A complete re-write of the cubic interpolation code.
The key change is that there is a new layer of abstract,
a Array object that the interpolator depends on.
The Array provides a one dimension or two dimensional
array like interface independent of the underlying representation
of the data.
Also included here is support for vector valued functions.
Change-Id: Ica68f03778cf0d84192db00cd55653f8b4124d51
diff --git a/include/ceres/cubic_interpolation.h b/include/ceres/cubic_interpolation.h
index 7e477c8..8b91f96 100644
--- a/include/ceres/cubic_interpolation.h
+++ b/include/ceres/cubic_interpolation.h
@@ -28,25 +28,93 @@
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
-#include "ceres/internal/port.h"
-
#ifndef CERES_PUBLIC_CUBIC_INTERPOLATION_H_
#define CERES_PUBLIC_CUBIC_INTERPOLATION_H_
+#include "ceres/internal/port.h"
+#include "Eigen/Core"
+#include "glog/logging.h"
+
namespace ceres {
-// This class takes as input a one dimensional array of values that is
-// assumed to be integer valued samples from a function f(x),
-// evaluated at x = 0, ... , n - 1 and uses cubic Hermite splines to
-// produce a smooth approximation to it that can be used to evaluate
-// the f(x) and f'(x) at any fractional point in the interval [0,
-// n-1].
+// Given samples from a function sampled at four equally spaced points,
//
-// Besides this, the reason this class is included with Ceres is that
-// the Evaluate method is overloaded so that the user can use it as
-// part of their automatically differentiated CostFunction objects
-// without worrying about the fact that they are working with a
-// numerically interpolated object.
+// p0 = f(-1)
+// p1 = f(0)
+// p2 = f(1)
+// p3 = f(2)
+//
+// Evaluate the cubic Hermite spline (also known as the Catmull-Rom
+// spline) at a point x that lies in the interval [0, 1].
+//
+// This is also the interpolation kernel (for the case of a = 0.5) as
+// proposed by R. Keys, in:
+//
+// "Cubic convolution interpolation for digital image processing".
+// IEEE Transactions on Acoustics, Speech, and Signal Processing
+// 29 (6): 1153–1160.
+//
+// For more details see
+//
+// http://en.wikipedia.org/wiki/Cubic_Hermite_spline
+// http://en.wikipedia.org/wiki/Bicubic_interpolation
+//
+// f if not NULL will contain the interpolated function values.
+// dfdx if not NULL will contain the interpolated derivative values.
+template <int kDataDimension>
+void CubicHermiteSpline(const Eigen::Matrix<double, kDataDimension, 1>& p0,
+ const Eigen::Matrix<double, kDataDimension, 1>& p1,
+ const Eigen::Matrix<double, kDataDimension, 1>& p2,
+ const Eigen::Matrix<double, kDataDimension, 1>& p3,
+ const double x,
+ double* f,
+ double* dfdx) {
+ DCHECK_GE(x, 0.0);
+ DCHECK_LE(x, 1.0);
+ typedef Eigen::Matrix<double, kDataDimension, 1> VType;
+ const VType a = 0.5 * (-p0 + 3.0 * p1 - 3.0 * p2 + p3);
+ const VType b = 0.5 * (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3);
+ const VType c = 0.5 * (-p0 + p2);
+ const VType d = p1;
+
+ // Use Horner's rule to evaluate the function value and its
+ // derivative.
+
+ // f = ax^3 + bx^2 + cx + d
+ if (f != NULL) {
+ Eigen::Map<VType>(f, kDataDimension) = d + x * (c + x * (b + x * a));
+ }
+
+ // dfdx = 3ax^2 + 2bx + c
+ if (dfdx != NULL) {
+ Eigen::Map<VType>(dfdx, kDataDimension) = c + x * (2.0 * b + 3.0 * a * x);
+ }
+}
+
+// Given as input a one dimensional array like object, which provides
+// the following interface.
+//
+// struct Array {
+// enum { DATA_DIMENSION = 2; };
+// void GetValue(int n, double* f) const;
+// int NumValues() const;
+// };
+//
+// Where, GetValue gives us the value of a function f (possibly vector
+// valued) on the integers:
+//
+// [0, ..., NumValues() - 1].
+//
+// and the enum DATA_DIMENSION indicates the dimensionality of the
+// function being interpolated. For example if you are interpolating a
+// color image with three channels (Red, Green & Blue), then
+// DATA_DIMENSION = 3.
+//
+// CubicInterpolator uses cubic Hermite splines to produce a smooth
+// approximation to it that can be used to evaluate the f(x) and f'(x)
+// at any real valued point in the interval:
+//
+// [0, NumValues() - 1].
//
// For more details on cubic interpolation see
//
@@ -55,20 +123,63 @@
// Example usage:
//
// const double x[] = {1.0, 2.0, 5.0, 6.0};
-// CubicInterpolator interpolator(x, 4);
+// Array1D data(x, 4);
+// CubicInterpolator interpolator(data);
// double f, dfdx;
// CHECK(interpolator.Evaluator(1.5, &f, &dfdx));
+template<typename Array>
class CERES_EXPORT CubicInterpolator {
public:
- // values is an array containing the values of the function to be
- // interpolated on the integer lattice [0, num_values - 1].
- //
- // values should be a valid pointer for the lifetime of this object.
- CubicInterpolator(const double* values, int num_values);
+ explicit CubicInterpolator(const Array& array)
+ : array_(array) {
+ CHECK_GT(array.NumValues(), 1);
+ // The + casts the enum into an int before doing the
+ // comparison. It is needed to prevent
+ // "-Wunnamed-type-template-args" related errors.
+ CHECK_GE(+Array::DATA_DIMENSION, 1);
+ }
- // Evaluate the interpolated function value and/or its
- // derivative. Returns false if x is out of bounds.
