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246 lines
9.4 KiB
246 lines
9.4 KiB
// 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: 4.0.2019.12.28
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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 NURBSVolume
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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 or weights, pass
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// null pointers and later access the control points or weights via
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// GetControls(), GetWeights(), SetControl(), or SetWeight() member
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// functions. The 'controls' and 'weights' must be stored in
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// lexicographical order,
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// attribute[i0 + numControls0 * (i1 + numControls1 * i2)]
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// As a 3D array, this corresponds to attribute3D[i2][i1][i0].
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NURBSVolume(BasisFunctionInput<Real> const& input0,
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BasisFunctionInput<Real> const& input1,
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BasisFunctionInput<Real> const& input2,
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Vector<N, Real> const* controls, Real const* weights)
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:
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mConstructed(false)
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{
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BasisFunctionInput<Real> const* input[3] = { &input0, &input1, &input2 };
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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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mWeights.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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if (weights)
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{
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std::copy(weights, weights + numControls, mWeights.begin());
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}
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else
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{
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std::fill(mWeights.begin(), mWeights.end(), (Real)0);
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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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// NURBSVolume<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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inline Real const* GetWeights() const
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{
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return mWeights.data();
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}
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inline Real* GetWeights()
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{
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return mWeights.data();
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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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// Errors were already generated during construction.
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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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Vector<N, Real> X;
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Real h;
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Compute(0, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax, X, h);
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Real invH = (Real)1 / h;
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jet[0] = invH * X;
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if (order >= 1)
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{
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// Compute first-order derivatives.
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Vector<N, Real> XDerU;
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Real hDerU;
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Compute(1, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerU, hDerU);
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jet[1] = invH * (XDerU - hDerU * jet[0]);
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Vector<N, Real> XDerV;
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Real hDerV;
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Compute(0, 1, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerV, hDerV);
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jet[2] = invH * (XDerV - hDerV * jet[0]);
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Vector<N, Real> XDerW;
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Real hDerW;
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Compute(0, 0, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerW, hDerW);
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jet[3] = invH * (XDerW - hDerW * jet[0]);
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if (order >= 2)
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{
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// Compute second-order derivatives.
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Vector<N, Real> XDerUU;
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Real hDerUU;
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Compute(2, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerUU, hDerUU);
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jet[4] = invH * (XDerUU - (Real)2 * hDerU * jet[1] - hDerUU * jet[0]);
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Vector<N, Real> XDerVV;
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Real hDerVV;
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Compute(0, 2, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerVV, hDerVV);
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jet[5] = invH * (XDerVV - (Real)2 * hDerV * jet[2] - hDerVV * jet[0]);
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Vector<N, Real> XDerWW;
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Real hDerWW;
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Compute(0, 0, 2, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerWW, hDerWW);
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jet[6] = invH * (XDerWW - (Real)2 * hDerW * jet[3] - hDerWW * jet[0]);
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Vector<N, Real> XDerUV;
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Real hDerUV;
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Compute(1, 1, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerUV, hDerUV);
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jet[7] = invH * (XDerUV - hDerU * jet[2] - hDerV * jet[1] - hDerUV * jet[0]);
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Vector<N, Real> XDerUW;
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Real hDerUW;
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Compute(1, 0, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerUW, hDerUW);
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jet[8] = invH * (XDerUW - hDerU * jet[3] - hDerW * jet[1] - hDerUW * jet[0]);
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Vector<N, Real> XDerVW;
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Real hDerVW;
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Compute(0, 1, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax, XDerVW, hDerVW);
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jet[9] = invH * (XDerVW - hDerV * jet[3] - hDerW * jet[2] - hDerVW * jet[0]);
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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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void 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, Vector<N, Real>& X, Real& h) 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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X.MakeZero();
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h = (Real)0;
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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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int index = ju + numControls0 * (jv + numControls1 * jw);
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Real tmp = (tmpu * tmpvw) * mWeights[index];
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X += tmp * mControls[index];
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h += tmp;
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}
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}
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}
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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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std::vector<Real> mWeights;
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bool mConstructed;
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};
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}
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