xeokit Spline Curve Math Utilities

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Math helpers for working with spline curves.

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This module contains lightweight curve utilities for evaluating common spline types, currently focused on Bézier (quadratic/cubic) and Catmull–Rom interpolation. These functions are handy when you need smooth parametric motion, easing-like blends, or curve-based sampling in 1D, 2D, or 3D workflows (for example: camera rails, animated values, or generating polyline samples).

All evaluators use a normalized parameter t in the range [0..1].

Installation

npm install @xeokit/sdk
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Usage

Below are examples of a few commonly used helpers.

Import the functions:

import {
  tangentQuadraticBezier,
  tangentQuadraticBezier3,
  tangentSpline,
  catmullRomInterpolate,
  b2,
  b3
} from "@xeokit/sdk/math/curves";
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Quadratic Bézier tangent at t

const t = 0.5; // 0 ≤ t ≤ 1
const p0 = 0, p1 = 10, p2 = 20; // Control points
const tangentQuad = tangentQuadraticBezier(t, p0, p1, p2);
console.log("Quadratic Bézier tangent:", tangentQuad);
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Cubic Bézier tangent at t

const p3 = 30; // Fourth control point
const tangentCubic = tangentQuadraticBezier3(t, p0, p1, p2, p3);
console.log("Cubic Bézier tangent:", tangentCubic);
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Spline tangent basis at t

const tangentSplineValue = tangentSpline(t);
console.log("Spline tangent basis:", tangentSplineValue);
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Catmull–Rom interpolation at t

const interpolatedValue = catmullRomInterpolate(p0, p1, p2, p3, t);
console.log("Catmull–Rom interpolation:", interpolatedValue);
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Quadratic Bézier value at t

const quadBezierResult = b2(t, p0, p1, p2);
console.log("Quadratic Bézier value:", quadBezierResult);
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Cubic Bézier value at t

const cubicBezierResult = b3(t, p0, p1, p2, p3);
console.log("Cubic Bézier value:", cubicBezierResult);
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