Geometric Queries

Querying mesh properties and measurements.

Rodin provides various methods to query geometric properties of meshes, including volumes, areas, perimeters, and spatial information.

Introduction

After creating or loading a mesh, you often need to query its properties: dimensions, entity counts, volumes, and other geometric measurements.

Basic Properties

Dimensions

#include <Rodin/Geometry.h>

using namespace Rodin;
using namespace Rodin::Geometry;

int main() {
  Mesh mesh;
  mesh = mesh.UniformGrid(Polytope::Type::Triangle, {16, 16});

  // Topological dimension (2 for 2D meshes)
  std::cout << "Dimension: " << mesh.getDimension() << std::endl;

  // Space dimension (dimension of embedding space)
  std::cout << "Space dimension: " << mesh.getSpaceDimension() << std::endl;

  return 0;
}

Entity Counts

std::cout << "Vertices: " << mesh.getVertexCount() << std::endl;
std::cout << "Faces: " << mesh.getFaceCount() << std::endl;
std::cout << "Cells: " << mesh.getCellCount() << std::endl;

// Count polytopes by dimension
for (size_t d = 0; d <= mesh.getDimension(); ++d) {
  std::cout << "Polytopes of dimension " << d << ": " 
            << mesh.getPolytopeCount(d) << std::endl;
}

// Count by geometry type
std::cout << "Triangles: " 
          << mesh.getPolytopeCount(Polytope::Type::Triangle) << std::endl;

Empty Check

if (mesh.isEmpty()) {
  std::cout << "Mesh is empty" << std::endl;
}

Geometric Measurements

Volume

// Total volume (area in 2D)
Real totalVolume = mesh.getVolume();
std::cout << "Total volume: " << totalVolume << std::endl;

// Volume by attribute
Real volume1 = mesh.getVolume(1);
std::cout << "Volume of region 1: " << volume1 << std::endl;

// Volume of multiple attributes
FlatSet<Attribute> attrs = {1, 2, 3};
Real combinedVolume = mesh.getVolume(attrs);
std::cout << "Combined volume: " << combinedVolume << std::endl;

Perimeter

// Total perimeter
Real totalPerimeter = mesh.getPerimeter();
std::cout << "Total perimeter: " << totalPerimeter << std::endl;

// Perimeter by attribute
Real perimeter1 = mesh.getPerimeter(1);

Area

// Total area
Real totalArea = mesh.getArea();

// Area by attribute
Real area1 = mesh.getArea(1);

// Area of multiple attributes
Real combinedArea = mesh.getArea(attrs);

Measure

Generic measure for polytopes of any dimension:

// Measure of all edges (dimension 1)
Real edgeMeasure = mesh.getMeasure(1);

// Measure of edges with attribute 1
Real edgeMeasure1 = mesh.getMeasure(1, 1);

// Measure of edges with multiple attributes
Real combinedEdgeMeasure = mesh.getMeasure(1, attrs);

Attribute Queries

Getting Attributes

// Get cell attribute
Attribute cellAttr = mesh.getCellAttribute(5);

// Get face attribute
Attribute faceAttr = mesh.getFaceAttribute(10);

// Get arbitrary polytope attribute
Attribute attr = mesh.getAttribute(2, 7);  // Cell 7

Setting Attributes

// Set cell attribute
mesh.setAttribute({2, 5}, 2);  // Set cell 5 to attribute 2

// Set face attribute
mesh.setAttribute({1, 10}, 3);  // Set face 10 to attribute 3

Spatial Queries

Vertex Coordinates

// Get coordinates of vertex 0
auto coords = mesh.getVertexCoordinates(0);
std::cout << "Vertex 0: (" << coords[0] << ", " << coords[1] << ")" 
          << std::endl;

Surface Check

// Check if mesh is a surface mesh (codimension 1)
if (mesh.isSurface()) {
  std::cout << "This is a surface mesh" << std::endl;
}

Boundary Checks

mesh.getConnectivity().compute(1, 2);  // Required

// Check if face is on boundary
if (mesh.isBoundary(5)) {
  std::cout << "Face 5 is on the boundary" << std::endl;
}

// Check if face is an interface
if (mesh.isInterface(10)) {
  std::cout << "Face 10 is an interface" << std::endl;
}

Complete Example

#include <Rodin/Geometry.h>

using namespace Rodin;
using namespace Rodin::Geometry;

int main() {
  Mesh mesh;
  mesh = mesh.UniformGrid(Polytope::Type::Triangle, {32, 32});
  mesh.getConnectivity().compute(1, 2);

  // Basic information
  std::cout << "=== Mesh Information ===" << std::endl;
  std::cout << "Dimension: " << mesh.getDimension() << std::endl;
  std::cout << "Space dimension: " << mesh.getSpaceDimension() << std::endl;
  std::cout << "Vertices: " << mesh.getVertexCount() << std::endl;
  std::cout << "Edges: " << mesh.getFaceCount() << std::endl;
  std::cout << "Cells: " << mesh.getCellCount() << std::endl;

  // Geometric measurements
  std::cout << "\n=== Measurements ===" << std::endl;
  std::cout << "Total volume: " << mesh.getVolume() << std::endl;
  std::cout << "Total perimeter: " << mesh.getPerimeter() << std::endl;

  // Boundary information
  size_t boundaryEdges = 0;
  for (auto it = mesh.getBoundary(); it; ++it) {
    boundaryEdges++;
  }
  std::cout << "\n=== Boundary ===" << std::endl;
  std::cout << "Boundary edges: " << boundaryEdges << std::endl;

  // Average cell size
  Real avgCellSize = mesh.getVolume() / mesh.getCellCount();
  std::cout << "\n=== Statistics ===" << std::endl;
  std::cout << "Average cell size: " << avgCellSize << std::endl;

  return 0;
}