Initial project import

node_modules/three-stdlib/curves/NURBSUtils.js

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+import { Vector4, Vector3 } from "three";
+function findSpan(p, u, U) {
+  const n = U.length - p - 1;
+  if (u >= U[n]) {
+    return n - 1;
+  }
+  if (u <= U[p]) {
+    return p;
+  }
+  let low = p;
+  let high = n;
+  let mid = Math.floor((low + high) / 2);
+  while (u < U[mid] || u >= U[mid + 1]) {
+    if (u < U[mid]) {
+      high = mid;
+    } else {
+      low = mid;
+    }
+    mid = Math.floor((low + high) / 2);
+  }
+  return mid;
+}
+function calcBasisFunctions(span, u, p, U) {
+  const N = [];
+  const left = [];
+  const right = [];
+  N[0] = 1;
+  for (let j = 1; j <= p; ++j) {
+    left[j] = u - U[span + 1 - j];
+    right[j] = U[span + j] - u;
+    let saved = 0;
+    for (let r = 0; r < j; ++r) {
+      const rv = right[r + 1];
+      const lv = left[j - r];
+      const temp = N[r] / (rv + lv);
+      N[r] = saved + rv * temp;
+      saved = lv * temp;
+    }
+    N[j] = saved;
+  }
+  return N;
+}
+function calcBSplinePoint(p, U, P, u) {
+  const span = findSpan(p, u, U);
+  const N = calcBasisFunctions(span, u, p, U);
+  const C = new Vector4(0, 0, 0, 0);
+  for (let j = 0; j <= p; ++j) {
+    const point = P[span - p + j];
+    const Nj = N[j];
+    const wNj = point.w * Nj;
+    C.x += point.x * wNj;
+    C.y += point.y * wNj;
+    C.z += point.z * wNj;
+    C.w += point.w * Nj;
+  }
+  return C;
+}
+function calcBasisFunctionDerivatives(span, u, p, n, U) {
+  const zeroArr = [];
+  for (let i = 0; i <= p; ++i)
+    zeroArr[i] = 0;
+  const ders = [];
+  for (let i = 0; i <= n; ++i)
+    ders[i] = zeroArr.slice(0);
+  const ndu = [];
+  for (let i = 0; i <= p; ++i)
+    ndu[i] = zeroArr.slice(0);
+  ndu[0][0] = 1;
+  const left = zeroArr.slice(0);
+  const right = zeroArr.slice(0);
+  for (let j = 1; j <= p; ++j) {
+    left[j] = u - U[span + 1 - j];
+    right[j] = U[span + j] - u;
+    let saved = 0;
+    for (let r2 = 0; r2 < j; ++r2) {
+      const rv = right[r2 + 1];
+      const lv = left[j - r2];
+      ndu[j][r2] = rv + lv;
+      const temp = ndu[r2][j - 1] / ndu[j][r2];
+      ndu[r2][j] = saved + rv * temp;
+      saved = lv * temp;
+    }
+    ndu[j][j] = saved;
+  }
+  for (let j = 0; j <= p; ++j) {
+    ders[0][j] = ndu[j][p];
+  }
+  for (let r2 = 0; r2 <= p; ++r2) {
+    let s1 = 0;
+    let s2 = 1;
+    const a = [];
+    for (let i = 0; i <= p; ++i) {
+      a[i] = zeroArr.slice(0);
+    }
+    a[0][0] = 1;
+    for (let k = 1; k <= n; ++k) {
+      let d = 0;
+      const rk = r2 - k;
+      const pk = p - k;
+      if (r2 >= k) {
+        a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
+        d = a[s2][0] * ndu[rk][pk];
+      }
+      const j1 = rk >= -1 ? 1 : -rk;
+      const j2 = r2 - 1 <= pk ? k - 1 : p - r2;
+      for (let j3 = j1; j3 <= j2; ++j3) {
+        a[s2][j3] = (a[s1][j3] - a[s1][j3 - 1]) / ndu[pk + 1][rk + j3];
+        d += a[s2][j3] * ndu[rk + j3][pk];
+      }
+      if (r2 <= pk) {