- bool Evaluate(double x, double* f, double* dfdx) const;
+ bool Evaluate(double x, double* f, double* dfdx) const {
+ const int num_values = array_.NumValues();
+ if (x < 0 || x > num_values - 1) {
+ LOG(ERROR) << "x = " << x
+ << " is not in the interval [0, " << num_values - 1 << "].";
+ return false;
+ }
+
+ int n = floor(x);
+ // Deal with the case where the point sits exactly on the right
+ // boundary.
+ if (n == num_values - 1) {
+ n -= 1;
+ }
+
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> p0, p1, p2, p3;
+
+ // The point being evaluated is now expected to lie in the
+ // internal corresponding to p1 and p2.
+ array_.GetValue(n, p1.data());
+ array_.GetValue(n + 1, p2.data());
+
+ // If we are at n >=1, the choose the element at n - 1, otherwise
+ // linearly interpolate from p1 and p2.
+ if (n > 0) {
+ array_.GetValue(n - 1, p0.data());
+ } else {
+ p0 = 2 * p1 - p2;
+ }
+
+ // If we are at n < num_values_ - 2, then choose the element n +
+ // 2, otherwise linearly interpolate from p1 and p2.
+ if (n < num_values - 2) {
+ array_.GetValue(n + 2, p3.data());
+ } else {
+ p3 = 2 * p2 - p1;
+ }
+
+ CubicHermiteSpline(p0, p1, p2, p3, x - n, f, dfdx);
+ return true;
+ }
// The following two Evaluate overloads are needed for interfacing
// with automatic differentiation. The first is for when a scalar
@@ -78,50 +189,223 @@
}
template<typename JetT> bool Evaluate(const JetT& x, JetT* f) const {
- double dfdx;
- if (!Evaluate(x.a, &f->a, &dfdx)) {
+ double fx[Array::DATA_DIMENSION], dfdx[Array::DATA_DIMENSION];
+ if (!Evaluate(x.a, fx, dfdx)) {
return false;
}
- f->v = dfdx * x.v;
+
+ for (int i = 0; i < Array::DATA_DIMENSION; ++i) {
+ f[i].a = fx[i];
+ f[i].v = dfdx[i] * x.v;
+ }
return true;
}
- int num_values() const { return num_values_; }
+ int NumValues() const { return array_.NumValues(); }
- private:
- const double* values_;
- const int num_values_;
+private:
+ const Array& array_;
};
-// This class takes as input a row-major array of values that is
-// assumed to be integer valued samples from a function f(x),
-// evaluated on the integer lattice [0, num_rows - 1] x [0, num_cols -
-// 1]; and uses the cubic convolution interpolation algorithm of
-// R. Keys, to produce a smooth approximation to it that can be used
-// to evaluate the f(r,c), df(r, c)/dr and df(r,c)/dc at any
-// fractional point inside this lattice.
+// Given as input a two dimensional array like object, which provides
+// the following interface:
//
-// For more details on cubic interpolation see
+// struct Array {
+// enum { DATA_DIMENSION = 1 };
+// void GetValue(int row, int col, double* f) const;
+// int NumRows() const;
+// int NumCols() const;
+// };
+//
+// Where, GetValue gives us the value of a function f (possibly vector
+// valued) on the integer grid:
+//
+// [0, ..., NumRows() - 1] x [0, ..., NumCols() - 1]
+//
+// and the enum DATA_DIMENSION indicates the dimensionality of the
+// function being interpolated. For example if you are interpolating a
+// color image with three channels (Red, Green & Blue), then
+// DATA_DIMENSION = 3.
+//
+// BiCubicInterpolator uses the cubic convolution interpolation
+// algorithm of R. Keys, to produce a smooth approximation to it that
+// can be used to evaluate the f(r,c), df(r, c)/dr and df(r,c)/dc at
+// any real valued point in the quad:
+//
+// [0, NumRows() - 1] x [0, NumCols() - 1]
+//
+// For more details on the algorithm used here see:
//
// "Cubic convolution interpolation for digital image processing".
-// IEEE Transactions on Acoustics, Speech, and Signal Processing
-// 29 (6): 1153–1160.
+// Robert G. Keys, IEEE Trans. on Acoustics, Speech, and Signal
+// Processing 29 (6): 1153–1160, 1981.
//
// http://en.wikipedia.org/wiki/Cubic_Hermite_spline
// http://en.wikipedia.org/wiki/Bicubic_interpolation
+template<typename Array>
class CERES_EXPORT BiCubicInterpolator {
public:
- // values is a row-major array containing the values of the function
- // to be interpolated on the integer lattice [0, num_rows - 1] x [0,
- // num_cols - 1];
- //
- // values should be a valid pointer for the lifetime of this object.
- BiCubicInterpolator(const double* values, int num_rows, int num_cols);
+ BiCubicInterpolator(const Array& array)
+ : array_(array) {
+ CHECK_GT(array.NumRows(), 1);
+ CHECK_GT(array.NumCols(), 1);
+ // The + casts the enum into an int before doing the
+ // comparison. It is needed to prevent
+ // "-Wunnamed-type-template-args" related errors.
+ CHECK_GE(+Array::DATA_DIMENSION, 1);
+ }
// Evaluate the interpolated function value and/or its
// derivative. Returns false if r or c is out of bounds.
bool Evaluate(double r, double c,
- double* f, double* dfdr, double* dfdc) const;
+ double* f, double* dfdr, double* dfdc) const {
+ const int num_rows = array_.NumRows();
+ const int num_cols = array_.NumCols();
+
+ if (r < 0 || r > num_rows - 1 || c < 0 || c > num_cols - 1) {
+ LOG(ERROR) << "(r, c) = (" << r << ", " << c << ")"
+ << " is not in the square defined by [0, 0] "
+ << " and [" << num_rows - 1 << ", " << num_cols - 1 << "]";
+ return false;
+ }
+
+ int row = floor(r);
+ // Handle the case where the point sits exactly on the bottom
+ // boundary.
