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205 lines
7.8 KiB
205 lines
7.8 KiB
3 months ago
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// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/BasisFunction.h>
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#include <Mathematics/Vector.h>
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namespace gte
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{
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template <int N, typename Real>
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class BSplineVolume
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{
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public:
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// Construction. If the input controls is non-null, a copy is made of
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// the controls. To defer setting the control points, pass a null
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// pointer and later access the control points via GetControls() or
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// SetControl() member functions. The input 'controls' must be stored
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// in lexicographical order,
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// control[i0+numControls0*(i1+numControls1*i2)]. As a 3D array, this
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// corresponds to control3D[i2][i1][i0].
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BSplineVolume(BasisFunctionInput<Real> const input[3], Vector<N, Real> const* controls)
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:
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mConstructed(false)
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{
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for (int i = 0; i < 3; ++i)
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{
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mNumControls[i] = input[i].numControls;
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mBasisFunction[i].Create(input[i]);
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}
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// The replication of control points for periodic splines is
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// avoided by wrapping the i-loop index in Evaluate.
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int numControls = mNumControls[0] * mNumControls[1] * mNumControls[2];
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mControls.resize(numControls);
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if (controls)
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{
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std::copy(controls, controls + numControls, mControls.begin());
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}
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else
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{
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Vector<N, Real> zero{ (Real)0 };
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std::fill(mControls.begin(), mControls.end(), zero);
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}
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mConstructed = true;
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}
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// To validate construction, create an object as shown:
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// BSplineVolume<N, Real> volume(parameters);
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// if (!volume) { <constructor failed, handle accordingly>; }
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inline operator bool() const
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{
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return mConstructed;
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}
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// Member access. The index 'dim' must be in {0,1,2}.
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inline BasisFunction<Real> const& GetBasisFunction(int dim) const
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{
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return mBasisFunction[dim];
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}
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inline Real GetMinDomain(int dim) const
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{
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return mBasisFunction[dim].GetMinDomain();
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}
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inline Real GetMaxDomain(int dim) const
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{
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return mBasisFunction[dim].GetMaxDomain();
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}
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inline int GetNumControls(int dim) const
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{
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return mNumControls[dim];
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}
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inline Vector<N, Real> const* GetControls() const
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{
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return mControls.data();
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}
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inline Vector<N, Real>* GetControls()
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{
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return mControls.data();
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}
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void SetControl(int i0, int i1, int i2, Vector<N, Real> const& control)
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{
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if (0 <= i0 && i0 < GetNumControls(0)
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&& 0 <= i1 && i1 < GetNumControls(1)
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&& 0 <= i2 && i2 < GetNumControls(2))
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{
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mControls[i0 + mNumControls[0] * (i1 + mNumControls[1] * i2)] = control;
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}
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}
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Vector<N, Real> const& GetControl(int i0, int i1, int i2) const
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{
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if (0 <= i0 && i0 < GetNumControls(0)
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&& 0 <= i1 && i1 < GetNumControls(1)
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&& 0 <= i2 && i2 < GetNumControls(2))
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{
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return mControls[i0 + mNumControls[0] * (i1 + mNumControls[1] * i2)];
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}
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else
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{
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return mControls[0];
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}
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}
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// Evaluation of the volume. The function supports derivative
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// calculation through order 2; that is, order <= 2 is required. If
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// you want only the position, pass in order of 0. If you want the
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// position and first-order derivatives, pass in order of 1, and so
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// on. The output array 'jet' muist have enough storage to support
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// the maximum order. The values are ordered as: position X;
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// first-order derivatives dX/du, dX/dv, dX/dw; second-order
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// derivatives d2X/du2, d2X/dv2, d2X/dw2, d2X/dudv, d2X/dudw,
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// d2X/dvdw.
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enum { SUP_ORDER = 10 };
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void Evaluate(Real u, Real v, Real w, unsigned int order, Vector<N, Real>* jet) const
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{
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if (!mConstructed || order >= SUP_ORDER)
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{
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// Return a zero-valued jet for invalid state.
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for (unsigned int i = 0; i < SUP_ORDER; ++i)
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{
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jet[i].MakeZero();
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}
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return;
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}
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int iumin, iumax, ivmin, ivmax, iwmin, iwmax;
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mBasisFunction[0].Evaluate(u, order, iumin, iumax);
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mBasisFunction[1].Evaluate(v, order, ivmin, ivmax);
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mBasisFunction[2].Evaluate(w, order, iwmin, iwmax);
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// Compute position.
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jet[0] = Compute(0, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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if (order >= 1)
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{
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// Compute first-order derivatives.
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jet[1] = Compute(1, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[2] = Compute(0, 1, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[3] = Compute(0, 0, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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if (order >= 2)
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{
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// Compute second-order derivatives.
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jet[4] = Compute(2, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[5] = Compute(0, 2, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[6] = Compute(0, 0, 2, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[7] = Compute(1, 1, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[8] = Compute(1, 0, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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jet[9] = Compute(0, 1, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
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}
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}
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}
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private:
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// Support for Evaluate(...).
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Vector<N, Real> Compute(unsigned int uOrder, unsigned int vOrder,
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unsigned int wOrder, int iumin, int iumax, int ivmin, int ivmax,
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int iwmin, int iwmax) const
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{
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// The j*-indices introduce a tiny amount of overhead in order to
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// handle both aperiodic and periodic splines. For aperiodic
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// splines, j* = i* always.
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int const numControls0 = mNumControls[0];
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int const numControls1 = mNumControls[1];
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int const numControls2 = mNumControls[2];
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Vector<N, Real> result;
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result.MakeZero();
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for (int iw = iwmin; iw <= iwmax; ++iw)
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{
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Real tmpw = mBasisFunction[2].GetValue(wOrder, iw);
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int jw = (iw >= numControls2 ? iw - numControls2 : iw);
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for (int iv = ivmin; iv <= ivmax; ++iv)
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{
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Real tmpv = mBasisFunction[1].GetValue(vOrder, iv);
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Real tmpvw = tmpv * tmpw;
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int jv = (iv >= numControls1 ? iv - numControls1 : iv);
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for (int iu = iumin; iu <= iumax; ++iu)
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{
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Real tmpu = mBasisFunction[0].GetValue(uOrder, iu);
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int ju = (iu >= numControls0 ? iu - numControls0 : iu);
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result += (tmpu * tmpvw) *
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mControls[ju + numControls0 * (jv + numControls1 * jw)];
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}
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}
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}
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return result;
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}
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std::array<BasisFunction<Real>, 3> mBasisFunction;
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std::array<int, 3> mNumControls;
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std::vector<Vector<N, Real>> mControls;
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bool mConstructed;
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};
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}
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