136#include "vtkCommonCoreModule.h"
137#include "vtkMathPrivate.hxx"
143#include "vtkMathConfigure.h"
147#include <type_traits>
150#define VTK_DBL_MIN 2.2250738585072014e-308
152#define VTK_DBL_MIN DBL_MIN
156#define VTK_DBL_EPSILON 2.2204460492503131e-16
158#define VTK_DBL_EPSILON DBL_EPSILON
161#ifndef VTK_DBL_EPSILON
163#define VTK_DBL_EPSILON 2.2204460492503131e-16
165#define VTK_DBL_EPSILON DBL_EPSILON
169VTK_ABI_NAMESPACE_BEGIN
172class vtkMathInternal;
179VTK_ABI_NAMESPACE_BEGIN
181template <
typename OutT>
186VTK_ABI_NAMESPACE_BEGIN
195 template <
class VectorT,
class =
void>
196 struct VectorImplementsSize : std::false_type
200 template <
class VectorT>
201 struct VectorImplementsSize<VectorT, decltype((void)
std::declval<VectorT>().size(), void())>
209 template <
class VectorT>
210 using EnableIfVectorImplementsSize =
211 typename std::enable_if<VectorImplementsSize<VectorT>::value>::type;
227 static constexpr double Pi() {
return 3.141592653589793; }
233 static float RadiansFromDegrees(
float degrees);
234 static double RadiansFromDegrees(
double degrees);
241 static float DegreesFromRadians(
float radians);
242 static double DegreesFromRadians(
double radians);
249 static int Round(
float f) {
return static_cast<int>(f + (f >= 0.0 ? 0.5 : -0.5)); }
250 static int Round(
double f) {
return static_cast<int>(f + (f >= 0.0 ? 0.5 : -0.5)); }
257 template <
typename OutT>
270 static int Floor(
double x);
277 static int Ceil(
double x);
291 static T Min(
const T& a,
const T& b);
298 static T Max(
const T& a,
const T& b);
303 static bool IsPowerOfTwo(vtkTypeUInt64 x);
310 static int NearestPowerOfTwo(
int x);
446 template <
class VectorT1,
class VectorT2>
447 static void Assign(
const VectorT1& a, VectorT2&& b)
457 static void Assign(
const double a[3],
double b[3]) { vtkMath::Assign<>(a, b); }
462 static void Add(
const float a[3],
const float b[3],
float c[3])
464 for (
int i = 0; i < 3; ++i)
473 static void Add(
const double a[3],
const double b[3],
double c[3])
475 for (
int i = 0; i < 3; ++i)
486 template <
class VectorT1,
class VectorT2,
class VectorT3>
487 static void Add(VectorT1&& a, VectorT2&& b, VectorT3& c)
489 for (
int i = 0; i < 3; ++i)
498 static void Subtract(
const float a[3],
const float b[3],
float c[3])
500 for (
int i = 0; i < 3; ++i)
509 static void Subtract(
const double a[3],
const double b[3],
double c[3])
511 for (
int i = 0; i < 3; ++i)
522 template <
class VectorT1,
class VectorT2,
class VectorT3>
523 static void Subtract(
const VectorT1& a,
const VectorT2& b, VectorT3&& c)
536 for (
int i = 0; i < 3; ++i)
548 for (
int i = 0; i < 2; ++i)
560 for (
int i = 0; i < 3; ++i)
572 for (
int i = 0; i < 2; ++i)
581 static float Dot(
const float a[3],
const float b[3])
583 return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
589 static double Dot(
const double a[3],
const double b[3])
591 return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
609 template <
typename ReturnTypeT = double,
typename TupleRangeT1,
typename TupleRangeT2,
610 typename EnableT =
typename std::conditional<!std::is_pointer<TupleRangeT1>::value &&
611 !std::is_array<TupleRangeT1>::value,
612 TupleRangeT1, TupleRangeT2>::type::value_type>
613 static ReturnTypeT
Dot(
const TupleRangeT1& a,
const TupleRangeT2& b)
615 return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
621 static void Outer(
const float a[3],
const float b[3],
float c[3][3])
623 for (
int i = 0; i < 3; ++i)
625 for (
int j = 0; j < 3; ++j)
627 c[i][j] = a[i] * b[j];
635 static void Outer(
const double a[3],
const double b[3],
double c[3][3])
637 for (
int i = 0; i < 3; ++i)
639 for (
int j = 0; j < 3; ++j)
641 c[i][j] = a[i] * b[j];
651 template <
class VectorT1,
class VectorT2,
class VectorT3>
652 static void Cross(VectorT1&& a, VectorT2&& b, VectorT3& c);
658 static void Cross(
const float a[3],
const float b[3],
float c[3]);
664 static void Cross(
const double a[3],
const double b[3],
double c[3]);
670 static float Norm(
const float* x,
int n);
671 static double Norm(
const double* x,
int n);
677 static float Norm(
const float v[3]) {
return std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); }
682 static double Norm(
const double v[3])
684 return std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
696 template <
typename ReturnTypeT =
double,
typename TupleRangeT>
699 return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
706 static float Normalize(
float v[3]);
712 static double Normalize(
double v[3]);
722 static void Perpendiculars(
const double v1[3],
double v2[3],
double v3[3],
double theta);
723 static void Perpendiculars(
const float v1[3],
float v2[3],
float v3[3],
double theta);
732 static bool ProjectVector(
const float a[3],
const float b[3],
float projection[3]);
733 static bool ProjectVector(
const double a[3],
const double b[3],
double projection[3]);
744 static bool ProjectVector2D(
const double a[2],
const double b[2],
double projection[2]);
762 template <
typename ReturnTypeT = double,
typename TupleRangeT1,
typename TupleRangeT2,
763 typename EnableT =
typename std::conditional<!std::is_pointer<TupleRangeT1>::value &&
764 !std::is_array<TupleRangeT1>::value,
765 TupleRangeT1, TupleRangeT2>::type::value_type>
766 static ReturnTypeT Distance2BetweenPoints(
const TupleRangeT1& p1,
