// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2020
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2019.08.13
#pragma once
#include <Mathematics/BasisFunction.h>
#include <Mathematics/Vector.h>
namespace WwiseGTE
{
template <int N, typename Real>
class BSplineVolume
{
public:
// Construction. If the input controls is non-null, a copy is made of
// the controls. To defer setting the control points, pass a null
// pointer and later access the control points via GetControls() or
// SetControl() member functions. The input 'controls' must be stored
// in lexicographical order,
// control[i0+numControls0*(i1+numControls1*i2)]. As a 3D array, this
// corresponds to control3D[i2][i1][i0].
BSplineVolume(BasisFunctionInput<Real> const input[3], Vector<N, Real> const* controls)
:
mConstructed(false)
{
for (int i = 0; i < 3; ++i)
{
mNumControls[i] = input[i].numControls;
mBasisFunction[i].Create(input[i]);
}
// The replication of control points for periodic splines is
// avoided by wrapping the i-loop index in Evaluate.
int numControls = mNumControls[0] * mNumControls[1] * mNumControls[2];
mControls.resize(numControls);
if (controls)
{
std::copy(controls, controls + numControls, mControls.begin());
}
else
{
Vector<N, Real> zero{ (Real)0 };
std::fill(mControls.begin(), mControls.end(), zero);
}
mConstructed = true;
}
// To validate construction, create an object as shown:
// BSplineVolume<N, Real> volume(parameters);
// if (!volume) { <constructor failed, handle accordingly>; }
inline operator bool() const
{
return mConstructed;
}
// Member access. The index 'dim' must be in {0,1,2}.
inline BasisFunction<Real> const& GetBasisFunction(int dim) const
{
return mBasisFunction[dim];
}
inline Real GetMinDomain(int dim) const
{
return mBasisFunction[dim].GetMinDomain();
}
inline Real GetMaxDomain(int dim) const
{
return mBasisFunction[dim].GetMaxDomain();
}
inline int GetNumControls(int dim) const
{
return mNumControls[dim];
}
inline Vector<N, Real> const* GetControls() const
{
return mControls.data();
}
inline Vector<N, Real>* GetControls()
{
return mControls.data();
}
void SetControl(int i0, int i1, int i2, Vector<N, Real> const& control)
{
if (0 <= i0 && i0 < GetNumControls(0)
&& 0 <= i1 && i1 < GetNumControls(1)
&& 0 <= i2 && i2 < GetNumControls(2))
{
mControls[i0 + mNumControls[0] * (i1 + mNumControls[1] * i2)] = control;
}
}
Vector<N, Real> const& GetControl(int i0, int i1, int i2) const
{
if (0 <= i0 && i0 < GetNumControls(0)
&& 0 <= i1 && i1 < GetNumControls(1)
&& 0 <= i2 && i2 < GetNumControls(2))
{
return mControls[i0 + mNumControls[0] * (i1 + mNumControls[1] * i2)];
}
else
{
return mControls[0];
}
}
// Evaluation of the volume. The function supports derivative
// calculation through order 2; that is, order <= 2 is required. If
// you want only the position, pass in order of 0. If you want the
// position and first-order derivatives, pass in order of 1, and so
// on. The output array 'jet' muist have enough storage to support
// the maximum order. The values are ordered as: position X;
// first-order derivatives dX/du, dX/dv, dX/dw; second-order
// derivatives d2X/du2, d2X/dv2, d2X/dw2, d2X/dudv, d2X/dudw,
// d2X/dvdw.
enum { SUP_ORDER = 10 };
void Evaluate(Real u, Real v, Real w, unsigned int order, Vector<N, Real>* jet) const
{
if (!mConstructed || order >= SUP_ORDER)
{
// Return a zero-valued jet for invalid state.
for (unsigned int i = 0; i < SUP_ORDER; ++i)
{
jet[i].MakeZero();
}
return;
}
int iumin, iumax, ivmin, ivmax, iwmin, iwmax;
mBasisFunction[0].Evaluate(u, order, iumin, iumax);
mBasisFunction[1].Evaluate(v, order, ivmin, ivmax);
mBasisFunction[2].Evaluate(w, order, iwmin, iwmax);
// Compute position.
jet[0] = Compute(0, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
if (order >= 1)
{
// Compute first-order derivatives.
jet[1] = Compute(1, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[2] = Compute(0, 1, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[3] = Compute(0, 0, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
if (order >= 2)
{
// Compute second-order derivatives.
jet[4] = Compute(2, 0, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[5] = Compute(0, 2, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[6] = Compute(0, 0, 2, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[7] = Compute(1, 1, 0, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[8] = Compute(1, 0, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
jet[9] = Compute(0, 1, 1, iumin, iumax, ivmin, ivmax, iwmin, iwmax);
}
}
}
private:
// Support for Evaluate(...).
Vector<N, Real> Compute(unsigned int uOrder, unsigned int vOrder,
unsigned int wOrder, int iumin, int iumax, int ivmin, int ivmax,
int iwmin, int iwmax) const
{
// The j*-indices introduce a tiny amount of overhead in order to
// handle both aperiodic and periodic splines. For aperiodic
// splines, j* = i* always.
int const numControls0 = mNumControls[0];
int const numControls1 = mNumControls[1];
int const numControls2 = mNumControls[2];
Vector<N, Real> result;
result.MakeZero();
for (int iw = iwmin; iw <= iwmax; ++iw)
{
Real tmpw = mBasisFunction[2].GetValue(wOrder, iw);
int jw = (iw >= numControls2 ? iw - numControls2 : iw);
for (int iv = ivmin; iv <= ivmax; ++iv)
{
Real tmpv = mBasisFunction[1].GetValue(vOrder, iv);
Real tmpvw = tmpv * tmpw;
int jv = (iv >= numControls1 ? iv - numControls1 : iv);
for (int iu = iumin; iu <= iumax; ++iu)
{
Real tmpu = mBasisFunction[0].GetValue(uOrder, iu);
int ju = (iu >= numControls0 ? iu - numControls0 : iu);
result += (tmpu * tmpvw) *
mControls[ju + numControls0 * (jv + numControls1 * jw)];
}
}
}
return result;
}
std::array<BasisFunction<Real>, 3> mBasisFunction;
std::array<int, 3> mNumControls;
std::vector<Vector<N, Real>> mControls;
bool mConstructed;
};
}