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NURBS derivatives of degree > 2 #16

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22 changes: 15 additions & 7 deletions src/evaluate.js
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Original file line number Diff line number Diff line change
Expand Up @@ -33,9 +33,9 @@ module.exports = function (cacheKey, nurbs, accessors, debug, checkBounds, isBas
if (derivative[i] === undefined) derivative[i] = 0;
totalDerivativeOrder += derivative[i];
}
if (hasWeights && totalDerivativeOrder > 1) {
throw new Error('Analytical derivative not implemented for rational b-splines with order n = ' + totalDerivativeOrder + '.');
}
//if (hasWeights && totalDerivativeOrder > 1) {
//throw new Error('Analytical derivative not implemented for rational b-splines with order n = ' + totalDerivativeOrder + '.');
//}
}

if (isBasis) cacheKey = 'Basis' + cacheKey;
Expand Down Expand Up @@ -101,9 +101,9 @@ module.exports = function (cacheKey, nurbs, accessors, debug, checkBounds, isBas
function debugLine (str) {
if (debug) line(str);
}
// function clog (str) {
// if (debug) code.push('console.log("' + str + ' =", ' + str + ');');
// }
//function clog (str) {
//if (debug) code.push('console.log("' + str + ' =", ' + str + ');');
//}

if (isBasis) {
var indexArgs = [];
Expand Down Expand Up @@ -300,6 +300,10 @@ module.exports = function (cacheKey, nurbs, accessors, debug, checkBounds, isBas
for (i = 0; i < degree[d]; i++) {
debugLine('\n // Degree ' + degree[d] + ' evaluation in dimension ' + d + ', step ' + (i + 1) + '\n');
for (j = degree[d]; j > i; j--) {
/*if (derivative) {
console.log('derivative, degree[d], i:', derivative, degree[d], i);
console.log('degree[d] - i - derivative[d]:', degree[d] - i - derivative[d]);
}*/
var isDerivative = derivative && (degree[d] - i - derivative[d] <= 0);

if (isDerivative) {
Expand Down Expand Up @@ -343,7 +347,11 @@ module.exports = function (cacheKey, nurbs, accessors, debug, checkBounds, isBas
var ij1WithDimension = ij1.slice();
for (m = 0; m < spaceDimension; m++) {
ijWithDimension[splineDimension] = ij1WithDimension[splineDimension] = m;
weightFactor = hasWeights ? 'h * ' + weightVar(ij1) + ' / ' + weightVar(ij) + ' * ' : '';
//if (i === degree[d] - 1) {
//weightFactor = hasWeights ? 'h * ' + weightVar(ij1) + ' / (' + weightVar(ij) + ' * '+weightVar(ij)+') * ' : '';
//} else {
weightFactor = hasWeights ? 'h * ' + weightVar(ij1) + ' / ' + weightVar(ij) +' * ' : '';
//}
pt1 = pointVar(ijWithDimension) + (hasWeights ? ' / h' : '');
pt2 = pointVar(ij1WithDimension) + (hasWeights ? ' / ' + weightVar(ij1) : '');
line(pointVar(ijWithDimension) + ' = ' + derivCoeff + ' * ' + weightFactor + '(' + pt1 + ' - ' + pt2 + ') * m;');
Expand Down
51 changes: 51 additions & 0 deletions test/derivative.js
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Original file line number Diff line number Diff line change
Expand Up @@ -381,4 +381,55 @@ test('array-of-array style nurbs', function (t) {
t.end();
});
});

t.test('second derivative of NURBS curves', function (t) {
t.test('of a quartic b-spline', function (t) {
var deg = 4;
var points = [[0], [1], [4], [2], [4], [6], [8]];
var spline = nurbs({
points: points,
knots: [new Array(points.length + deg + 1).fill(0).map((d, i) => Math.sqrt(2 + i))],
//weights: new Array(points.length).fill(0).map((d, i) => Math.pow(i + 1, 2)),
degree: deg,
});

var der1 = spline.evaluator([1]);
var der2 = spline.evaluator([2]);
var der3 = spline.evaluator([3]);
var der4 = spline.evaluator([4]);
var domain = spline.domain[0];
var samples = 3;

var h = 1e-3;

for (var i = 0; i < samples; i++) {
var u = domain[0] + (domain[1] - domain[0]) * (i + 1) / (samples + 1);

var ym2 = spline.evaluate([], u - 2 * h)[0];
var ym = spline.evaluate([], u - h)[0];
var y0 = spline.evaluate([], u)[0];
var yp = spline.evaluate([], u + h)[0];
var yp2 = spline.evaluate([], u + 2 * h)[0];

var expectedDer1 = (yp - ym) / (2 * h);
var actualDer1 = der1([], u)[0];

var expectedDer2 = (yp - 2 * y0 + ym) / (h * h);
var actualDer2 = der2([], u)[0];

var expectedDer3 = ((yp2 - ym2) - 2 * (yp - ym)) / 2 / (h * h * h);
var actualDer3 = der3([], u)[0];

var expectedDer4 = (ym2 + yp2 - 4 * (yp + ym) + 6 * y0) / (h * h * h * h);
var actualDer4 = der4([], u)[0];

t.ok(almostEqual(actualDer1, expectedDer1, 2e-3), 'first derivative at t = ' + u + ', expected: ' + expectedDer1 + ', actual: ' + actualDer1);
t.ok(almostEqual(actualDer2, expectedDer2, 2e-3), 'second derivative at t = ' + u + ', expected: ' + expectedDer2 + ', actual: ' + actualDer2);
t.ok(almostEqual(actualDer3, expectedDer3, 2e-3), 'third derivative at t = ' + u + ', expected: ' + expectedDer3 + ', actual: ' + actualDer3);
t.ok(almostEqual(actualDer4, expectedDer4, 2e-3), 'fourth derivative at t = ' + u + ', expected: ' + expectedDer4 + ', actual: ' + actualDer4);
}

t.end();
});
});
});