Examples and tutorials » Mesh geometry examples » Generating uniform grids

Introduction

The Mesh::UniformGrid() method creates structured grids of various polytope types. This is the quickest way to get started with Rodin — no mesh files needed.

2D Grids

#include <Rodin/Geometry.h>

using namespace Rodin;
using namespace Rodin::Geometry;

int main()
{
  Mesh mesh;

  // Triangular grid: 16×16 subdivisions → 512 triangles, 289 vertices
  mesh = mesh.UniformGrid(Polytope::Type::Triangle, { 16, 16 });

  // Quadrilateral grid: 32×32 subdivisions → 1024 quads, 1089 vertices
  mesh = mesh.UniformGrid(Polytope::Type::Quadrilateral, { 32, 32 });

  return 0;
}

The grid is created on the unit square where are the subdivision counts. Use Mesh::scale() to rescale to a different domain:

// Create grid on [0,1]^2
mesh = mesh.UniformGrid(Polytope::Type::Triangle, { 32, 32 });
mesh.scale(1.0 / 31.0);  // Normalize to unit square

3D Grids

// Tetrahedral grid: 8×8×8 subdivisions
mesh = mesh.UniformGrid(Polytope::Type::Tetrahedron, { 8, 8, 8 });

// Hexahedral grid: 16×16×16 subdivisions
mesh = mesh.UniformGrid(Polytope::Type::Hexahedron, { 16, 16, 16 });

// Wedge (prism) grid: 4×4×4 subdivisions
mesh = mesh.UniformGrid(Polytope::Type::Wedge, { 4, 4, 4 });

Computing Connectivity

After creating a mesh, compute the boundary connectivity before defining boundary conditions:

mesh = mesh.UniformGrid(Polytope::Type::Triangle, { 16, 16 });
mesh.getConnectivity().compute(1, 2);  // edges → cells (required for BC)

Mesh Queries

std::cout << "Vertices: " << mesh.getVertexCount() << std::endl;
std::cout << "Cells:    " << mesh.getCellCount() << std::endl;
std::cout << "Volume:   " << mesh.getVolume() << std::endl;
std::cout << "Perimeter: " << mesh.getPerimeter() << std::endl;

Full Source Code

• UniformGrid.cpp

See Also

• Meshes guide — Full mesh documentation
• Polytopes — Element types
• Connectivity — Incidence relations
• Poisson example — Uses UniformGrid