+        a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r2];
+        d += a[s2][k] * ndu[r2][pk];
+      }
+      ders[k][r2] = d;
+      const j = s1;
+      s1 = s2;
+      s2 = j;
+    }
+  }
+  let r = p;
+  for (let k = 1; k <= n; ++k) {
+    for (let j = 0; j <= p; ++j) {
+      ders[k][j] *= r;
+    }
+    r *= p - k;
+  }
+  return ders;
+}
+function calcBSplineDerivatives(p, U, P, u, nd) {
+  const du = nd < p ? nd : p;
+  const CK = [];
+  const span = findSpan(p, u, U);
+  const nders = calcBasisFunctionDerivatives(span, u, p, du, U);
+  const Pw = [];
+  for (let i = 0; i < P.length; ++i) {
+    const point = P[i].clone();
+    const w = point.w;
+    point.x *= w;
+    point.y *= w;
+    point.z *= w;
+    Pw[i] = point;
+  }
+  for (let k = 0; k <= du; ++k) {
+    const point = Pw[span - p].clone().multiplyScalar(nders[k][0]);
+    for (let j = 1; j <= p; ++j) {
+      point.add(Pw[span - p + j].clone().multiplyScalar(nders[k][j]));
+    }
+    CK[k] = point;
+  }
+  for (let k = du + 1; k <= nd + 1; ++k) {
+    CK[k] = new Vector4(0, 0, 0);
+  }
+  return CK;
+}
+function calcKoverI(k, i) {
+  let nom = 1;
+  for (let j = 2; j <= k; ++j) {
+    nom *= j;
+  }
+  let denom = 1;
+  for (let j = 2; j <= i; ++j) {
+    denom *= j;
+  }
+  for (let j = 2; j <= k - i; ++j) {
+    denom *= j;
+  }
+  return nom / denom;
+}
+function calcRationalCurveDerivatives(Pders) {
+  const nd = Pders.length;
+  const Aders = [];
+  const wders = [];
+  for (let i = 0; i < nd; ++i) {
+    const point = Pders[i];
+    Aders[i] = new Vector3(point.x, point.y, point.z);
+    wders[i] = point.w;
+  }
+  const CK = [];
+  for (let k = 0; k < nd; ++k) {
+    const v = Aders[k].clone();
+    for (let i = 1; i <= k; ++i) {
+      v.sub(CK[k - i].clone().multiplyScalar(calcKoverI(k, i) * wders[i]));
+    }
+    CK[k] = v.divideScalar(wders[0]);
+  }
+  return CK;
+}
+function calcNURBSDerivatives(p, U, P, u, nd) {
+  const Pders = calcBSplineDerivatives(p, U, P, u, nd);
+  return calcRationalCurveDerivatives(Pders);
+}
+function calcSurfacePoint(p, q, U, V, P, u, v, target) {
+  const uspan = findSpan(p, u, U);
+  const vspan = findSpan(q, v, V);
+  const Nu = calcBasisFunctions(uspan, u, p, U);
+  const Nv = calcBasisFunctions(vspan, v, q, V);
+  const temp = [];
+  for (let l = 0; l <= q; ++l) {
+    temp[l] = new Vector4(0, 0, 0, 0);
+    for (let k = 0; k <= p; ++k) {
+      const point = P[uspan - p + k][vspan - q + l].clone();
+      const w = point.w;
+      point.x *= w;
+      point.y *= w;
+      point.z *= w;
+      temp[l].add(point.multiplyScalar(Nu[k]));
+    }
+  }
+  const Sw = new Vector4(0, 0, 0, 0);
+  for (let l = 0; l <= q; ++l) {
+    Sw.add(temp[l].multiplyScalar(Nv[l]));
+  }
+  Sw.divideScalar(Sw.w);
+  target.set(Sw.x, Sw.y, Sw.z);
+}
+export {
+  calcBSplineDerivatives,
+  calcBSplinePoint,
+  calcBasisFunctionDerivatives,
+  calcBasisFunctions,
+  calcKoverI,
+  calcNURBSDerivatives,
+  calcRationalCurveDerivatives,
+  calcSurfacePoint,
+  findSpan
+};
+//# sourceMappingURL=NURBSUtils.js.map