const TupleRangeT2& p2);
772 static float Distance2BetweenPoints(
const float p1[3],
const float p2[3]);
778 static double Distance2BetweenPoints(
const double p1[3],
const double p2[3]);
789 const double v1[3],
const double v2[3],
const double vn[3]);
820 static float Dot2D(
const float x[2],
const float y[2]) {
return x[0] * y[0] + x[1] * y[1]; }
825 static double Dot2D(
const double x[2],
const double y[2]) {
return x[0] * y[0] + x[1] * y[1]; }
830 static void Outer2D(
const float x[2],
const float y[2],
float A[2][2])
832 for (
int i = 0; i < 2; ++i)
834 for (
int j = 0; j < 2; ++j)
836 A[i][j] = x[i] * y[j];
844 static void Outer2D(
const double x[2],
const double y[2],
double A[2][2])
846 for (
int i = 0; i < 2; ++i)
848 for (
int j = 0; j < 2; ++j)
850 A[i][j] = x[i] * y[j];
859 static float Norm2D(
const float x[2]) {
return std::sqrt(x[0] * x[0] + x[1] * x[1]); }
865 static double Norm2D(
const double x[2]) {
return std::sqrt(x[0] * x[0] + x[1] * x[1]); }
871 static float Normalize2D(
float v[2]);
877 static double Normalize2D(
double v[2]);
884 return c1[0] * c2[1] - c2[0] * c1[1];
891 static double Determinant2x2(
double a,
double b,
double c,
double d) {
return a * d - b * c; }
894 return c1[0] * c2[1] - c2[0] * c1[1];
910 static void LUSolve3x3(
const float A[3][3],
const int index[3],
float x[3]);
911 static void LUSolve3x3(
const double A[3][3],
const int index[3],
double x[3]);
920 static void LinearSolve3x3(
const double A[3][3],
const double x[3],
double y[3]);
927 static void Multiply3x3(
const float A[3][3],
const float v[3],
float u[3]);
928 static void Multiply3x3(
const double A[3][3],
const double v[3],
double u[3]);
935 static void Multiply3x3(
const float A[3][3],
const float B[3][3],
float C[3][3]);
936 static void Multiply3x3(
const double A[3][3],
const double B[3][3],
double C[3][3]);
962 template <
int RowsT,
int MidDimT,
int ColsT,
963 class LayoutT1 = vtkMatrixUtilities::Layout::Identity,
964 class LayoutT2 = vtkMatrixUtilities::Layout::Identity,
class MatrixT1,
class MatrixT2,
968 vtkMathPrivate::MultiplyMatrix<RowsT, MidDimT, ColsT, LayoutT1, LayoutT2>::Compute(
969 std::forward<MatrixT1>(M1), std::forward<MatrixT2>(M2), std::forward<MatrixT3>(M3));
992 template <
int RowsT,
int ColsT,
class LayoutT = vtkMatrixUtilities::Layout::Identity,
993 class MatrixT,
class VectorT1,
class VectorT2>
996 vtkMathPrivate::MultiplyMatrix<RowsT, ColsT, 1, LayoutT>::Compute(
997 std::forward<MatrixT>(M), std::forward<VectorT1>(X), std::forward<VectorT2>(Y));
1005 template <
class ScalarT,
int SizeT,
class VectorT1,
class VectorT2,
1006 class =
typename std::enable_if<SizeT != DYNAMIC_VECTOR_SIZE()>::type>
1007 static ScalarT
Dot(VectorT1&& x, VectorT2&& y)
1009 return vtkMathPrivate::ContractRowWithCol<ScalarT, 1, SizeT, 1, 0, 0,
1010 vtkMatrixUtilities::Layout::Identity,
1011 vtkMatrixUtilities::Layout::Transpose>::Compute(std::forward<VectorT1>(x),
1012 std::forward<VectorT2>(y));
1021 template <
class ScalarT,
int SizeT,
class VectorT1,
class VectorT2,
1022 class =
typename std::enable_if<SizeT == DYNAMIC_VECTOR_SIZE()>::type,
1023 class = EnableIfVectorImplementsSize<VectorT1>>
1024 static ScalarT
Dot(VectorT1&& x, VectorT2&& y)
1027 using SizeType =
decltype(std::declval<VectorT1>().size());
1028 for (SizeType dim = 0; dim < x.size(); ++dim)
1030 dot += x[dim] * y[dim];
1042 template <
int SizeT,
class VectorT>
1047 return vtkMath::Dot<Scalar, SizeT>(std::forward<VectorT>(x), std::forward<VectorT>(x));
1066 template <
int SizeT,
class LayoutT = vtkMatrixUtilities::Layout::Identity,
class MatrixT>
1070 return vtkMathPrivate::Determinant<SizeT, LayoutT>::Compute(std::forward<MatrixT>(M));
1088 template <
int SizeT,
class LayoutT = vtkMatrixUtilities::Layout::Identity,
class MatrixT1,
1092 vtkMathPrivate::InvertMatrix<SizeT, LayoutT>::Compute(
1093 std::forward<MatrixT1>(M1), std::forward<MatrixT2>(M2));
1109 template <
int RowsT,
int ColsT,
class LayoutT = vtkMatrixUtilities::Layout::Identity,
1110 class MatrixT,
class VectorT1,
class VectorT2>
1113 vtkMathPrivate::LinearSolve<RowsT, ColsT, LayoutT>::Compute(
1114 std::forward<MatrixT>(M), std::forward<VectorT1>(x), std::forward<VectorT2>(y));
1131 template <
class ScalarT,
int SizeT,
class LayoutT = vtkMatrixUtilities::Layout::Identity,
1132 class VectorT1,
class MatrixT,
class VectorT2,
1133 class =
typename std::enable_if<SizeT != DYNAMIC_VECTOR_SIZE()>::type>
1134 static ScalarT
Dot(VectorT1&& x, MatrixT&& M, VectorT2&& y)
1137 vtkMathPrivate::MultiplyMatrix<SizeT, SizeT, 1, LayoutT>::Compute(
1138 std::forward<MatrixT>(M), std::forward<VectorT2>(y), tmp);
1139 return vtkMathPrivate::ContractRowWithCol<ScalarT, 1, SizeT, 1, 0, 0,
1140 vtkMatrixUtilities::Layout::Identity,
1141 vtkMatrixUtilities::Layout::Transpose>::Compute(std::forward<VectorT1>(x), tmp);
1149 static void MultiplyMatrix(
const double*
const* A,
const double*
const* B,
unsigned int rowA,
1150 unsigned int colA,
unsigned int rowB,
unsigned int colB,
double** C);
1167 static void Invert3x3(
const double A[3][3],
double AI[3][3]);
1182 static double Determinant3x3(
const float A[3][3]);
1183 static double Determinant3x3(
const double A[3][3]);
1189 static float Determinant3x3(
const float c1[3],
const float c2[3],
const float c3[3]);
1194 static double Determinant3x3(