+ if (row == num_rows - 1) {
+ row -= 1;
+ }
+
+ int col = floor(c);
+ // Handle the case where the point sits exactly on the right
+ // boundary.
+ if (col == num_cols - 1) {
+ col -= 1;
+ }
+
+ // BiCubic interpolation requires 16 values around the point being
+ // evaluated. We will use pij, to indicate the elements of the
+ // 4x4 array of values.
+ //
+ // col
+ // p00 p01 p02 p03
+ // row p10 p11 p12 p13
+ // p20 p21 p22 p23
+ // p30 p31 p32 p33
+ //
+ // The point (r,c) being evaluated is assumed to lie in the square
+ // defined by p11, p12, p22 and p21.
+
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> p00, p01, p02, p03;
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> p10, p11, p12, p13;
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> p20, p21, p22, p23;
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> p30, p31, p32, p33;
+
+ array_.GetValue(row, col, p11.data());
+ array_.GetValue(row, col + 1, p12.data());
+ array_.GetValue(row + 1, col, p21.data());
+ array_.GetValue(row + 1, col + 1, p22.data());
+
+ // If we are in rows >= 1, then choose the element from the row - 1,
+ // otherwise linearly interpolate from row and row + 1.
+ if (row > 0) {
+ array_.GetValue(row - 1, col, p01.data());
+ array_.GetValue(row - 1, col + 1, p02.data());
+ } else {
+ p01 = 2 * p11 - p21;
+ p02 = 2 * p12 - p22;
+ }
+
+ // If we are in row < num_rows - 2, then pick the element from the
+ // row + 2, otherwise linearly interpolate from row and row + 1.
+ if (row < num_rows - 2) {
+ array_.GetValue(row + 2, col, p31.data());
+ array_.GetValue(row + 2, col + 1, p32.data());
+ } else {
+ p31 = 2 * p21 - p22;
+ p32 = 2 * p22 - p12;
+ }
+
+ // Same logic as above, applies to the columns instead of rows.
+ if (col > 0) {
+ array_.GetValue(row, col - 1, p10.data());
+ array_.GetValue(row + 1, col - 1, p20.data());
+ } else {
+ p10 = 2 * p11 - p12;
+ p20 = 2 * p21 - p22;
+ }
+
+ if (col < num_cols - 2) {
+ array_.GetValue(row, col + 2, p13.data());
+ array_.GetValue(row + 1, col + 2, p23.data());
+ } else {
+ p13 = 2 * p12 - p11;
+ p23 = 2 * p22 - p21;
+ }
+
+ // The four corners of the block require a bit more care. Let us
+ // consider the evaluation of p00, the other three corners follow
+ // in the same manner.
+ //
+ // There are four cases in which we need to evaluate p00.
+ //
+ // row > 0, col > 0 : v(row, col)
+ // row = 0, col > 0 : Interpolate p10 & p20
+ // row > 0, col = 0 : Interpolate p01 & p02
+ // row = 0, col = 0 : Interpolate p10 & p20, or p01 & p02.
+ if (row > 0) {
+ if (col > 0) {
+ array_.GetValue(row - 1, col - 1, p00.data());
+ } else {
+ p00 = 2 * p01 - p02;
+ }
+
+ if (col < num_cols - 2) {
+ array_.GetValue(row - 1, col + 2, p03.data());
+ } else {
+ p03 = 2 * p02 - p01;
+ }
+ } else {
+ p00 = 2 * p10 - p20;
+ p03 = 2 * p13 - p23;
+ }
+
+ if (row < num_rows - 2) {
+ if (col > 0) {
+ array_.GetValue(row + 2, col - 1, p30.data());
+ } else {
+ p30 = 2 * p31 - p32;
+ }
+
+ if (col < num_cols - 2) {
+ array_.GetValue(row + 2, col + 2, p33.data());
+ } else {
+ p33 = 2 * p32 - p31;
+ }
+ } else {
+ p30 = 2 * p20 - p10;
+ p33 = 2 * p23 - p13;
+ }
+
+ // Interpolate along each of the four rows, evaluating the function
+ // value and the horizontal derivative in each row.
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> f0, f1, f2, f3;
+ Eigen::Matrix<double, Array::DATA_DIMENSION, 1> df0dc, df1dc, df2dc, df3dc;
+ CubicHermiteSpline(p00, p01, p02, p03, c - col, f0.data(), df0dc.data());
+ CubicHermiteSpline(p10, p11, p12, p13, c - col, f1.data(), df1dc.data());
+ CubicHermiteSpline(p20, p21, p22, p23, c - col, f2.data(), df2dc.data());
+ CubicHermiteSpline(p30, p31, p32, p33, c - col, f3.data(), df3dc.data());
+
+ // Interpolate vertically the interpolated value from each row and
+ // compute the derivative along the columns.
+ CubicHermiteSpline(f0, f1, f2, f3, r - row, f, dfdr);
+ if (dfdc != NULL) {
+ // Interpolate vertically the derivative along the columns.
+ CubicHermiteSpline(df0dc, df1dc, df2dc, df3dc, r - row, dfdc, NULL);
+ }
+
+ return true;
+ }
// The following two Evaluate overloads are needed for interfacing
// with automatic differentiation. The first is for when a scalar
@@ -133,19 +417,125 @@
template<typename JetT> bool Evaluate(const JetT& r,
const JetT& c,
JetT* f) const {
- double dfdr, dfdc;
- if (!Evaluate(r.a, c.a, &f->a, &dfdr, &dfdc)) {
+ double frc[Array::DATA_DIMENSION];
+ double dfdr[Array::DATA_DIMENSION];
+ double dfdc[Array::DATA_DIMENSION];
+ if (!Evaluate(r.a, c.a, frc, dfdr, dfdc)) {
return false;
}
- f->v = dfdr * r.v + dfdc * c.v;
+
+ for (int i = 0; i < Array::DATA_DIMENSION; ++i) {
+ f[i].a = frc[i];
+ f[i].v = dfdr[i] * r.v + dfdc[i] * c.v;
+ }
+
return true;
}
- int num_rows() const { return num_rows_; }
- int num_cols() const { return num_cols_; }
+ int NumRows() const { return array_.NumRows(); }
+ int NumCols() const { return array_.NumCols(); }
private:
- const double* values_;
+ const Array& array_;
+};
+
+// An object that implements the one dimensional array like object
+// needed by the CubicInterpolator where the source of the function
+// values is an array of type T.
