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Interpolation

Namespace: DISP3DLIB  ·  Library: 3D Display Library

#include <disp3D/interpolation.h>

class DISP3DLIB::Interpolation

This class holds methods for creating distance-based weight matrices and for interpolating signals.

This class holds methods for creating distance-based weight matrices and for interpolating signals

src/examples/ex_disp3d_scene/main.cpp
QSharedPointer<SparseMatrix<float>> weights = Interpolation::createInterpolationMat(projected, distances, Interpolation::linear); // inverse-distance weights
const VectorXf atVertices = Interpolation::interpolateSignal(*weights, Vector2f(1.0f, 4.0f));                                     // one value per sensor

Public Methods​

Interpolation()​

Static Methods​

createInterpolationMat(vecProjectedSensors, matDistanceTable, interpolationFunction, dCancelDist, vecExcludeIndex)​

createInterpolationMat Calculates the weight matrix for interpolation.

Parameters:

  • vecProjectedSensors : const Eigen::VectorXi & Mesh vertex index of each sensor (one column per sensor).

  • matDistanceTable : const QSharedPointer<Eigen::MatrixXd> Distance table (nVertices x nSensors), e.g. from GeometryInfo::scdc.

  • interpolationFunction : double()(double)* Distance function whose inverse magnitude gives the weight.

  • dCancelDist : const double Distances at or above this value get zero weight.

  • vecExcludeIndex : const Eigen::VectorXi & Sensor column indices that are not pinned to their own vertex.

Returns:

  • QSharedPointer< Eigen::SparseMatrix< float > > — Row-normalised sparse weight matrix (nVertices x nSensors), or an empty matrix if the table is empty.

interpolateSignal(matInterpolationMatrix, vecMeasurementData)​

interpolateSignal Interpolates sensor data using the weight matrix (shared pointer version).

Parameters:

  • matInterpolationMatrix : const QSharedPointer< Eigen::SparseMatrix< float > > Weight matrix (nVertices x nSensors).

  • vecMeasurementData : const QSharedPointer<Eigen::VectorXf> & Sensor values (nSensors).

Returns:

  • Eigen::VectorXf — Interpolated vertex values, or an empty vector on dimension mismatch.

interpolateSignal(matInterpolationMatrix, vecMeasurementData)​

interpolateSignal Interpolates sensor data using the weight matrix (reference version).

Parameters:

  • matInterpolationMatrix : const Eigen::SparseMatrix< float > & Weight matrix (nVertices x nSensors).

  • vecMeasurementData : const Eigen::VectorXf & Sensor values (nSensors).

Returns:

  • Eigen::VectorXf — Interpolated vertex values, or an empty vector on dimension mismatch.

linear(dIn)​

linear Identity interpolation function.

Parameters:

  • dIn : const double Input distance.

Returns:

  • double — dIn unchanged.

gaussian(dIn)​

gaussian Gaussian interpolation function (sigma=1).

Parameters:

  • dIn : const double Input distance.

Returns:

  • double — exp(-dIn^2 / 2).

square(dIn)​

square Negative parabola interpolation function with y-offset of 1.

Parameters:

  • dIn : const double Input distance.

Returns:

  • double — max(1 - dIn^2 / 9, 0).

cubic(dIn)​

cubic Cubic hyperbola interpolation function.

Parameters:

  • dIn : const double Input distance.

Returns:

  • double — dIn^3.

Example​

Used in examples​

ex_disp3d_scene​

Disp3D scene data: sensor-to-surface interpolation, electrodes, MRI slices, video overlay and layers.

src/examples/ex_disp3d_scene/main.cpp, line 126
QSharedPointer<SparseMatrix<float>> weights = Interpolation::createInterpolationMat(projected, distances, Interpolation::linear); // inverse-distance weights
const VectorXf atVertices = Interpolation::interpolateSignal(*weights, Vector2f(1.0f, 4.0f));                                     // one value per sensor
// vertex 5: weights 1/2 and 1/4, normalised to 2/3 and 1/3 -> 1 * 2/3 + 4 * 1/3 = 2; vertex 3 is equidistant -> 2.5
ok &= expect(std::fabs(atVertices(0) - 1.0f) < 1e-6f && std::fabs(atVertices(15) - 4.0f) < 1e-6f && std::fabs(atVertices(5) - 2.0f) < 1e-6f && std::fabs(atVertices(3) - 2.5f) < 1e-6f,
             QString("Interpolation: sensors kept, vertex 5 = %1, vertex 3 = %2").arg(atVertices(5)).arg(atVertices(3)));

ex_interpolation​

Example of using the interpolation library and geometryInfo library.

src/examples/ex_interpolation/main.cpp, line 143
//weight matrix
qint64 startTimeWMat = QDateTime::currentMSecsSinceEpoch();
QSharedPointer<SparseMatrix<float>> interpolationMatrix = Interpolation::createInterpolationMat(mappedSubSet,
                                                                                                distanceMatrix,
                                                                                                Interpolation::linear,
                                                                                                FLOAT_INFINITY);
std::cout << "Weight matrix duration: " << QDateTime::currentMSecsSinceEpoch() - startTimeWMat << " ms " << std::endl;

Authors of this file​