const double c1[3],
const double c2[3],
const double c3[3]);
1202 static double Determinant3x3(
double a1,
double a2,
double a3,
double b1,
double b2,
double b3,
1203 double c1,
double c2,
double c3);
1213 static void QuaternionToMatrix3x3(
const float quat[4],
float A[3][3]);
1214 static void QuaternionToMatrix3x3(
const double quat[4],
double A[3][3]);
1215 template <
class QuaternionT,
class MatrixT,
1216 class EnableT =
typename std::enable_if<!vtkMatrixUtilities::MatrixIs2DArray<MatrixT>()>::type>
1217 static void QuaternionToMatrix3x3(QuaternionT&& q, MatrixT&& A);
1230 static void Matrix3x3ToQuaternion(
const float A[3][3],
float quat[4]);
1231 static void Matrix3x3ToQuaternion(
const double A[3][3],
double quat[4]);
1232 template <
class MatrixT,
class QuaternionT,
1233 class EnableT =
typename std::enable_if<!vtkMatrixUtilities::MatrixIs2DArray<MatrixT>()>::type>
1234 static void Matrix3x3ToQuaternion(MatrixT&& A, QuaternionT&& q);
1298 const float A[3][3],
float U[3][3],
float w[3],
float VT[3][3]);
1300 const double A[3][3],
double U[3][3],
double w[3],
double VT[3][3]);
1311 double a00,
double a01,
double a10,
double a11,
double b0,
double b1,
double& x0,
double& x1);
1337 double** A,
double** AI,
int size,
int* tmp1Size,
double* tmp2Size);
1431 int numberOfSamples,
double** xt,
int xOrder,
double**
mt);
1448 int yOrder,
double**
mt,
int checkHomogeneous = 1);
1460 RGBToHSV(rgb[0], rgb[1], rgb[2], hsv, hsv + 1, hsv + 2);
1462 static void RGBToHSV(
float r,
float g,
float b,
float*
h,
float* s,
float* v);
1463 static void RGBToHSV(
const double rgb[3],
double hsv[3])
1465 RGBToHSV(rgb[0], rgb[1], rgb[2], hsv, hsv + 1, hsv + 2);
1467 static void RGBToHSV(
double r,
double g,
double b,
double*
h,
double* s,
double* v);
1480 HSVToRGB(hsv[0], hsv[1], hsv[2], rgb, rgb + 1, rgb + 2);
1482 static void HSVToRGB(
float h,
float s,
float v,
float* r,
float* g,
float* b);
1483 static void HSVToRGB(
const double hsv[3],
double rgb[3])
1485 HSVToRGB(hsv[0], hsv[1], hsv[2], rgb, rgb + 1, rgb + 2);
1487 static void HSVToRGB(
double h,
double s,
double v,
double* r,
double* g,
double* b);
1497 ProLabToXYZ(prolab[0], prolab[1], prolab[2], xyz + 0, xyz + 1, xyz + 2);
1499 static void ProLabToXYZ(
double L,
double a,
double b,
double* x,
double* y,
double* z);
1509 XYZToProLab(xyz[0], xyz[1], xyz[2], prolab + 0, prolab + 1, prolab + 2);
1511 static void XYZToProLab(
double x,
double y,
double z,
double* L,
double* a,
double* b);
1518 static void LabToXYZ(
const double lab[3],
double xyz[3])
1520 LabToXYZ(lab[0], lab[1], lab[2], xyz + 0, xyz + 1, xyz + 2);
1522 static void LabToXYZ(
double L,
double a,
double b,
double* x,
double* y,
double* z);
1529 static void XYZToLab(
const double xyz[3],
double lab[3])
1531 XYZToLab(xyz[0], xyz[1], xyz[2], lab + 0, lab + 1, lab + 2);
1533 static void XYZToLab(
double x,
double y,
double z,
double* L,
double* a,
double* b);
1540 static void XYZToRGB(
const double xyz[3],
double rgb[3])
1542 XYZToRGB(xyz[0], xyz[1], xyz[2], rgb + 0, rgb + 1, rgb + 2);
1544 static void XYZToRGB(
double x,
double y,
double z,
double* r,
double* g,
double* b);
1551 static void RGBToXYZ(
const double rgb[3],
double xyz[3])
1553 RGBToXYZ(rgb[0], rgb[1], rgb[2], xyz + 0, xyz + 1, xyz + 2);
1555 static void RGBToXYZ(
double r,
double g,
double b,
double* x,
double* y,
double* z);
1566 static void RGBToLab(
const double rgb[3],
double lab[3])
1568 RGBToLab(rgb[0], rgb[1], rgb[2], lab + 0, lab + 1, lab + 2);
1570 static void RGBToLab(
double red,
double green,
double blue,
double* L,
double* a,
double* b);
1579 ProLabToRGB(prolab[0], prolab[1], prolab[2], rgb + 0, rgb + 1, rgb + 2);
1581 static void ProLabToRGB(
double L,
double a,
double b,
double* red,
double* green,
double* blue);
1594 RGBToProLab(rgb[0], rgb[1], rgb[2], prolab + 0, prolab + 1, prolab + 2);
1596 static void RGBToProLab(
double red,
double green,
double blue,
double* L,
double* a,
double* b);
1603 static void LabToRGB(
const double lab[3],
double rgb[3])
1605 LabToRGB(lab[0], lab[1], lab[2], rgb + 0, rgb + 1, rgb + 2);
1607 static void LabToRGB(
double L,
double a,
double b,
double* red,
double* green,
double* blue);
1631 if (bounds[1] - bounds[0] < 0.0)
1644 static T ClampValue(
const T& value,
const T& min,
const T&
max);
1651 static void ClampValue(
double* value,
const double range[2]);
1652 static void ClampValue(
double value,
const double range[2],
double* clamped_value);
1653 static void ClampValues(
double* values,
int nb_values,
const double range[2]);
1655 const double* values,
int nb_values,
const double range[2],
double* clamped_values);
1664 static double ClampAndNormalizeValue(
double value,
const double range[2]);
1670 template <
class T1,
class T2>
1679 static void TensorFromSymmetricTensor(T tensor[9]);
1690 double range_min,
double range_max,
double scale = 1.0,
double shift = 0.0);
1714 const double bounds1[6],
const double bounds2[6],
const double delta[3]);
1722 const double point[3],
const double bounds[6],
const double delta[3]);
1734 const double bounds[6],
const double normal[3],
const double point[3]);
1746 const double p1[3],
const double p2[3],
const double p3[3],
double center[3]);
1824 template <
class Iter1,
class Iter2,
class Iter3>
