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#ifndef BICUBIC_HPP
#define BICUBIC_HPP
#include <algorithm>
#include <vector>
#include <cmath>
#include <Eigen/Dense>
namespace Slic3r {
namespace BicubicInternal {
// Linear kernel, to be able to test cubic methods with hat kernels.
template<typename T>
struct LinearKernel
{
typedef T FloatType;
static T a00() { return T(0.); }
static T a01() { return T(0.); }
static T a02() { return T(0.); }
static T a03() { return T(0.); }
static T a10() { return T(1.); }
static T a11() { return T(-1.); }
static T a12() { return T(0.); }
static T a13() { return T(0.); }
static T a20() { return T(0.); }
static T a21() { return T(1.); }
static T a22() { return T(0.); }
static T a23() { return T(0.); }
static T a30() { return T(0.); }
static T a31() { return T(0.); }
static T a32() { return T(0.); }
static T a33() { return T(0.); }
};
// Interpolation kernel aka Catmul-Rom aka Keyes kernel.
template<typename T>
struct CubicCatmulRomKernel
{
typedef T FloatType;
static T a00() { return 0; }
static T a01() { return (T)-0.5; }
static T a02() { return (T) 1.; }
static T a03() { return (T)-0.5; }
static T a10() { return (T) 1.; }
static T a11() { return 0; }
static T a12() { return (T)-5./2.; }
static T a13() { return (T) 3./2.; }
static T a20() { return 0; }
static T a21() { return (T) 0.5; }
static T a22() { return (T) 2.; }
static T a23() { return (T)-3./2.; }
static T a30() { return 0; }
static T a31() { return 0; }
static T a32() { return (T)-0.5; }
static T a33() { return (T) 0.5; }
};
// B-spline kernel
template<typename T>
struct CubicBSplineKernel
{
typedef T FloatType;
static T a00() { return (T) 1./6.; }
static T a01() { return (T) -3./6.; }
static T a02() { return (T) 3./6.; }
static T a03() { return (T) -1./6.; }
static T a10() { return (T) 4./6.; }
static T a11() { return 0; }
static T a12() { return (T) -6./6.; }
static T a13() { return (T) 3./6.; }
static T a20() { return (T) 1./6.; }
static T a21() { return (T) 3./6.; }
static T a22() { return (T) 3./6.; }
static T a23() { return (T)- 3./6.; }
static T a30() { return 0; }
static T a31() { return 0; }
static T a32() { return 0; }
static T a33() { return (T) 1./6.; }
};
template<class T>
inline T clamp(T a, T lower, T upper)
{
return (a < lower) ? lower :
(a > upper) ? upper : a;
}
}
template<typename KERNEL>
struct CubicKernel
{
typedef typename KERNEL KernelInternal;
typedef typename KERNEL::FloatType FloatType;
static FloatType kernel(FloatType x)
{
x = fabs(x);
if (x >= (FloatType)2.)
