# CurvaturesDemo

VTKExamples/Cxx/PolyData/CurvaturesDemo

### Description¶

How to get the Gaussian and Mean curvatures of a surface.

Two different surfaces are used in this demonstration with each surface coloured according to its Gaussian and Mean curvatures.

• The first surface is a superquadric surface, this demonstrates the use of extra filters that are needed to get a nice smooth surface.

• The second surface is a parametric surface, in this case the surface has already been triangulated so no extra processing is necessary.

In order to get a nice coloured image, a vtkColorTransferFunction has been used to generate a set of colours for the vtkLookupTable tables. We have used a diverging colour space. Because of the symmetry of the ranges selected for the lookup tables, the white colouration represents a midpoint value whilst the blue represents values less than the midopoint value and red represents colours greater than the midpoint value.

In the case of the Random Hills Gaussian curvature surface, this colouration shows the nature of the surface quite nicely. The blue areas are saddle points (negative Gaussian curvature) and the red areas have a positive Gaussian curvature. In the case of the mean curvature the blue colouration is representing negative curvature perpendicular to one of the principal axes.

This example also demonstrates the use of std::vector's and the linking of the elements of the vectors together to form a pipeline.

Other Languages

See (Python)

Question

### Code¶

CurvaturesDemo.cxx

/*
The purpose of this is to demonstrate how to get the Gaussian and Mean
curvatures of a surface.

Two different surfaces are used in this demonstration with each
surface coloured according to its Gaussian and Mean curvatures.

The first surface is a superquadric surface, this demonstrates the use
of extra filters that are needed to get a nice smooth surface.

The second surface is a parametric surface, in this case the surface
has already been triangulated so no extra processing is necessary.

In order to get a nice coloured image, a vtkColorTransferFunction has
been used to generate a set of colours for the vtkLookUp tables. We
have used a diverging colour space.  Because of the symmetry of the
ranges selected for the lookup tables, the white colouration
represents a midpoint value whilst the blue represents values less
than the midopoint value and red represents colours greater than the
midpoint value.

In the case of the Random Hills Gaussian Curvature surface, this
colouration shows the nature of the surface quite nicely. The blue
areas are saddle points (negative Gaussian curvature) and the red
areas have a positive Gaussian curvature.  In the case of the mean
curvature the blue colouration is representing negative curvature
perpendicular to one of the principal axes.

This example also demonstrates the use of std::vector and the linking
of the elements of the vector together to form a pipeline.
*/

#include <vtkActor.h>
#include <vtkActor2D.h>
#include <vtkCleanPolyData.h>
#include <vtkColorTransferFunction.h>
#include <vtkCurvatures.h>
#include <vtkLookupTable.h>
#include <vtkNamedColors.h>
#include <vtkParametricFunctionSource.h>
#include <vtkParametricRandomHills.h>
#include <vtkPolyDataAlgorithm.h>
#include <vtkPolyDataMapper.h>
#include <vtkRenderWindow.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkRenderer.h>
#include <vtkSmartPointer.h>
#include <vtkTextMapper.h>
#include <vtkTextProperty.h>
#include <vtkTransform.h>
#include <vtkTransformFilter.h>
#include <vtkTriangleFilter.h>

#include <array>
#include <vector>

int main(int, char* argv[])
{
auto colors = vtkSmartPointer<vtkNamedColors>::New();
// We are going to handle two different sources.
// The first source is a superquadric source.
torus->SetCenter(0.0, 0.0, 0.0);
torus->SetScale(1.0, 1.0, 1.0);
torus->SetPhiResolution(64);
torus->SetThetaResolution(64);
torus->SetThetaRoundness(1);
torus->SetThickness(0.5);
torus->SetSize(0.5);
torus->SetToroidal(1);