+//
+// The function being provided can be vector valued, in which case
+// kDataDimension > 1. The dimensional slices of the function maybe
+// interleaved, or they maybe stacked, i.e, if the function has
+// kDataDimension = 2, if kInterleaved = true, then it is stored as
+//
+// f01, f02, f11, f12 ....
+//
+// and if kInterleaved = false, then it is stored as
+//
+// f01, f11, .. fn1, f02, f12, .. , fn2
+template <typename T, int kDataDimension = 1, bool kInterleaved = true>
+struct Array1D {
+ enum { DATA_DIMENSION = kDataDimension };
+
+ Array1D(const T* data, const int num_values)
+ : data_(data), num_values_(num_values) {
+ }
+
+ void GetValue(const int n, double* f) const {
+ if (n < 0 || n > num_values_ - 1) {
+ LOG(FATAL) << "n = " << n
+ << " is not in the interval [0, " << num_values_ - 1 << "].";
+ }
+
+ for (int i = 0; i < kDataDimension; ++i) {
+ if (kInterleaved) {
+ f[i] = static_cast<double>(data_[kDataDimension * n + i]);
+ } else {
+ f[i] = static_cast<double>(data_[i * num_values_ + n]);
+ }
+ }
+ }
+
+ int NumValues() const { return num_values_; }
+
+ private:
+ const T* data_;
+ const int num_values_;
+};
+
+// An object that implements the two dimensional array like object
+// needed by the BiCubicInterpolator where the source of the function
+// values is an array of type T.
+//
+// The function being provided can be vector valued, in which case
+// kDataDimension > 1. The data maybe stored in row or column major
+// format and the various dimensional slices of the function maybe
+// interleaved, or they maybe stacked, i.e, if the function has
+// kDataDimension = 2, is stored in row-major format and if
+// kInterleaved = true, then it is stored as
+//
+// f001, f002, f011, f012, ...
+//
+// A commonly occuring example are color images (RGB) where the three
+// channels are stored interleaved.
+//
+// If kInterleaved = false, then it is stored as
+//
+// f001, f011, ..., fnm1, f002, f012, ...
+template <typename T,
+ int kDataDimension = 1,
+ bool kRowMajor = true,
+ bool kInterleaved = true>
+struct Array2D {
+ enum Foo { DATA_DIMENSION = kDataDimension };
+
+ Array2D(const T* data, const int num_rows, const int num_cols)
+ : data_(data), num_rows_(num_rows), num_cols_(num_cols) {
+ CHECK_GE(kDataDimension, 1);
+ }
+
+ void GetValue(const int r, const int c, double* f) const {
+ if (r < 0 || r > num_rows_ - 1 || c < 0 || c > num_cols_ - 1) {
+ LOG(FATAL) << "(r, c) = (" << r << ", " << c << ")"
+ << " is not in the square defined by [0, 0] "
+ << " and [" << num_rows_ - 1 << ", " << num_cols_ - 1 << "]";
+ }
+
+ const int n = (kRowMajor) ? num_cols_ * r + c : num_rows_ * c + r;
+ for (int i = 0; i < kDataDimension; ++i) {
+ if (kInterleaved) {
+ f[i] = static_cast<double>(data_[kDataDimension * n + i]);
+ } else {
+ f[i] = static_cast<double>(data_[i * (num_rows_ * num_cols_) + n]);
+ }
+ }
+ }
+
+ int NumRows() const { return num_rows_; }
+ int NumCols() const { return num_cols_; }
+
+ private:
+ const T* data_;
const int num_rows_;
const int num_cols_;
};
diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt
index f2f8a85..a64ea52 100644
--- a/internal/ceres/CMakeLists.txt
+++ b/internal/ceres/CMakeLists.txt
@@ -53,7 +53,6 @@
corrector.cc
covariance.cc
covariance_impl.cc
- cubic_interpolation.cc
cxsparse.cc
dense_normal_cholesky_solver.cc
dense_qr_solver.cc
diff --git a/internal/ceres/cubic_interpolation.cc b/internal/ceres/cubic_interpolation.cc
deleted file mode 100644
index 764b306..0000000
--- a/internal/ceres/cubic_interpolation.cc
+++ /dev/null
@@ -1,258 +0,0 @@
-// Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2014 Google Inc. All rights reserved.
-// http://code.google.com/p/ceres-solver/
-//
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are met:
-//
-// * Redistributions of source code must retain the above copyright notice,
-// this list of conditions and the following disclaimer.
-// * Redistributions in binary form must reproduce the above copyright notice,
-// this list of conditions and the following disclaimer in the documentation
-// and/or other materials provided with the distribution.
-// * Neither the name of Google Inc. nor the names of its contributors may be
-// used to endorse or promote products derived from this software without
-// specific prior written permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
-// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
-// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
-// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
-// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
-// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
-// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-// POSSIBILITY OF SUCH DAMAGE.
-//
-// Author: sameeragarwal@google.com (Sameer Agarwal)
-
-#include "ceres/cubic_interpolation.h"
-
-#include <math.h>
-#include "glog/logging.h"
-
-namespace ceres {
-namespace {
-
-// Given samples from a function sampled at four equally spaced points,
-//
-// p0 = f(-1)
-// p1 = f(0)
-// p2 = f(1)
-// p3 = f(2)
-//
-// Evaluate the cubic Hermite spline (also known as the Catmull-Rom
-// spline) at a point x that lies in the interval [0, 1].