1825 static void Convolve1D(Iter1 beginSample, Iter1 endSample, Iter2 beginKernel, Iter2 endKernel,
1826 Iter3 beginOut, Iter3 endOut,
ConvolutionMode mode = ConvolutionMode::FULL)
1828 int sampleSize = std::distance(beginSample, endSample);
1829 int kernelSize = std::distance(beginKernel, endKernel);
1830 int outSize = std::distance(beginOut, endOut);
1832 if (sampleSize <= 0 || kernelSize <= 0 || outSize <= 0)
1842 case ConvolutionMode::SAME:
1843 begin =
static_cast<int>(std::ceil((std::min)(sampleSize, kernelSize) / 2.0)) - 1;
1844 end = begin + (std::max)(sampleSize, kernelSize);
1846 case ConvolutionMode::VALID:
1847 begin = (std::min)(sampleSize, kernelSize) - 1;
1848 end = begin + std::abs(sampleSize - kernelSize) + 1;
1850 case ConvolutionMode::FULL:
1855 for (
int i = begin; i < end; i++)
1857 Iter3 out = beginOut + i - begin;
1859 for (
int j = (std::max)(i - sampleSize + 1, 0); j <= (std::min)(i, kernelSize - 1); j++)
1861 *out += *(beginSample + (i - j)) * *(beginKernel + j);
1872 double directionVector[3] = { p2[0] - p1[0], p2[1] - p1[1], p2[2] - p1[2] };
1874 result[0] = p2[0] + (offset * directionVector[0]);
1875 result[1] = p2[1] + (offset * directionVector[1]);
1876 result[2] = p2[2] + (offset * directionVector[2]);
1887 void operator=(
const vtkMath&) =
delete;
1893 return x * 0.017453292f;
1899 return x * 0.017453292519943295;
1905 return x * 57.2957795131f;
1911 return x * 57.29577951308232;
1917 return ((x != 0) & ((x & (x - 1)) == 0));
1924 unsigned int z =
static_cast<unsigned int>(((x > 0) ? x - 1 : 0));
1930 return static_cast<int>(z + 1);
1938 int i =
static_cast<int>(x);
1947 int i =
static_cast<int>(x);
1955 return (b <= a ? b : a);
1962 return (b > a ? b : a);
1971 for (
int i = 0; i < 3; ++i)
1985 for (
int i = 0; i < 3; ++i)
1999 for (
int i = 0; i < 2; ++i)
2013 for (
int i = 0; i < 2; ++i)
2024 return c1[0] * c2[1] * c3[2] + c2[0] * c3[1] * c1[2] + c3[0] * c1[1] * c2[2] -
2025 c1[0] * c3[1] * c2[2] - c2[0] * c1[1] * c3[2] - c3[0] * c2[1] * c1[2];
2031 return c1[0] * c2[1] * c3[2] + c2[0] * c3[1] * c1[2] + c3[0] * c1[1] * c2[2] -
2032 c1[0] * c3[1] * c2[2] - c2[0] * c1[1] * c3[2] - c3[0] * c2[1] * c1[2];
2037 double a1,
double a2,
double a3,
double b1,
double b2,
double b3,
double c1,
double c2,
double c3)
2046 return ((p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]) +
2047 (p1[2] - p2[2]) * (p1[2] - p2[2]));
2053 return ((p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]) +
2054 (p1[2] - p2[2]) * (p1[2] - p2[2]));
2058template <
typename ReturnTypeT,
typename TupleRangeT1,
typename TupleRangeT2,
typename EnableT>
2061 return ((p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]) +
2062 (p1[2] - p2[2]) * (p1[2] - p2[2]));
2066template <
class VectorT1,
class VectorT2,
class VectorT3>
2070 ValueType Cx = a[1] * b[2] - a[2] * b[1];
2071 ValueType Cy = a[2] * b[0] - a[0] * b[2];
2072 ValueType Cz = a[0] * b[1] - a[1] * b[0];
2082 float Cx = a[1] * b[2] - a[2] * b[1];
2083 float Cy = a[2] * b[0] - a[0] * b[2];
2084 float Cz = a[0] * b[1] - a[1] * b[0];
2094 double Cx = a[1] * b[2] - a[2] * b[1];
2095 double Cy = a[2] * b[0] - a[0] * b[2];
2096 double Cz = a[0] * b[1] - a[1] * b[0];
2106 return A[0][0] * A[1][1] * A[2][2] + A[1][0] * A[2][1] * A[0][2] + A[2][0] * A[0][1] * A[1][2] -
2107 A[0][0] * A[2][1] * A[1][2] - A[1][0] * A[0][1] * A[2][2] - A[2][0] * A[1][1] * A[0][2];
2126 assert(
"pre: valid_range" && min <=
max);
2127 return std::clamp(value, min,
max);
2135 assert(
"pre: valid_range" && range[0] <= range[1]);
2144 if (range && clamped_value)
2146 assert(
"pre: valid_range" && range[0] <= range[1]);
2155 assert(
"pre: valid_range" && range[0] <= range[1]);
2158 if (range[0] == range[1])
2168 result = (result - range[0]) / (range[1] - range[0]);
2171 assert(
"post: valid_result" && result >= 0.0 && result <= 1.0);
2177template <
class T1,
class T2>
2180 for (
int i = 0; i < 3; ++i)
2182 tensor[4 * i] = symmTensor[i];
2184 tensor[1] = tensor[3] = symmTensor[3];
2185 tensor[2] = tensor[6] = symmTensor[5];
2186 tensor[5] = tensor[7] = symmTensor[4];
2193 tensor[6] = tensor[5];
2194 tensor[7] = tensor[4];
2195 tensor[8] = tensor[2];
2196 tensor[4] = tensor[1];
2197 tensor[5] = tensor[7];
2198 tensor[2] = tensor[6];
2199 tensor[1] = tensor[3];
2201VTK_ABI_NAMESPACE_END
2205template <
class QuaternionT,
class MatrixT>
2206inline void vtkQuaternionToMatrix3x3(QuaternionT&& quat, MatrixT&& A)
2210 Scalar
ww = quat[0] * quat[0];
2211 Scalar wx = quat[0] * quat[1];
2212 Scalar wy = quat[0] * quat[2];
2213 Scalar wz = quat[0] * quat[3];
2215 Scalar xx = quat[1] * quat[1];
2216 Scalar yy = quat[2] * quat[2];
2217 Scalar zz = quat[3] * quat[3];
2219 Scalar xy = quat[1] * quat[2];
2220 Scalar xz = quat[1] * quat[3];
2221 Scalar yz = quat[2] * quat[3];
2223 Scalar rr = xx + yy + zz;
2225 Scalar f = 1 / (
ww + rr);
2226 Scalar s = (
ww - rr) * f;
2231 Wrapper::template Get<0, 0>(std::forward<MatrixT>(A)) = xx * f + s;
2232 Wrapper::template Get<1, 0>(std::forward<MatrixT>(A)) = (xy + wz) * f;
2233 Wrapper::template Get<2, 0>(std::forward<MatrixT>(A)) = (xz - wy) * f;
2235 Wrapper::template Get<0, 1>(std::forward<MatrixT>(A)) = (xy - wz) * f;
2236 Wrapper::template Get<1, 1>(std::forward<MatrixT>(A)) = yy * f + s;
2237 Wrapper::template Get<2, 1>(std::forward<MatrixT>(A)) = (yz + wx) * f;
