------------
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 k = 1; k < N; k++) {
const xlk = x[k] - x[k - 1];
const 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);
}
const xlk = x[N] - x[N - 1];
const 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);
const aN = model.coefficients[4 * N + 0];
const bN = model.coefficients[4 * N + 1];
const cN = model.coefficients[4 * N + 2];
const dN = work[N];
// solve resulting set of equations.
model.coefficients[4 * 0 + 2] = 0;
work[0] = 0;
model.coefficients[4 * 0 + 3] = 1;
for (let 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 (let k = N - 1; k > 0; k--) {
model.coefficients[4 * k + 0] = model.coefficients[4 * k + 3] - model.coefficients[4 * k + 2] * model.coefficients[4 * (k + 1) + 0];
model.coefficients[4 * k + 1] = work[k] - model.coefficients[4 * k + 2] * model.coefficients[4 * (k + 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 (let k = 1; k < N; k++) {
work[k] = model.coefficients[4 * k + 0] * work[N] + model.coefficients[4 * k + 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 (let k = 0; k < N; k++) {
const b = x[k + 1] - x[k];
model.coefficients[4 * k + 0] = y[k];
model.coefficients[4 * k + 1] = work[k];
model.coefficients[4 * k + 2] = 3 * (y[k + 1] - y[k]) / (b * b) - (work[k + 1] + 2 * work[k]) / b;
model.coefficients[4 * k + 3] = 2 * (y[k] - y[k + 1]) / (b * b * b) + (work[k + 1] + work[k]) / (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 = (size, work, x, y, options = {}) => {
if (!model.coefficients || model.coefficients.length !== 4 * size) {
model.coefficients = new Float32Array(4 * size);
}
const 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 (let k = 1; k < N; k++) {
const xlk = x[k] - x[k - 1];
const 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 (let 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 + 1];
work[k] = (work[k] - model.coefficients[4 * k + 0] * work[k - 1]) / model.coefficients[4 * k + 1];
}
for (let k = N - 1; k >= 0; k--) {
work[k] -= model.coefficients[4 * k + 2] * work[k + 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 (let k = 0; k < N; k++) {
const b = x[k + 1] - x[k];
model.coefficients[4 * k + 0] = y[k];
model.coefficients[4 * k + 1] = work[k];
model.coefficients[4 * k + 2] = 3 * (y[k + 1] - y[k]) / (b * b) - (work[k + 1] + 2 * work[k]) / b;
model.coefficients[4 * k + 3] = 2 * (y[k] - y[k + 1]) / (b * b * b) + (work[k + 1] + work[k]) / (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 = (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 = {};
// ----------------------------------------------------------------------------
function extend(publicAPI, model, initialValues = {}) {
Object.assign(model, DEFAULT_VALUES, initialValues);
vtkSpline1D.extend(publicAPI, model, initialValues);
// Build VTK API
macro.obj(publicAPI, model);
vtkCardinalSpline1D(publicAPI, model);
}
// ----------------------------------------------------------------------------
const newInstance = macro.newInstance(extend, 'vtkCardinalSpline1D');
// ----------------------------------------------------------------------------
var vtkCardinalSpline1D$1 = {
newInstance,
extend
};
export { vtkCardinalSpline1D$1 as default, extend, newInstance };