-//
-// This is also the interpolation kernel (for the case of a = 0.5) as
-// proposed by R. Keys, in:
-//
-// "Cubic convolution interpolation for digital image processing".
-// IEEE Transactions on Acoustics, Speech, and Signal Processing
-// 29 (6): 1153–1160.
-//
-// For more details see
-//
-// http://en.wikipedia.org/wiki/Cubic_Hermite_spline
-// http://en.wikipedia.org/wiki/Bicubic_interpolation
-inline void CubicHermiteSpline(const double p0,
- const double p1,
- const double p2,
- const double p3,
- const double x,
- double* f,
- double* dfdx) {
- const double a = 0.5 * (-p0 + 3.0 * p1 - 3.0 * p2 + p3);
- const double b = 0.5 * (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3);
- const double c = 0.5 * (-p0 + p2);
- const double d = p1;
-
- // Use Horner's rule to evaluate the function value and its
- // derivative.
-
- // f = ax^3 + bx^2 + cx + d
- if (f != NULL) {
- *f = d + x * (c + x * (b + x * a));
- }
-
- // dfdx = 3ax^2 + 2bx + c
- if (dfdx != NULL) {
- *dfdx = c + x * (2.0 * b + 3.0 * a * x);
- }
-}
-
-} // namespace
-
-CubicInterpolator::CubicInterpolator(const double* values, const int num_values)
- : values_(CHECK_NOTNULL(values)),
- num_values_(num_values) {
- CHECK_GT(num_values, 1);
-}
-
-bool CubicInterpolator::Evaluate(const double x,
- double* f,
- double* dfdx) const {
- if (x < 0 || x > num_values_ - 1) {
- LOG(ERROR) << "x = " << x
- << " is not in the interval [0, " << num_values_ - 1 << "].";
- return false;
- }
-
- int n = floor(x);
-
- // Handle the case where the point sits exactly on the right boundary.
- if (n == num_values_ - 1) {
- n -= 1;
- }
-
- const double p1 = values_[n];
- const double p2 = values_[n + 1];
- const double p0 = (n > 0) ? values_[n - 1] : (2.0 * p1 - p2);
- const double p3 = (n < (num_values_ - 2)) ? values_[n + 2] : (2.0 * p2 - p1);
- CubicHermiteSpline(p0, p1, p2, p3, x - n, f, dfdx);
- return true;
-}
-
-BiCubicInterpolator::BiCubicInterpolator(const double* values,
- const int num_rows,
- const int num_cols)
- : values_(CHECK_NOTNULL(values)),
- num_rows_(num_rows),
- num_cols_(num_cols) {
- CHECK_GT(num_rows, 1);
- CHECK_GT(num_cols, 1);
-}
-
-bool BiCubicInterpolator::Evaluate(const double r,
- const double c,
- double* f,
- double* dfdr,
- double* dfdc) const {
- if (r < 0 || r > num_rows_ - 1 || c < 0 || c > num_cols_ - 1) {
- LOG(ERROR) << "(r, c) = " << r << ", " << c
- << " is not in the square defined by [0, 0] "
- << " and [" << num_rows_ - 1 << ", " << num_cols_ - 1 << "]";
- return false;
- }
-
- int row = floor(r);
- // Handle the case where the point sits exactly on the bottom
- // boundary.
- if (row == num_rows_ - 1) {
- row -= 1;
- }
-
- int col = floor(c);
- // Handle the case where the point sits exactly on the right
- // boundary.
- if (col == num_cols_ - 1) {
- col -= 1;
- }
-
-#define v(n, m) values_[(n) * num_cols_ + m]
-
- // BiCubic interpolation requires 16 values around the point being
- // evaluated. We will use pij, to indicate the elements of the 4x4
- // array of values.
- //
- // col
- // p00 p01 p02 p03
- // row p10 p11 p12 p13
- // p20 p21 p22 p23
- // p30 p31 p32 p33
- //
- // The point (r,c) being evaluated is assumed to lie in the square
- // defined by p11, p12, p22 and p21.
-
- // These four entries are guaranteed to be in the values_ array.
- const double p11 = v(row, col);
- const double p12 = v(row, col + 1);
- const double p21 = v(row + 1, col);
- const double p22 = v(row + 1, col + 1);
-
- // If we are in rows >= 1, then choose the element from the row - 1,
- // otherwise linearly interpolate from row and row + 1.
- const double p01 = (row > 0) ? v(row - 1, col) : 2 * p11 - p21;
- const double p02 = (row > 0) ? v(row - 1, col + 1) : 2 * p12 - p22;
-
- // If we are in row < num_rows_ - 2, then pick the element from the
- // row + 2, otherwise linearly interpolate from row and row + 1.
- const double p31 = (row < num_rows_ - 2) ? v(row + 2, col) : 2 * p21 - p11;
- const double p32 = (row < num_rows_ - 2) ? v(row + 2, col + 1) : 2 * p22 - p12; // NOLINT
-
- // Same logic as above, applies to the columns instead of rows.
- const double p10 = (col > 0) ? v(row, col - 1) : 2 * p11 - p12;
- const double p20 = (col > 0) ? v(row + 1, col - 1) : 2 * p21 - p22;
- const double p13 = (col < num_cols_ - 2) ? v(row, col + 2) : 2 * p12 - p11;
- const double p23 = (col < num_cols_ - 2) ? v(row + 1, col + 2) : 2 * p22 - p21; // NOLINT
-
- // The four corners of the block require a bit more care. Let us
- // consider the evaluation of p00, the other three corners follow in
- // the same manner.
- //
- // There are four cases in which we need to evaluate p00.
- //
- // row > 0, col > 0 : v(row, col)
- // row = 0, col > 1 : Interpolate p10 & p20
- // row > 1, col = 0 : Interpolate p01 & p02
- // row = 0, col = 0 : Interpolate p10 & p20, or p01 & p02.