2239 Wrapper::template Get<0, 2>(std::forward<MatrixT>(A)) = (xz + wy) * f;
2240 Wrapper::template Get<1, 2>(std::forward<MatrixT>(A)) = (yz - wx) * f;
2241 Wrapper::template Get<2, 2>(std::forward<MatrixT>(A)) = zz * f + s;
2245VTK_ABI_NAMESPACE_BEGIN
2249 vtkQuaternionToMatrix3x3(quat, A);
2255 vtkQuaternionToMatrix3x3(quat, A);
2259template <
class QuaternionT,
class MatrixT,
class EnableT>
2262 vtkQuaternionToMatrix3x3(std::forward<QuaternionT>(q), std::forward<MatrixT>(A));
2264VTK_ABI_NAMESPACE_END
2273template <
class MatrixT,
class QuaternionT>
2274inline void vtkMatrix3x3ToQuaternion(MatrixT&& A, QuaternionT&& quat)
2283 N[0][0] = Wrapper::template Get<0, 0>(std::forward<MatrixT>(A)) +
2284 Wrapper::template Get<1, 1>(std::forward<MatrixT>(A)) +
2285 Wrapper::template Get<2, 2>(std::forward<MatrixT>(A));
2286 N[1][1] = Wrapper::template Get<0, 0>(std::forward<MatrixT>(A)) -
2287 Wrapper::template Get<1, 1>(std::forward<MatrixT>(A)) -
2288 Wrapper::template Get<2, 2>(std::forward<MatrixT>(A));
2289 N[2][2] = -Wrapper::template Get<0, 0>(std::forward<MatrixT>(A)) +
2290 Wrapper::template Get<1, 1>(std::forward<MatrixT>(A)) -
2291 Wrapper::template Get<2, 2>(std::forward<MatrixT>(A));
2292 N[3][3] = -Wrapper::template Get<0, 0>(std::forward<MatrixT>(A)) -
2293 Wrapper::template Get<1, 1>(std::forward<MatrixT>(A)) +
2294 Wrapper::template Get<2, 2>(std::forward<MatrixT>(A));
2297 N[0][1] = N[1][0] = Wrapper::template Get<2, 1>(std::forward<MatrixT>(A)) -
2298 Wrapper::template Get<1, 2>(std::forward<MatrixT>(A));
2299 N[0][2] = N[2][0] = Wrapper::template Get<0, 2>(std::forward<MatrixT>(A)) -
2300 Wrapper::template Get<2, 0>(std::forward<MatrixT>(A));
2301 N[0][3] = N[3][0] = Wrapper::template Get<1, 0>(std::forward<MatrixT>(A)) -
2302 Wrapper::template Get<0, 1>(std::forward<MatrixT>(A));
2304 N[1][2] = N[2][1] = Wrapper::template Get<1, 0>(std::forward<MatrixT>(A)) +
2305 Wrapper::template Get<0, 1>(std::forward<MatrixT>(A));
2306 N[1][3] = N[3][1] = Wrapper::template Get<0, 2>(std::forward<MatrixT>(A)) +
2307 Wrapper::template Get<2, 0>(std::forward<MatrixT>(A));
2308 N[2][3] = N[3][2] = Wrapper::template Get<2, 1>(std::forward<MatrixT>(A)) +
2309 Wrapper::template Get<1, 2>(std::forward<MatrixT>(A));
2311 Scalar eigenvectors[4][4], eigenvalues[4];
2315 Scalar *NTemp[4], *eigenvectorsTemp[4];
2316 for (
int i = 0; i < 4; ++i)
2319 eigenvectorsTemp[i] = eigenvectors[i];
2324 quat[0] = eigenvectors[0][0];
2325 quat[1] = eigenvectors[1][0];
2326 quat[2] = eigenvectors[2][0];
2327 quat[3] = eigenvectors[3][0];
2331VTK_ABI_NAMESPACE_BEGIN
2335 vtkMatrix3x3ToQuaternion(A, quat);
2341 vtkMatrix3x3ToQuaternion(A, quat);
2345template <
class MatrixT,
class QuaternionT,
class EnableT>
2348 vtkMatrix3x3ToQuaternion(std::forward<MatrixT>(A), std::forward<QuaternionT>(q));
2350VTK_ABI_NAMESPACE_END
2354VTK_ABI_NAMESPACE_BEGIN
2356template <
typename OutT>
2364 *ret =
static_cast<OutT
>((val >= 0.0) ? (val + 0.5) : (val - 0.5));
2384 *retVal =
static_cast<float>(val);
2386VTK_ABI_NAMESPACE_END
2389VTK_ABI_NAMESPACE_BEGIN
2391#if defined(VTK_HAS_ISINF) || defined(VTK_HAS_STD_ISINF)
2392#define VTK_MATH_ISINF_IS_INLINE
2395#if defined(VTK_HAS_STD_ISINF)
2396 return std::isinf(x);
2398 return (isinf(x) != 0);
2404#if defined(VTK_HAS_ISNAN) || defined(VTK_HAS_STD_ISNAN)
2405#define VTK_MATH_ISNAN_IS_INLINE
2408#if defined(VTK_HAS_STD_ISNAN)
2409 return std::isnan(x);
2411 return (
isnan(x) != 0);
2417#if defined(VTK_HAS_ISFINITE) || defined(VTK_HAS_STD_ISFINITE) || defined(VTK_HAS_FINITE)
2418#define VTK_MATH_ISFINITE_IS_INLINE
2421#if defined(VTK_HAS_STD_ISFINITE)
2422 return std::isfinite(x);
2423#elif defined(VTK_HAS_ISFINITE)
2424 return (isfinite(x) != 0);
2426 return (finite(x) != 0);
2431VTK_ABI_NAMESPACE_END
Gaussian sequence of pseudo random numbers implemented with the Box-Mueller transform.
abstract superclass for arrays of numeric data
a simple class to control print indentation
performs common math operations
static ReturnTypeT Distance2BetweenPoints(const TupleRangeT1 &p1, const TupleRangeT2 &p2)
Compute distance squared between two points p1 and p2.
static void Multiply3x3(const float A[3][3], const float B[3][3], float C[3][3])
Multiply one 3x3 matrix by another according to C = AB.
static double Dot(const double a[3], const double b[3])
Dot product of two 3-vectors (double version).
static int GetScalarTypeFittingRange(double range_min, double range_max, double scale=1.0, double shift=0.0)
Return the scalar type that is most likely to have enough precision to store a given range of data on...
static void RGBToXYZ(double r, double g, double b, double *x, double *y, double *z)
Convert color from the RGB system to CIE XYZ.
static void Multiply3x3(const double A[3][3], const double B[3][3], double C[3][3])
Multiply one 3x3 matrix by another according to C = AB.
static double Norm(const double *x, int n)
Compute the norm of n-vector.
static int Round(float f)
Rounds a float to the nearest integer.
static vtkIdType ComputeGCD(vtkIdType m, vtkIdType n)
Compute the greatest common divisor (GCD) of two positive integers m and n.
static void XYZToProLab(const double xyz[3], double prolab[3])
Convert Color from the CIE XYZ system to ProLAB.
static double Norm2D(const double x[2])
Compute the norm of a 2-vector.
