88 lines
2.2 KiB
TypeScript
88 lines
2.2 KiB
TypeScript
import round10 from './round10'
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/**
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* 复制和移植到代码标准，因为b样条库不再维护。
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* Source:
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* https://github.com/thibauts/b-spline
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*/
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export default (t:number, degree:number, points, knots, weights?:number[] | undefined) => {
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const n = points.length // 点数量
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const d = points[0].length // 分维数
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if ((t < 0) || (t > 1)) {
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throw new Error('t 在区间 [0,1] 外: t = ' + t)
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}
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if (degree < 1) throw new Error('degree 必须至少为1(线性)')
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if (degree > (n - 1)) throw new Error('degree 必须小于或等于点数量 - 1')
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if (!weights) {
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// 构建长度为[n]的权重向量
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weights = []
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for (let i = 0; i < n; i++) {
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weights[i] = 1
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}
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}
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if (!knots) {
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// 建立长度为[n + degree + 1]的结向量
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knots = []
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for (let i = 0; i < n + degree + 1; i++) {
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knots[i] = i
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}
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} else {
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if (knots.length !== n + degree + 1) throw new Error('坏结矢量长度')
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}
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const domain = [
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degree,
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knots.length - 1 - degree
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]
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// 将t重新映射到定义样条的域
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const low = knots[domain[0]]
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const high = knots[domain[1]]
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t = t * (high - low) + low
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// 夹紧到上限和下限，而不是像在原始库中那样抛出错误
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t = Math.max(t, low)
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t = Math.min(t, high)
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// 为提供的[t]值找到s(样条段)
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let s
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for (s = domain[0]; s < domain[1]; s++) {
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if (t >= knots[s] && t <= knots[s + 1]) {
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break
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}
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}
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// 将点转换为齐次坐标
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const v:any = []
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for (let i = 0; i < n; i++) {
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v[i] = []
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for (let j = 0; j < d; j++) {
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v[i][j] = points[i][j] * weights[i]
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}
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v[i][d] = weights[i]
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}
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// l (level) 从 1 到 curve degree + 1
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let alpha
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for (let l = 1; l <= degree + 1; l++) {
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// build level l of the pyramid
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for (let i = s; i > s - degree - 1 + l; i--) {
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alpha = (t - knots[i]) / (knots[i + degree + 1 - l] - knots[i])
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// interpolate each component
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for (let j = 0; j < d + 1; j++) {
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v[i][j] = (1 - alpha) * v[i - 1][j] + alpha * v[i][j]
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}
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}
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}
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// 转换回笛卡尔坐标，然后返回
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const result:number[] = []
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for (let i = 0; i < d; i++) {
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result[i] = round10(v[s][i] / v[s][d], -9)
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}
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return result
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} |