return 0.0f;
if (x <= (FloatType)1.) {
FloatType x2 = x * x;
FloatType x3 = x2 * x;
return KERNEL::a10() + KERNEL::a11() * x + KERNEL::a12() * x2 + KERNEL::a13() * x3;
}
assert(x > (FloatType)1. && x < (FloatType)2.);
x -= (FloatType)1.;
FloatType x2 = x * x;
FloatType x3 = x2 * x;
return KERNEL::a00() + KERNEL::a01() * x + KERNEL::a02() * x2 + KERNEL::a03() * x3;
}
static FloatType interpolate(FloatType f0, FloatType f1, FloatType f2, FloatType f3, FloatType x)
{
const FloatType x2 = x*x;
const FloatType x3 = x*x*x;
return f0*(KERNEL::a00() + KERNEL::a01() * x + KERNEL::a02() * x2 + KERNEL::a03() * x3) +
f1*(KERNEL::a10() + KERNEL::a11() * x + KERNEL::a12() * x2 + KERNEL::a13() * x3) +
f2*(KERNEL::a20() + KERNEL::a21() * x + KERNEL::a22() * x2 + KERNEL::a23() * x3) +
f3*(KERNEL::a30() + KERNEL::a31() * x + KERNEL::a32() * x2 + KERNEL::a33() * x3);
}
};
// Linear splines
typedef CubicKernel<BicubicInternal::LinearKernel<float>> LinearKernelf;
typedef CubicKernel<BicubicInternal::LinearKernel<double>> LinearKerneld;
// Catmul-Rom splines
typedef CubicKernel<BicubicInternal::CubicCatmulRomKernel<float>> CubicCatmulRomKernelf;
typedef CubicKernel<BicubicInternal::CubicCatmulRomKernel<double>> CubicCatmulRomKerneld;
typedef CubicKernel<BicubicInternal::CubicCatmulRomKernel<float>> CubicInterpolationKernelf;
typedef CubicKernel<BicubicInternal::CubicCatmulRomKernel<double>> CubicInterpolationKerneld;
// Cubic B-splines
typedef CubicKernel<BicubicInternal::CubicBSplineKernel<float>> CubicBSplineKernelf;
typedef CubicKernel<BicubicInternal::CubicBSplineKernel<double>> CubicBSplineKerneld;
template<typename KERNEL, typename Derived>
static float cubic_interpolate(const Eigen::ArrayBase<Derived> &F, const typename KERNEL::FloatType pt, const typename KERNEL::FloatType dx)
{
typedef typename KERNEL::FloatType T;
const int w = int(F.size());
const int ix = (int)floor(pt);
const T s = pt - (T)ix;
if (ix > 1 && ix + 2 < w) {
// Inside the fully interpolated region.
return KERNEL::interpolate(F[ix - 1], F[ix], F[ix + 1], F[ix + 2], s);
}
// Transition region. Extend with a constant function.
auto f = [&F, w](x) { return F[BicubicInternal::clamp(x, 0, w - 1)]; }
return KERNEL::interpolate(f(ix - 1), f(ix), f(ix + 1), f(ix + 2), s);
}
template<typename KERNEL, typename Derived>
static float bicubic_interpolate(const Eigen::MatrixBase<Derived> &F, const Eigen::Matrix<typename KERNEL::FloatType, 2, 1, Eigen::DontAlign> &pt, const typename KERNEL::FloatType dx)
{
typedef typename KERNEL::FloatType T;
const int w = F.cols();
const int h = F.rows();
const int ix = (int)floor(pt[0]);
const int iy = (int)floor(pt[1]);
const T s = pt[0] - (T)ix;
const T t = pt[1] - (T)iy;
if (ix > 1 && ix + 2 < w && iy > 1 && iy + 2 < h) {
// Inside the fully interpolated region.
return KERNEL::interpolate(
KERNEL::interpolate(F(ix-1,iy-1),F(ix ,iy-1),F(ix+1,iy-1),F(ix+2,iy-1),s),
KERNEL::interpolate(F(ix-1,iy ),F(ix ,iy ),F(ix+1,iy ),F(ix+2,iy ),s),
KERNEL::interpolate(F(ix-1,iy+1),F(ix ,iy+1),F(ix+1,iy+1),F(ix+2,iy+1),s),
KERNEL::interpolate(F(ix-1,iy+2),F(ix ,iy+2),F(ix+1,iy+2),F(ix+2,iy+2),s),t);
}
// Transition region. Extend with a constant function.
auto f = [&f, w, h](int x, int y) { return F(BicubicInternal::clamp(x,0,w-1),BicubicInternal::clamp(y,0,h-1)); }
return KERNEL::interpolate(
KERNEL::interpolate(f(ix-1,iy-1),f(ix ,iy-1),f(ix+1,iy-1),f(ix+2,iy-1),s),
KERNEL::interpolate(f(ix-1,iy ),f(ix ,iy ),f(ix+1,iy ),f(ix+2,iy ),s),
KERNEL::interpolate(f(ix-1,iy+1),f(ix ,iy+1),f(ix+1,iy+1),f(ix+2,iy+1),s),
KERNEL::interpolate(f(ix-1,iy+2),f(ix ,iy+2),f(ix+1,iy+2),f(ix+2,iy+2),s),t);
}
} // namespace Slic3r
#endif /* BICUBIC_HPP */
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