static void XYZToProLab(double x, double y, double z, double *L, double *a, double *b)
Convert Color from the CIE XYZ system to ProLAB.
static double GaussianAmplitude(double variance, double distanceFromMean)
Compute the amplitude of a Gaussian function with mean=0 and specified variance.
static void XYZToRGB(double x, double y, double z, double *r, double *g, double *b)
Convert color from the CIE XYZ system to RGB.
static void GetPointAlongLine(double result[3], double p1[3], double p2[3], const double offset)
Get the coordinates of a point along a line defined by p1 and p2, at a specified offset relative to p...
static void Subtract(const float a[3], const float b[3], float c[3])
Subtraction of two 3-vectors (float version).
static void LUSolve3x3(const double A[3][3], const int index[3], double x[3])
LU back substitution for a 3x3 matrix.
static vtkTypeBool SolveHomogeneousLeastSquares(int numberOfSamples, double **xt, int xOrder, double **mt)
Solves for the least squares best fit matrix for the homogeneous equation X'M' = 0'.
static void Outer2D(const float x[2], const float y[2], float A[2][2])
Outer product of two 2-vectors (float version).
static bool ProjectVector(const double a[3], const double b[3], double projection[3])
Compute the projection of vector a on vector b and return it in projection[3].
static vtkSmartPointer< vtkMathInternal > Internal
static float Norm(const float *x, int n)
Compute the norm of n-vector.
static vtkTypeBool ExtentIsWithinOtherExtent(const int extent1[6], const int extent2[6])
Return true if first 3D extent is within second 3D extent Extent is x-min, x-max, y-min,...
static double GaussianAmplitude(double mean, double variance, double position)
Compute the amplitude of a Gaussian function with specified mean and variance.
static void Add(const double a[3], const double b[3], double c[3])
Addition of two 3-vectors (double version).
static void RGBToHSV(float r, float g, float b, float *h, float *s, float *v)
Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value).
static float Norm(const float v[3])
Compute the norm of 3-vector (float version).
static ReturnTypeT Dot(const TupleRangeT1 &a, const TupleRangeT2 &b)
Compute dot product between two points p1 and p2.
static vtkTypeBool Jacobi(double **a, double *w, double **v)
Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix.
static ScalarT Dot(VectorT1 &&x, VectorT2 &&y)
Computes the dot product between 2 vectors x and y.
static void XYZToLab(const double xyz[3], double lab[3])
Convert Color from the CIE XYZ system to CIE-L*ab.
void PrintSelf(ostream &os, vtkIndent indent) override
Methods invoked by print to print information about the object including superclasses.
static vtkTypeInt64 Factorial(int N)
Compute N factorial, N! = N*(N-1) * (N-2)...*3*2*1.
static vtkTypeInt64 Binomial(int m, int n)
The number of combinations of n objects from a pool of m objects (m>n).
static double Random()
Generate pseudo-random numbers distributed according to the uniform distribution between 0....
static void Identity3x3(float A[3][3])
Set A to the identity matrix.
static void SingularValueDecomposition3x3(const float A[3][3], float U[3][3], float w[3], float VT[3][3])
Perform singular value decomposition on a 3x3 matrix.
static double Nan()
Special IEEE-754 number used to represent Not-A-Number (Nan).
static void Perpendiculars(const float v1[3], float v2[3], float v3[3], double theta)
Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (i....
static double Gaussian(double mean, double std)
Generate pseudo-random numbers distributed according to the Gaussian distribution with mean mean and ...
static bool IsFinite(double x)
Test if a number has finite value i.e.
static void LUSolveLinearSystem(double **A, int *index, double *x, int size)
Solve linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U ...
static double EstimateMatrixCondition(const double *const *A, int size)
Estimate the condition number of a LU factored matrix.
static void LUFactor3x3(float A[3][3], int index[3])
LU Factorization of a 3x3 matrix.
static void LinearSolve(MatrixT &&M, VectorT1 &&x, VectorT2 &&y)
This method solves linear systems M * x = y.
static void FreeCombination(int *combination)
Free the "iterator" array created by vtkMath::BeginCombination.
static double Random(double min, double max)
Generate pseudo-random numbers distributed according to the uniform distribution between min and max.
static void TensorFromSymmetricTensor(const T1 symmTensor[6], T2 tensor[9])
Convert a 6-Component symmetric tensor into a 9-Component tensor, no allocation performed.
static void LabToXYZ(const double lab[3], double xyz[3])
Convert color from the CIE-L*ab system to CIE XYZ.
static double Solve3PointCircle(const double p1[3], const double p2[3], const double p3[3], double center[3])
In Euclidean space, there is a unique circle passing through any given three non-collinear points P1,...
static vtkTypeBool PointIsWithinBounds(const double point[3], const double bounds[6], const double delta[3])
Return true if point is within the given 3D bounds Bounds is x-min, x-max, y-min, y-max,...
static float Dot(const float a[3], const float b[3])
Dot product of two 3-vectors (float version).
static void Diagonalize3x3(const float A[3][3], float w[3], float V[3][3])
Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the column...
static void LabToXYZ(double L, double a, double b, double *x, double *y, double *z)
Convert color from the CIE-L*ab system to CIE XYZ.
static vtkTypeBool GetAdjustedScalarRange(vtkDataArray *array, int comp, double range[2])
Get a vtkDataArray's scalar range for a given component.
static bool ProjectVector(const float a[3], const float b[3], float projection[3])
Compute the projection of vector a on vector b and return it in projection[3].
static void MultiplyScalar2D(float a[2], float s)
Multiplies a 2-vector by a scalar (float version).
static void HSVToRGB(const float hsv[3], float rgb[3])
Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue).
static void Assign(const double a[3], double b[3])
Assign values to a 3-vector (double version).
static double Determinant2x2(const double c1[2], const double c2[2])
Calculate the determinant of a 2x2 matrix: | a b | | c d |.
static T Max(const T &a, const T &b)
Returns the maximum of the two arguments provided.
static void Outer2D(const double x[2], const double y[2], double A[2][2])
Outer product of two 2-vectors (double version).
static void RandomSeed(int s)
Initialize seed value.
static double NegInf()
Special IEEE-754 number used to represent negative infinity.
static void MultiplyScalar2D(double a[2], double s)
Multiplies a 2-vector by a scalar (double version).
static void LabToRGB(double L, double a, double b, double *red, double *green, double *blue)
Convert color from the CIE-L*ab system to RGB.
static double Gaussian()
Generate pseudo-random numbers distributed according to the standard normal distribution.
static int Ceil(double x)
Rounds a double to the nearest integer not less than itself.
static void HSVToRGB(const double hsv[3], double rgb[3])
Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue).
