// 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: 4.0.2019.12.28
#pragma once
#include <Mathematics/BasisFunction.h>
#include <Mathematics/ParametricSurface.h>
#include <Mathematics/Vector.h>
namespace WwiseGTE
{
template <int N, typename Real>
class NURBSSurface : public ParametricSurface<N, Real>
{
public:
// Construction. If the input controls is non-null, a copy is made of
// the controls. To defer setting the control points or weights, pass
// null pointers and later access the control points or weights via
// GetControls(), GetWeights(), SetControl(), or SetWeight() member
// functions. The 'controls' and 'weights' must be stored in
// row-major order, attribute[i0 + numControls0*i1]. As a 2D array,
// this corresponds to attribute2D[i1][i0].
NURBSSurface(BasisFunctionInput<Real> const& input0,
BasisFunctionInput<Real> const& input1,
Vector<N, Real> const* controls, Real const* weights)
:
ParametricSurface<N, Real>((Real)0, (Real)1, (Real)0, (Real)1, true)
{
BasisFunctionInput<Real> const* input[2] = { &input0, &input1 };
for (int i = 0; i < 2; ++i)
{
mNumControls[i] = input[i]->numControls;
mBasisFunction[i].Create(*input[i]);
}
// The mBasisFunction stores the domain but so does
// ParametricSurface.
this->mUMin = mBasisFunction[0].GetMinDomain();
this->mUMax = mBasisFunction[0].GetMaxDomain();
this->mVMin = mBasisFunction[1].GetMinDomain();
this->mVMax = mBasisFunction[1].GetMaxDomain();
// The replication of control points for periodic splines is
// avoided by wrapping the i-loop index in Evaluate.
int numControls = mNumControls[0] * mNumControls[1];
mControls.resize(numControls);
mWeights.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);
}
if (weights)
{
std::copy(weights, weights + numControls, mWeights.begin());
}
else
{
std::fill(mWeights.begin(), mWeights.end(), (Real)0);
}
this->mConstructed = true;
}
// Member access. The index 'dim' must be in {0,1}.
inline BasisFunction<Real> const& GetBasisFunction(int dim) const
{
return mBasisFunction[dim];
}
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();
}
inline Real const* GetWeights() const
{
return mWeights.data();
}
inline Real* GetWeights()
{
return mWeights.data();
}
void SetControl(int i0, int i1, Vector<N, Real> const& control)
{
if (0 <= i0 && i0 < GetNumControls(0) && 0 <= i1 && i1 < GetNumControls(1))
{
mControls[i0 + mNumControls[0] * i1] = control;
}
}
Vector<N, Real> const& GetControl(int i0, int i1) const
{
if (0 <= i0 && i0 < GetNumControls(0) && 0 <= i1 && i1 < GetNumControls(1))
{
return mControls[i0 + mNumControls[0] * i1];
}
else
{
return mControls[0];
}
}
void SetWeight(int i0, int i1, Real weight)
{
if (0 <= i0 && i0 < GetNumControls(0) && 0 <= i1 && i1 < GetNumControls(1))
{
mWeights[i0 + mNumControls[0] * i1] = weight;
}
}
Real const& GetWeight(int i0, int i1) const
{
if (0 <= i0 && i0 < GetNumControls(0) && 0 <= i1 && i1 < GetNumControls(1))
{
return mWeights[i0 + mNumControls[0] * i1];
}
else
{
return mWeights[0];
}
}
// Evaluation of the surface. 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' must have enough storage to support the
// maximum order. The values are ordered as: position X; first-order
// derivatives dX/du, dX/dv; second-order derivatives d2X/du2,
// d2X/dudv, d2X/dv2.
virtual void Evaluate(Real u, Real v, unsigned int order, Vector<N, Real>* jet) const override
{
unsigned int const supOrder = ParametricSurface<N, Real>::SUP_ORDER;
if (!this->mConstructed || order >= supOrder)
{
// Return a zero-valued jet for invalid state.
for (unsigned int i = 0; i < supOrder; ++i)
{
jet[i].MakeZero();
}
return;
}
int iumin, iumax, ivmin, ivmax;
mBasisFunction[0].Evaluate(u, order, iumin, iumax);
mBasisFunction[1].Evaluate(v, order, ivmin, ivmax);
// Compute position.
Vector<N, Real> X;
Real w;
Compute(0, 0, iumin, iumax, ivmin, ivmax, X, w);
Real invW = (Real)1 / w;
jet[0] = invW * X;
if (order >= 1)
{
// Compute first-order derivatives.
Vector<N, Real> XDerU;
Real wDerU;
Compute(1, 0, iumin, iumax, ivmin, ivmax, XDerU, wDerU);
jet[1] = invW * (XDerU - wDerU * jet[0]);
Vector<N, Real> XDerV;
Real wDerV;
Compute(0, 1, iumin, iumax, ivmin, ivmax, XDerV, wDerV);
jet[2] = invW * (XDerV - wDerV * jet[0]);
if (order >= 2)
{
// Compute second-order derivatives.
Vector<N, Real> XDerUU;
Real wDerUU;
Compute(2, 0, iumin, iumax, ivmin, ivmax, XDerUU, wDerUU);
jet[3] = invW * (XDerUU - (Real)2 * wDerU * jet[1] - wDerUU * jet[0]);
Vector<N, Real> XDerUV;
Real wDerUV;
Compute(1, 1, iumin, iumax, ivmin, ivmax, XDerUV, wDerUV);
jet[4] = invW * (XDerUV - wDerU * jet[2] - wDerV * jet[1]
- wDerUV * jet[0]);
Vector<N, Real> XDerVV;
Real wDerVV;
Compute(0, 2, iumin, iumax, ivmin, ivmax, XDerVV, wDerVV);
jet[5] = invW * (XDerVV - (Real)2 * wDerV * jet[2] - wDerVV * jet[0]);
}
}
}
protected:
// Support for Evaluate(...).
void Compute(unsigned int uOrder, unsigned int vOrder, int iumin,
int iumax, int ivmin, int ivmax, Vector<N, Real>& X, Real& w) 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];
X.MakeZero();
w = (Real)0;
for (int iv = ivmin; iv <= ivmax; ++iv)
{
Real tmpv = mBasisFunction[1].GetValue(vOrder, iv);
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);
int index = ju + numControls0 * jv;
Real tmp = tmpu * tmpv * mWeights[index];
X += tmp * mControls[index];
w += tmp;
}
}
}
std::array<BasisFunction<Real>, 2> mBasisFunction;
std::array<int, 2> mNumControls;
std::vector<Vector<N, Real>> mControls;
std::vector<Real> mWeights;
};
}