- double p00, p03;
- if (row > 0) {
- if (col > 0) {
- p00 = v(row - 1, col - 1);
- } else {
- p00 = 2 * p01 - p02;
- }
-
- if (col < num_cols_ - 2) {
- p03 = v(row - 1, col + 2);
- } else {
- p03 = 2 * p02 - p01;
- }
- } else {
- p00 = 2 * p10 - p20;
- p03 = 2 * p13 - p23;
- }
-
- double p30, p33;
- if (row < num_rows_ - 2) {
- if (col > 0) {
- p30 = v(row + 2, col - 1);
- } else {
- p30 = 2 * p31 - p32;
- }
-
- if (col < num_cols_ - 2) {
- p33 = v(row + 2, col + 2);
- } else {
- p33 = 2 * p32 - p31;
- }
- } else {
- p30 = 2 * p20 - p10;
- p33 = 2 * p23 - p13;
- }
-
- // Interpolate along each of the four rows, evaluating the function
- // value and the horizontal derivative in each row.
- double f0, f1, f2, f3;
- double df0dc, df1dc, df2dc, df3dc;
- CubicHermiteSpline(p00, p01, p02, p03, c - col, &f0, &df0dc);
- CubicHermiteSpline(p10, p11, p12, p13, c - col, &f1, &df1dc);
- CubicHermiteSpline(p20, p21, p22, p23, c - col, &f2, &df2dc);
- CubicHermiteSpline(p30, p31, p32, p33, c - col, &f3, &df3dc);
-
- // Interpolate vertically the interpolated value from each row and
- // compute the derivative along the columns.
- CubicHermiteSpline(f0, f1, f2, f3, r - row, f, dfdr);
- if (dfdc != NULL) {
- // Interpolate vertically the derivative along the columns.
- CubicHermiteSpline(df0dc, df1dc, df2dc, df3dc, r - row, dfdc, NULL);
- }
-
- return true;
-#undef v
-}
-
-} // namespace ceres
diff --git a/internal/ceres/cubic_interpolation_test.cc b/internal/ceres/cubic_interpolation_test.cc
index 0b4bb12..04a7b33 100644
--- a/internal/ceres/cubic_interpolation_test.cc
+++ b/internal/ceres/cubic_interpolation_test.cc
@@ -31,31 +31,147 @@
#include "ceres/cubic_interpolation.h"
#include "ceres/jet.h"
+#include "ceres/internal/scoped_ptr.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
-TEST(CubicInterpolator, NeedsAtleastTwoValues) {
- double x[] = {1};
- EXPECT_DEATH_IF_SUPPORTED(CubicInterpolator c(x, 0), "num_values > 1");
- EXPECT_DEATH_IF_SUPPORTED(CubicInterpolator c(x, 1), "num_values > 1");
+static const double kTolerance = 1e-12;
+
+TEST(Array1D, OneDataDimension) {
+ int x[] = {1, 2, 3};
+ Array1D<int, 1> array(x, 3);
+ for (int i = 0; i < 3; ++i) {
+ double value;
+ array.GetValue(i, &value);
+ EXPECT_EQ(value, static_cast<double>(i + 1));
+ }
}
-static const double kTolerance = 1e-12;
+TEST(Array1D, TwoDataDimensionIntegerDataInterleaved) {
+ int x[] = {1, 5,
+ 2, 6,
+ 3, 7};
+
+ Array1D<int, 2, true> array(x, 3);
+ for (int i = 0; i < 3; ++i) {
+ double value[2];
+ array.GetValue(i, value);
+ EXPECT_EQ(value[0], static_cast<double>(i + 1));
+ EXPECT_EQ(value[1], static_cast<double>(i + 5));
+ }
+}
+
+TEST(Array1D, TwoDataDimensionIntegerDataStacked) {
+ int x[] = {1, 2, 3,
+ 5, 6, 7};
+
+ Array1D<int, 2, false> array(x, 3);
+ for (int i = 0; i < 3; ++i) {
+ double value[2];
+ array.GetValue(i, value);
+ EXPECT_EQ(value[0], static_cast<double>(i + 1));
+ EXPECT_EQ(value[1], static_cast<double>(i + 5));
+ }
+}
+
+TEST(Array2D, OneDataDimensionRowMajor) {
+ int x[] = {1, 2, 3,
+ 2, 3, 4};
+ Array2D<int, 1, true, true> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value;
+ array.GetValue(r, c, &value);
+ EXPECT_EQ(value, static_cast<double>(r + c + 1));
+ }
+ }
+}
+
+TEST(Array2D, TwoDataDimensionRowMajorInterleaved) {
+ int x[] = {1, 4, 2, 8, 3, 12,
+ 2, 8, 3, 12, 4, 16};
+ Array2D<int, 2, true, true> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.GetValue(r, c, value);
+ EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
+ EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
+ }
+ }
+}
+
+TEST(Array2D, TwoDataDimensionRowMajorStacked) {
+ int x[] = {1, 2, 3,
+ 2, 3, 4,
+ 4, 8, 12,
+ 8, 12, 16};
+ Array2D<int, 2, true, false> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.GetValue(r, c, value);
+ EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
+ EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
+ }
+ }
+}
+
+TEST(Array2D, TwoDataDimensionColMajorInterleaved) {
+ int x[] = { 1, 4, 2, 8,
+ 2, 8, 3, 12,
+ 3, 12, 4, 16};
+ Array2D<int, 2, false, true> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.GetValue(r, c, value);
+ EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
+ EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
+ }
+ }
+}
+
+TEST(Array2D, TwoDataDimensionColMajorStacked) {
+ int x[] = {1, 2,
+ 2, 3,
+ 3, 4,
+ 4, 8,
+ 8, 12,
+ 12, 16};
+ Array2D<int, 2, false, false> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.GetValue(r, c, value);
+ EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
+ EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
+ }
+ }
+}
+
class CubicInterpolatorTest : public ::testing::Test {
public:
+ template <int kDataDimension>
void RunPolynomialInterpolationTest(const double a,
const double b,
const double c,
const double d) {
+ values_.reset(new double[kDataDimension * kNumSamples]);
+
for (int x = 0; x < kNumSamples; ++x) {
- values_[x] = a * x * x * x + b * x * x + c * x + d;
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ values_[x * kDataDimension + dim] =
+ (dim * dim + 1) * (a * x * x * x + b * x * x + c * x + d);
+ }
}
- CubicInterpolator interpolator(values_, kNumSamples);
+ Array1D<double, kDataDimension> array(values_.get(), kNumSamples);
+ CubicInterpolator<Array1D<double, kDataDimension> > interpolator(array);
// Check values in the all the cells but the first and the last
// ones. In these cells, the interpolated function values should
@@ -66,46 +182,63 @@
// function values and its derivatives not to match.