~vtkMath() override=default
static double Inf()
Special IEEE-754 number used to represent positive infinity.
static vtkTypeBool Jacobi(float **a, float *w, float **v)
Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix.
static int PlaneIntersectsAABB(const double bounds[6], const double normal[3], const double point[3])
Implements Plane / Axis-Aligned Bounding-Box intersection as described in Graphics Gems IV,...
static ScalarT Dot(VectorT1 &&x, VectorT2 &&y)
Computes the dot product between 2 vectors x and y.
static void RGBToXYZ(const double rgb[3], double xyz[3])
Convert color from the RGB system to CIE XYZ.
static void QuaternionToMatrix3x3(const float quat[4], float A[3][3])
Convert a quaternion to a 3x3 rotation matrix.
static int NearestPowerOfTwo(int x)
Compute the nearest power of two that is not less than x.
static void HSVToRGB(double h, double s, double v, double *r, double *g, double *b)
Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue).
static void SingularValueDecomposition3x3(const double A[3][3], double U[3][3], double w[3], double VT[3][3])
Perform singular value decomposition on a 3x3 matrix.
static double SignedAngleBetweenVectors(const double v1[3], const double v2[3], const double vn[3])
Compute signed angle in radians between two vectors with regard to a third orthogonal vector.
static ScalarT Dot(VectorT1 &&x, MatrixT &&M, VectorT2 &&y)
Computes the dot product x^T M y, where x and y are vectors and M is a metric matrix.
static float Normalize2D(float v[2])
Normalize (in place) a 2-vector.
static void Invert3x3(const double A[3][3], double AI[3][3])
Invert a 3x3 matrix.
static void HSVToRGB(float h, float s, float v, float *r, float *g, float *b)
Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue).
static constexpr int DYNAMIC_VECTOR_SIZE()
When this value is passed to a select templated functions in vtkMath, the computation can be performe...
static void MultiplyQuaternion(const double q1[4], const double q2[4], double q[4])
Multiply two quaternions.
static void Multiply3x3(const double A[3][3], const double v[3], double u[3])
Multiply a vector by a 3x3 matrix.
static void Outer(const double a[3], const double b[3], double c[3][3])
Outer product of two 3-vectors (double version).
static vtkTypeBool InvertMatrix(double **A, double **AI, int size, int *tmp1Size, double *tmp2Size)
Thread safe version of InvertMatrix method.
static vtkTypeBool InvertMatrix(double **A, double **AI, int size)
Invert input square matrix A into matrix AI.
static void LUSolve3x3(const float A[3][3], const int index[3], float x[3])
LU back substitution for a 3x3 matrix.
static int GetSeed()
Return the current seed used by the random number generator.
static void Assign(const VectorT1 &a, VectorT2 &&b)
Assign values to a 3-vector (templated version).
static float RadiansFromDegrees(float degrees)
Convert degrees into radians.
static void Convolve1D(Iter1 beginSample, Iter1 endSample, Iter2 beginKernel, Iter2 endKernel, Iter3 beginOut, Iter3 endOut, ConvolutionMode mode=ConvolutionMode::FULL)
Compute the convolution of a sampled 1D signal by a given kernel.
static void RotateVectorByWXYZ(const double v[3], const double q[4], double r[3])
rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
static void Add(const float a[3], const float b[3], float c[3])
Addition of two 3-vectors (float version).
static int CeilLog2(vtkTypeUInt64 x)
Gives the exponent of the lowest power of two not less than x.
static void RGBToProLab(double red, double green, double blue, double *L, double *a, double *b)
Convert color from the RGB system to Prolab The input RGB must be values in the range [0,...
static void ProLabToXYZ(const double prolab[3], double xyz[3])
Convert color from the ProLAB system to CIE XYZ.
static vtkTypeBool AreBoundsInitialized(const double bounds[6])
Are the bounds initialized?
static bool ProjectVector2D(const double a[2], const double b[2], double projection[2])
Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2].
static vtkTypeBool JacobiN(float **a, int n, float *w, float **v)
JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix.
static int NextCombination(int m, int n, int *combination)
Given m, n, and a valid combination of n integers in the range [0,m[, this function alters the intege...
static constexpr double Pi()
A mathematical constant.
static void Multiply3x3(const float A[3][3], const float v[3], float u[3])
Multiply a vector by a 3x3 matrix.
static void Subtract(const double a[3], const double b[3], double c[3])
Subtraction of two 3-vectors (double version).
static void ProLabToXYZ(double L, double a, double b, double *x, double *y, double *z)
Convert color from the ProLAB system to CIE XYZ.
static void RGBToProLab(const double rgb[3], double prolab[3])
Convert color from the RGB system to Prolab The input RGB must be values in the range [0,...
static void ProLabToRGB(double L, double a, double b, double *red, double *green, double *blue)
Convert color from the ProLab system to RGB.
static void Matrix3x3ToQuaternion(const float A[3][3], float quat[4])
Convert a 3x3 matrix into a quaternion.
static void Orthogonalize3x3(const double A[3][3], double B[3][3])
Orthogonalize a 3x3 matrix and put the result in B.
static void XYZToRGB(const double xyz[3], double rgb[3])
Convert color from the CIE XYZ system to RGB.
static double ClampAndNormalizeValue(double value, const double range[2])
Clamp a value against a range and then normalize it between 0 and 1.
static void MultiplyScalar(double a[3], double s)
Multiplies a 3-vector by a scalar (double version).
static double Dot2D(const double x[2], const double y[2])
Dot product of two 2-vectors.
static void LinearSolve3x3(const float A[3][3], const float x[3], float y[3])
Solve Ay = x for y and place the result in y.
static vtkTypeBool IsNan(double x)
Test if a number is equal to the special floating point value Not-A-Number (Nan).
static void Diagonalize3x3(const double A[3][3], double w[3], double V[3][3])
Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the column...
static void RGBToLab(const double rgb[3], double lab[3])
Convert color from the RGB system to CIE-L*ab.
static void ProLabToRGB(const double prolab[3], double rgb[3])
Convert color from the ProLab system to RGB.
static int Floor(double x)
Rounds a double to the nearest integer not greater than itself.
static void RotateVectorByNormalizedQuaternion(const double v[3], const double q[4], double r[3])
rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotati...
static void Subtract(const VectorT1 &a, const VectorT2 &b, VectorT3 &&c)
Subtraction of two 3-vectors (templated version).
static vtkTypeBool BoundsIsWithinOtherBounds(const double bounds1[6], const double bounds2[6], const double delta[3])
Return true if first 3D bounds is within the second 3D bounds Bounds is x-min, x-max,...
static double Determinant2x2(double a, double b, double c, double d)
Calculate the determinant of a 2x2 matrix: | a b | | c d |.
static void RGBToHSV(const double rgb[3], double hsv[3])
Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value).
static vtkTypeBool JacobiN(double **a, int n, double *w, double **v)
JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix.
static double AngleBetweenVectors(const double v1[3], const double v2[3])
Compute angle in radians between two vectors.
