@woosh/meep-engine/src/core/math/spline/spline3_hermite_to_monomial.js

Pure JavaScript game engine. Fully featured and production ready.

import { assert } from "../../assert.js";

/**
 * One-dimensional cubic Hermite to monomial-basis conversion.
 *
 * Given a Hermite segment defined by `(p0, p1, m0, m1)` whose value at parameter
 * `t ∈ [0, 1]` is computed by {@link spline3_hermite}, this writes the monomial
 * coefficients `α₀, α₁, α₂, α₃` into the result array such that
 *
 *   spline3_hermite(t, p0, p1, m0, m1) === α₀ + α₁·t + α₂·t² + α₃·t³
 *
 * for all t.
 *
 * @param {number[]|Float32Array|Float64Array} result
 * @param {number} result_offset
 * @param {number} result_stride step between successive coefficient slots; useful when interleaving multiple dimensions in one array
 * @param {number} p0
 * @param {number} p1
 * @param {number} m0
 * @param {number} m1
 *
 * @author Alex Goldring
 * @copyright Company Named Limited (c) 2025
 */
export function spline3_hermite_to_monomial(
    result,
    result_offset,
    result_stride,
    p0, p1, m0, m1
) {
    assert.greaterThan(result_stride, 0, 'result_stride must be greater than 0');

    result[result_offset]                    = p0;
    result[result_offset + result_stride]    = m0;
    result[result_offset + 2 * result_stride] = -3 * p0 + 3 * p1 - 2 * m0 - m1;
    result[result_offset + 3 * result_stride] = 2 * p0 - 2 * p1 + m0 + m1;
}