// Rotate the torus towards the observer (around the x-axis)
auto torusT = vtkSmartPointer<vtkTransform>::New();
torusT->RotateX(55);

auto torusTF = vtkSmartPointer<vtkTransformFilter>::New();
torusTF->SetInputConnection(torus->GetOutputPort());
torusTF->SetTransform(torusT);

// The quadric is made of strips, so pass it through a triangle filter as
// the curvature filter only operates on polys
auto tri = vtkSmartPointer<vtkTriangleFilter>::New();
tri->SetInputConnection(torusTF->GetOutputPort());

// The quadric has nasty discontinuities from the way the edges are generated
// so let's pass it though a CleanPolyDataFilter and merge any points which
// are coincident, or very close
auto cleaner = vtkSmartPointer<vtkCleanPolyData>::New();
cleaner->SetInputConnection(tri->GetOutputPort());
cleaner->SetTolerance(0.005);

// The next source will be a parametric function
auto rh = vtkSmartPointer<vtkParametricRandomHills>::New();
auto rhFnSrc = vtkSmartPointer<vtkParametricFunctionSource>::New();
rhFnSrc->SetParametricFunction(rh);

// Now we have the sources, lets put them into a vector
std::vector<vtkSmartPointer<vtkPolyDataAlgorithm>> sources;
sources.push_back(cleaner);
sources.push_back(cleaner);
sources.push_back(rhFnSrc);
sources.push_back(rhFnSrc);

// Colour transfer function.
auto ctf = vtkSmartPointer<vtkColorTransferFunction>::New();
ctf->SetColorSpaceToDiverging();
colors->GetColor3d("MidnightBlue").GetGreen(),
colors->GetColor3d("MidnightBlue").GetBlue());
colors->GetColor3d("DarkOrange").GetGreen(),
colors->GetColor3d("DarkOrange").GetBlue());

// Lookup table.
std::vector<vtkSmartPointer<vtkLookupTable>> luts;
for (auto idx = 0; idx < sources.size(); ++idx)
{
auto lut = vtkSmartPointer<vtkLookupTable>::New();
lut->SetNumberOfColors(256);
for (auto i = 0; i < lut->GetNumberOfColors(); ++i)
{
std::array<double, 4> color;
ctf->GetColor(double(i) / lut->GetNumberOfColors(), color.data());
color[3] = 1.0;
lut->SetTableValue(i, color.data());
}
if (idx == 0)
{
lut->SetRange(-10, 10);
}
else if (idx == 1)
{
lut->SetRange(0, 4);
}
else if (idx == 2)
{
lut->SetRange(-1, 1);
}
else
{
lut->SetRange(-1, 1);
}
lut->Build();
luts.push_back(lut);
}

std::vector<vtkSmartPointer<vtkCurvatures>> curvatures;
for (auto idx = 0; idx < sources.size(); ++idx)
{
curvatures.push_back(vtkSmartPointer<vtkCurvatures>::New());
if (idx % 2 == 0)
{
curvatures[idx]->SetCurvatureTypeToGaussian();
}
else
{
curvatures[idx]->SetCurvatureTypeToMean();
}
}
std::vector<vtkSmartPointer<vtkRenderer>> renderers;
std::vector<vtkSmartPointer<vtkActor>> actors;
std::vector<vtkSmartPointer<vtkPolyDataMapper>> mappers;
std::vector<vtkSmartPointer<vtkTextMapper>> textmappers;
std::vector<vtkSmartPointer<vtkActor2D>> textactors;
for (auto idx = 0; idx < sources.size(); ++idx)
{
mappers.push_back(vtkSmartPointer<vtkPolyDataMapper>::New());
actors.push_back(vtkSmartPointer<vtkActor>::New());
textmappers.push_back(vtkSmartPointer<vtkTextMapper>::New());
textactors.push_back(vtkSmartPointer<vtkActor2D>::New());
renderers.push_back(vtkSmartPointer<vtkRenderer>::New());
}