for (int j = 0; j < kNumTestSamples; ++j) {
const double x = 1.0 + 7.0 / (kNumTestSamples - 1) * j;
- const double expected_f = a * x * x * x + b * x * x + c * x + d;
- const double expected_dfdx = 3.0 * a * x * x + 2.0 * b * x + c;
- double f, dfdx;
+ double expected_f[kDataDimension], expected_dfdx[kDataDimension];
+ double f[kDataDimension], dfdx[kDataDimension];
- EXPECT_TRUE(interpolator.Evaluate(x, &f, &dfdx));
- EXPECT_NEAR(f, expected_f, kTolerance)
- << "x: " << x
- << " actual f(x): " << expected_f
- << " estimated f(x): " << f;
- EXPECT_NEAR(dfdx, expected_dfdx, kTolerance)
- << "x: " << x
- << " actual df(x)/dx: " << expected_dfdx
- << " estimated df(x)/dx: " << dfdx;
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ expected_f[dim] =
+ (dim * dim + 1) * (a * x * x * x + b * x * x + c * x + d);
+ expected_dfdx[dim] = (dim * dim + 1) * (3.0 * a * x * x + 2.0 * b * x + c);
+ }
+
+ EXPECT_TRUE(interpolator.Evaluate(x, f, dfdx));
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ EXPECT_NEAR(f[dim], expected_f[dim], kTolerance)
+ << "x: " << x << " dim: " << dim
+ << " actual f(x): " << expected_f[dim]
+ << " estimated f(x): " << f[dim];
+ EXPECT_NEAR(dfdx[dim], expected_dfdx[dim], kTolerance)
+ << "x: " << x << " dim: " << dim
+ << " actual df(x)/dx: " << expected_dfdx[dim]
+ << " estimated df(x)/dx: " << dfdx[dim];
+ }
}
}
private:
static const int kNumSamples = 10;
static const int kNumTestSamples = 100;
- double values_[kNumSamples];
+ scoped_array<double> values_;
};
TEST_F(CubicInterpolatorTest, ConstantFunction) {
- RunPolynomialInterpolationTest(0.0, 0.0, 0.0, 0.5);
+ RunPolynomialInterpolationTest<1>(0.0, 0.0, 0.0, 0.5);
+ RunPolynomialInterpolationTest<2>(0.0, 0.0, 0.0, 0.5);
+ RunPolynomialInterpolationTest<3>(0.0, 0.0, 0.0, 0.5);
}
TEST_F(CubicInterpolatorTest, LinearFunction) {
- RunPolynomialInterpolationTest(0.0, 0.0, 1.0, 0.5);
+ RunPolynomialInterpolationTest<1>(0.0, 0.0, 1.0, 0.5);
+ RunPolynomialInterpolationTest<2>(0.0, 0.0, 1.0, 0.5);
+ RunPolynomialInterpolationTest<3>(0.0, 0.0, 1.0, 0.5);
}
TEST_F(CubicInterpolatorTest, QuadraticFunction) {
- RunPolynomialInterpolationTest(0.0, 0.4, 1.0, 0.5);
+ RunPolynomialInterpolationTest<1>(0.0, 0.4, 1.0, 0.5);
+ RunPolynomialInterpolationTest<2>(0.0, 0.4, 1.0, 0.5);
+ RunPolynomialInterpolationTest<3>(0.0, 0.4, 1.0, 0.5);
}
+
TEST(CubicInterpolator, JetEvaluation) {
- const double values[] = {1.0, 2.0, 2.0, 3.0};
- CubicInterpolator interpolator(values, 4);
- double f, dfdx;
+ const double values[] = {1.0, 2.0, 2.0, 5.0, 3.0, 9.0, 2.0, 7.0};
+
+ Array1D<double, 2, true> array(values, 4);
+ CubicInterpolator<Array1D<double, 2, true> > interpolator(array);
+
+ double f[2], dfdx[2];
const double x = 2.5;
- EXPECT_TRUE(interpolator.Evaluate(x, &f, &dfdx));
+ EXPECT_TRUE(interpolator.Evaluate(x, f, dfdx));
// Create a Jet with the same scalar part as x, so that the output
// Jet will be evaluated at x.
@@ -116,42 +249,48 @@
x_jet.v(2) = 1.2;
x_jet.v(3) = 1.3;
- Jet<double, 4> f_jet;
- EXPECT_TRUE(interpolator.Evaluate(x_jet, &f_jet));
+ Jet<double, 4> f_jets[2];
+ EXPECT_TRUE(interpolator.Evaluate(x_jet, f_jets));
// Check that the scalar part of the Jet is f(x).
- EXPECT_EQ(f_jet.a, f);
+ EXPECT_EQ(f_jets[0].a, f[0]);
+ EXPECT_EQ(f_jets[1].a, f[1]);
// Check that the derivative part of the Jet is dfdx * x_jet.v
// by the chain rule.
