feat(All):Initial

2025-10-04 23:36:07 +08:00
commit 2b4e5d2668
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+import round10 from './round10'
+
+/**
+ * 复制和移植到代码标准，因为b样条库不再维护。
+ * Source:
+ * https://github.com/thibauts/b-spline
+ */
+export default (t:number, degree:number, points, knots, weights?:number[] | undefined) => {
+  const n = points.length // 点数量
+  const d = points[0].length // 分维数
+
+  if ((t < 0) || (t > 1)) {
+    throw new Error('t 在区间 [0,1] 外: t = ' + t)
+  }
+  if (degree < 1) throw new Error('degree 必须至少为1(线性)')
+  if (degree > (n - 1)) throw new Error('degree 必须小于或等于点数量 - 1')
+
+  if (!weights) {
+    // 构建长度为[n]的权重向量
+    weights = []
+    for (let i = 0; i < n; i++) {
+      weights[i] = 1
+    }
+  }
+
+  if (!knots) {
+    // 建立长度为[n + degree + 1]的结向量
+    knots = []
+    for (let i = 0; i < n + degree + 1; i++) {
+      knots[i] = i
+    }
+  } else {
+    if (knots.length !== n + degree + 1) throw new Error('坏结矢量长度')
+  }
+
+  const domain = [
+    degree,
+    knots.length - 1 - degree
+  ]
+
+  // 将t重新映射到定义样条的域
+  const low = knots[domain[0]]
+  const high = knots[domain[1]]
+  t = t * (high - low) + low
+
+  // 夹紧到上限和下限，而不是像在原始库中那样抛出错误
+  t = Math.max(t, low)
+  t = Math.min(t, high)
+
+  // 为提供的[t]值找到s(样条段)
+  let s
+  for (s = domain[0]; s < domain[1]; s++) {
+    if (t >= knots[s] && t <= knots[s + 1]) {
+      break
+    }
+  }
+
+  // 将点转换为齐次坐标
+  const v:any = []
+  for (let i = 0; i < n; i++) {
+    v[i] = []
+    for (let j = 0; j < d; j++) {
+      v[i][j] = points[i][j] * weights[i]
+    }
+    v[i][d] = weights[i]
+  }
+
+  // l (level) 从 1 到 curve degree + 1
+  let alpha
+  for (let l = 1; l <= degree + 1; l++) {
+    // build level l of the pyramid
+    for (let i = s; i > s - degree - 1 + l; i--) {
+      alpha = (t - knots[i]) / (knots[i + degree + 1 - l] - knots[i])
+
+      // interpolate each component
+      for (let j = 0; j < d + 1; j++) {
+        v[i][j] = (1 - alpha) * v[i - 1][j] + alpha * v[i][j]
+      }
+    }
+  }
+
+  // 转换回笛卡尔坐标，然后返回
+  const result:number[] = []
+  for (let i = 0; i < d; i++) {
+    result[i] = round10(v[s][i] / v[s][d], -9)
+  }
+  return result
+}