64 lines
1.5 KiB
TypeScript
64 lines
1.5 KiB
TypeScript
/* bezier-spline.js
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*
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* computes cubic bezier coefficients to generate a smooth
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* line through specified points. couples with SVG graphics
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* for interactive processing.
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*
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* For more info see:
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* http://www.particleincell.com/2012/bezier-splines/
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*
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* Lubos Brieda, Particle In Cell Consulting LLC, 2012
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* you may freely use this algorithm in your codes however where feasible
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* please include a link/reference to the source article
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*/
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/* computes control points given knots K, this is the brain of the operation */
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export function computeControlPoints(K: number[]) {
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const p1 = []
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const p2 = []
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const n = K.length - 1
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/* rhs vector */
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const a = []
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const b = []
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const c = []
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const r = []
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/* left most segment */
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a[0] = 0
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b[0] = 2
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c[0] = 1
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r[0] = K[0] + 2 * K[1]
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/* internal segments */
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for (let i = 1; i < n - 1; i++) {
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a[i] = 1
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b[i] = 4
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c[i] = 1
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r[i] = 4 * K[i] + 2 * K[i + 1]
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}
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/* right segment */
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a[n - 1] = 2
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b[n - 1] = 7
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c[n - 1] = 0
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r[n - 1] = 8 * K[n - 1] + K[n]
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/* solves Ax=b with the Thomas algorithm (from Wikipedia) */
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for (let i = 1; i < n; i++) {
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const m: number = a[i] / b[i - 1]
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b[i] = b[i] - m * c[i - 1]
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r[i] = r[i] - m * r[i - 1]
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}
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p1[n - 1] = r[n - 1] / b[n - 1]
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for (let i = n - 2; i >= 0; --i) p1[i] = (r[i] - c[i] * p1[i + 1]) / b[i]
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/* we have p1, now compute p2 */
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for (let i = 0; i < n - 1; i++) p2[i] = 2 * K[i + 1] - p1[i + 1]
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p2[n - 1] = 0.5 * (K[n] + p1[n - 1])
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return { p1: p1.map((p) => Math.floor(p)), p2: p2.map((p) => Math.floor(p)) }
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}
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