- EXPECT_EQ((f_jet.v - dfdx * x_jet.v).norm(), 0.0);
+ EXPECT_NEAR((f_jets[0].v - dfdx[0] * x_jet.v).norm(), 0.0, kTolerance);
+ EXPECT_NEAR((f_jets[1].v - dfdx[1] * x_jet.v).norm(), 0.0, kTolerance);
}
class BiCubicInterpolatorTest : public ::testing::Test {
public:
+ template <int kDataDimension>
void RunPolynomialInterpolationTest(const Eigen::Matrix3d& coeff) {
+ values_.reset(new double[kNumRows * kNumCols * kDataDimension]);
coeff_ = coeff;
- double* v = values_;
+ double* v = values_.get();
for (int r = 0; r < kNumRows; ++r) {
for (int c = 0; c < kNumCols; ++c) {
- *v++ = EvaluateF(r, c);
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ *v++ = (dim * dim + 1) * EvaluateF(r, c);
+ }
}
}
- BiCubicInterpolator interpolator(values_, kNumRows, kNumCols);
+
+ Array2D<double, kDataDimension> array(values_.get(), kNumRows, kNumCols);
+ BiCubicInterpolator<Array2D<double, kDataDimension> > interpolator(array);
for (int j = 0; j < kNumRowSamples; ++j) {
const double r = 1.0 + 7.0 / (kNumRowSamples - 1) * j;
for (int k = 0; k < kNumColSamples; ++k) {
const double c = 1.0 + 7.0 / (kNumColSamples - 1) * k;
- const double expected_f = EvaluateF(r, c);
- const double expected_dfdr = EvaluatedFdr(r, c);
- const double expected_dfdc = EvaluatedFdc(r, c);
- double f, dfdr, dfdc;
-
- EXPECT_TRUE(interpolator.Evaluate(r, c, &f, &dfdr, &dfdc));
- EXPECT_NEAR(f, expected_f, kTolerance);
- EXPECT_NEAR(dfdr, expected_dfdr, kTolerance);
- EXPECT_NEAR(dfdc, expected_dfdc, kTolerance);
+ double f[kDataDimension], dfdr[kDataDimension], dfdc[kDataDimension];
+ EXPECT_TRUE(interpolator.Evaluate(r, c, f, dfdr, dfdc));
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ EXPECT_NEAR(f[dim], (dim * dim + 1) * EvaluateF(r, c), kTolerance);
+ EXPECT_NEAR(dfdr[dim], (dim * dim + 1) * EvaluatedFdr(r, c), kTolerance);
+ EXPECT_NEAR(dfdc[dim], (dim * dim + 1) * EvaluatedFdc(r, c), kTolerance);
+ }
}
}
}
@@ -187,18 +326,22 @@
static const int kNumCols = 10;
static const int kNumRowSamples = 100;
static const int kNumColSamples = 100;
- double values_[kNumRows * kNumCols];
+ scoped_array<double> values_;
};
TEST_F(BiCubicInterpolatorTest, ZeroFunction) {
Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero();
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree00Function) {
Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero();
coeff(2, 2) = 1.0;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree01Function) {
@@ -206,7 +349,9 @@
coeff(2, 2) = 1.0;
coeff(0, 2) = 0.1;
coeff(2, 0) = 0.1;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree10Function) {
@@ -214,7 +359,9 @@
coeff(2, 2) = 1.0;
coeff(0, 1) = 0.1;
coeff(1, 0) = 0.1;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree11Function) {
@@ -224,7 +371,9 @@
coeff(1, 0) = 0.1;
coeff(0, 2) = 0.2;
coeff(2, 0) = 0.2;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree12Function) {
@@ -235,7 +384,9 @@
coeff(0, 2) = 0.2;
coeff(2, 0) = 0.2;
coeff(1, 1) = 0.3;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree21Function) {
@@ -246,7 +397,9 @@
coeff(0, 2) = 0.2;
coeff(2, 0) = 0.2;
coeff(0, 0) = 0.3;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree22Function) {
@@ -259,17 +412,22 @@
coeff(0, 0) = 0.3;
coeff(0, 1) = -0.4;
coeff(1, 0) = -0.4;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST(BiCubicInterpolator, JetEvaluation) {
- const double values[] = {1.0, 2.0, 2.0, 3.0,
- 1.0, 2.0, 2.0, 3.0};
- BiCubicInterpolator interpolator(values, 2, 4);
- double f, dfdr, dfdc;
+ const double values[] = {1.0, 5.0, 2.0, 10.0, 2.0, 6.0, 3.0, 5.0,
+ 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 3.0, 1.0};
+
+ Array2D<double, 2> array(values, 2, 4);
+ BiCubicInterpolator<Array2D<double, 2> > interpolator(array);
+
+ double f[2], dfdr[2], dfdc[2];
const double r = 0.5;
const double c = 2.5;
- EXPECT_TRUE(interpolator.Evaluate(r, c, &f, &dfdr, &dfdc));
+ EXPECT_TRUE(interpolator.Evaluate(r, c, f, dfdr, dfdc));
// Create a Jet with the same scalar part as x, so that the output
// Jet will be evaluated at x.
@@ -287,10 +445,16 @@
c_jet.v(2) = 4.2;
c_jet.v(3) = 5.3;
- Jet<double, 4> f_jet;
- EXPECT_TRUE(interpolator.Evaluate(r_jet, c_jet, &f_jet));
- EXPECT_EQ(f_jet.a, f);
- EXPECT_EQ((f_jet.v - dfdr * r_jet.v - dfdc * c_jet.v).norm(), 0.0);
+ Jet<double, 4> f_jets[2];
+ EXPECT_TRUE(interpolator.Evaluate(r_jet, c_jet, f_jets));
+ EXPECT_EQ(f_jets[0].a, f[0]);
+ EXPECT_EQ(f_jets[1].a, f[1]);
+ EXPECT_NEAR((f_jets[0].v - dfdr[0] * r_jet.v - dfdc[0] * c_jet.v).norm(),
+ 0.0,
+ kTolerance);
+ EXPECT_NEAR((f_jets[1].v - dfdr[1] * r_jet.v - dfdc[1] * c_jet.v).norm(),
+ 0.0,
+ kTolerance);
}
} // namespace internal