static void MultiplyMatrix(const double *const *A, const double *const *B, unsigned int rowA, unsigned int colA, unsigned int rowB, unsigned int colB, double **C)
General matrix multiplication.
static float DegreesFromRadians(float radians)
Convert radians into degrees.
static float Determinant2x2(const float c1[2], const float c2[2])
Compute determinant of 2x2 matrix.
static int Round(double f)
static vtkTypeBool IsInf(double x)
Test if a number is equal to the special floating point value infinity.
static double GaussianWeight(double mean, double variance, double position)
Compute the amplitude of an unnormalized Gaussian function with specified mean and variance.
static void UninitializeBounds(double bounds[6])
Set the bounds to an uninitialized state.
static void RGBToHSV(double r, double g, double b, double *h, double *s, double *v)
Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value).
static void Outer(const float a[3], const float b[3], float c[3][3])
Outer product of two 3-vectors (float version).
static int * BeginCombination(int m, int n)
Start iterating over "m choose n" objects.
static double Norm(const double v[3])
Compute the norm of 3-vector (double version).
static void RoundDoubleToIntegralIfNecessary(double val, OutT *ret)
Round a double to type OutT if OutT is integral, otherwise simply clamp the value to the output range...
static void RotateVectorByWXYZ(const float v[3], const float q[4], float r[3])
rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
static bool IsPowerOfTwo(vtkTypeUInt64 x)
Returns true if integer is a power of two.
static void Invert3x3(const float A[3][3], float AI[3][3])
Invert a 3x3 matrix.
static float Normalize(float v[3])
Normalize (in place) a 3-vector.
static void Transpose3x3(const double A[3][3], double AT[3][3])
Transpose a 3x3 matrix.
static ReturnTypeT SquaredNorm(const TupleRangeT &v)
Compute the squared norm of a 3-vector.
static double Determinant3x3(const float A[3][3])
Return the determinant of a 3x3 matrix.
static float Dot2D(const float x[2], const float y[2])
Dot product of two 2-vectors.
ConvolutionMode
Support the convolution operations.
static void RotateVectorByNormalizedQuaternion(const float v[3], const float q[4], float r[3])
rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotati...
static void RGBToHSV(const float rgb[3], float hsv[3])
Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value).
static void Add(VectorT1 &&a, VectorT2 &&b, VectorT3 &c)
Addition of two 3-vectors (double version).
static void Orthogonalize3x3(const float A[3][3], float B[3][3])
Orthogonalize a 3x3 matrix and put the result in B.
static bool ProjectVector2D(const float a[2], const float b[2], float projection[2])
Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2].
static vtkTypeBool SolveLinearSystemGEPP2x2(double a00, double a01, double a10, double a11, double b0, double b1, double &x0, double &x1)
Solve linear equation Ax = b using Gaussian Elimination with Partial Pivoting for a 2x2 system.
static vtkMatrixUtilities::ScalarTypeExtractor< MatrixT >::value_type Determinant(MatrixT &&M)
Computes the determinant of input square SizeT x SizeT matrix M.
static vtkTypeBool SolveLinearSystem(double **A, double *x, int size)
Solve linear equations Ax = b using Crout's method.
static void LabToRGB(const double lab[3], double rgb[3])
Convert color from the CIE-L*ab system to RGB.
static float Norm2D(const float x[2])
Compute the norm of a 2-vector.
static vtkTypeBool LUFactorLinearSystem(double **A, int *index, int size, double *tmpSize)
Thread safe version of LUFactorLinearSystem method.
static void LinearSolve3x3(const double A[3][3], const double x[3], double y[3])
Solve Ay = x for y and place the result in y.
static void XYZToLab(double x, double y, double z, double *L, double *a, double *b)
Convert Color from the CIE XYZ system to CIE-L*ab.
static void MultiplyScalar(float a[3], float s)
Multiplies a 3-vector by a scalar (float version).
static T Min(const T &a, const T &b)
Returns the minimum of the two arguments provided.
static void InvertMatrix(MatrixT1 &&M1, MatrixT2 &&M2)
Computes the inverse of input matrix M1 into M2.
static void Cross(VectorT1 &&a, VectorT2 &&b, VectorT3 &c)
Cross product of two 3-vectors.
static void MultiplyMatrix(MatrixT1 &&M1, MatrixT2 &&M2, MatrixT3 &&M3)
Multiply matrices such that M3 = M1 x M2.
static void Perpendiculars(const double v1[3], double v2[3], double v3[3], double theta)
Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (i....
static T ClampValue(const T &value, const T &min, const T &max)
Clamp some value against a range, return the result.
static vtkTypeBool SolveLeastSquares(int numberOfSamples, double **xt, int xOrder, double **yt, int yOrder, double **mt, int checkHomogeneous=1)
Solves for the least squares best fit matrix for the equation X'M' = Y'.
static void Identity3x3(double A[3][3])
Set A to the identity matrix.
static void LUFactor3x3(double A[3][3], int index[3])
LU Factorization of a 3x3 matrix.
static vtkTypeBool LUFactorLinearSystem(double **A, int *index, int size)
Factor linear equations Ax = b using LU decomposition into the form A = LU where L is a unit lower tr...
static void RGBToLab(double red, double green, double blue, double *L, double *a, double *b)
Convert color from the RGB system to CIE-L*ab.
static void MultiplyQuaternion(const float q1[4], const float q2[4], float q[4])
Multiply two quaternions.
static double GaussianWeight(double variance, double distanceFromMean)
Compute the amplitude of an unnormalized Gaussian function with mean=0 and specified variance.
static void ClampValues(const double *values, int nb_values, const double range[2], double *clamped_values)
Clamp some values against a range The method without 'clamped_values' will perform in-place clamping.
static void Transpose3x3(const float A[3][3], float AT[3][3])
Transpose a 3x3 matrix.
static vtkMatrixUtilities::ScalarTypeExtractor< VectorT >::value_type SquaredNorm(VectorT &&x)
Computes the dot product between 2 vectors x and y.
static void ClampValues(double *values, int nb_values, const double range[2])
Clamp some values against a range The method without 'clamped_values' will perform in-place clamping.
static int QuadraticRoot(double a, double b, double c, double min, double max, double *u)
find roots of ax^2+bx+c=0 in the interval min,max.
static void MultiplyMatrixWithVector(MatrixT &&M, VectorT1 &&X, VectorT2 &&Y)
Multiply matrix M with vector Y such that Y = M x X.
Park and Miller Sequence of pseudo random numbers.
abstract base class for most VTK objects
represent and manipulate 3D points
Computes the portion of a dataset which is inside a selection.
Hold a reference to a vtkObjectBase instance.
void RoundDoubleToIntegralIfNecessary(double val, OutT *ret)
Template defining traits of native types used by VTK.
double vtkDeterminant3x3(const T A[3][3])