// Create a common text property.
auto textProperty = vtkSmartPointer<vtkTextProperty>::New();
textProperty->SetFontSize(24);
textProperty->SetJustificationToCentered();

std::vector<std::string> names;
names.push_back("Torus - Gaussian Curvature");
names.push_back("Torus - Mean Curvature");
names.push_back("Random Hills - Gaussian Curvature");
names.push_back("Random Hills - Mean Curvature");
for (auto idx = 0; idx < sources.size(); ++idx)
{
curvatures[idx]->SetInputConnection(sources[idx]->GetOutputPort());

mappers[idx]->SetInputConnection(curvatures[idx]->GetOutputPort());
mappers[idx]->SetLookupTable(luts[idx]);
mappers[idx]->SetUseLookupTableScalarRange(1);

actors[idx]->SetMapper(mappers[idx]);

textmappers[idx]->SetInput(names[idx].c_str());
textmappers[idx]->SetTextProperty(textProperty);

textactors[idx]->SetMapper(textmappers[idx]);
textactors[idx]->SetPosition(250, 16);
}

// Create the RenderWindow
//
auto rendererSize = 512;
auto gridDimensions = 2;

auto renderWindow = vtkSmartPointer<vtkRenderWindow>::New();
renderWindow->SetSize(rendererSize * gridDimensions,
rendererSize * gridDimensions);

// Add and position the renders to the render window.
for (auto row = 0; row < gridDimensions; ++row)
{
for (auto col = 0; col < gridDimensions; ++col)
{
auto idx = row * gridDimensions + col;
renderers[idx]->SetViewport(
double(col) / gridDimensions,
double(gridDimensions - (row + 1)) / gridDimensions,
double(col + 1) / gridDimensions,
double(gridDimensions - row) / gridDimensions);

renderers[idx]->SetBackground(
colors->GetColor3d("CornflowerBlue").GetData());
}
}

auto interactor = vtkSmartPointer<vtkRenderWindowInteractor>::New();
interactor->SetRenderWindow(renderWindow);

renderWindow->Render();

interactor->Start();

return EXIT_SUCCESS;
}


### CMakeLists.txt¶

cmake_minimum_required(VERSION 3.3 FATAL_ERROR)

project(CurvaturesDemo)

find_package(VTK COMPONENTS
vtkCommonColor
vtkCommonComputationalGeometry
vtkCommonCore
vtkCommonExecutionModel
vtkCommonTransforms
vtkFiltersCore
vtkFiltersGeneral
vtkInteractionStyle
vtkRenderingContextOpenGL2
vtkRenderingCore
vtkRenderingFreeType
vtkRenderingGL2PSOpenGL2
vtkRenderingOpenGL2 QUIET)
if (NOT VTK_FOUND)
message("Skipping CurvaturesDemo: ${VTK_NOT_FOUND_MESSAGE}") return () endif() message (STATUS "VTK_VERSION:${VTK_VERSION}")
if (VTK_VERSION VERSION_LESS "8.90.0")
# old system
include(${VTK_USE_FILE}) add_executable(CurvaturesDemo MACOSX_BUNDLE CurvaturesDemo.cxx ) target_link_libraries(CurvaturesDemo PRIVATE${VTK_LIBRARIES})
else ()
# include all components
target_link_libraries(CurvaturesDemo PRIVATE ${VTK_LIBRARIES}) # vtk_module_autoinit is needed vtk_module_autoinit( TARGETS CurvaturesDemo MODULES${VTK_LIBRARIES}
)
endif ()


cd CurvaturesDemo/build


If VTK is installed:

cmake ..


If VTK is not installed but compiled on your system, you will need to specify the path to your VTK build:

cmake -DVTK_DIR:PATH=/home/me/vtk_build ..


Build the project:

make


and run it:

./CurvaturesDemo


WINDOWS USERS

Be sure to add the VTK bin directory to your path. This will resolve the VTK dll's at run time.