Polygon Mesh Processing

1. Polygon Mesh Processing overview

The Polygon Mesh Processing [PMP] module offers a variety of tools for manipulating and analyzing polygonal meshes.

  • Key functionalities include:

    • Boolean Operations: Perform operations like union, intersection, and difference on meshes.

    • Mesh Smoothing: Techniques to smooth the surface of meshes.

    • Mesh Simplification: Reduce the complexity of meshes while preserving their essential shape and features.

    • Mesh Repair: Tools to detect and fix defects in meshes, such as holes or self-intersections.

    • Feature Detection: Identify and process features like edges and corners.

    • Subdivision Methods: Refine meshes by subdividing their faces.

  • Application:

    • Extrusion: Create base and interior walls

    • Union: Merge without break between floors and walls

    • Quality Check: triangulated faces, closed mesh, outward oriented mesh, self_intersection check

2. extrude_mesh Function in CGAL

The extrude_mesh function is used to create a 3D extrusion from a 2D polygonal mesh. This process extends the input mesh along its normal vectors to generate walls or other 3D structures. Below is an overview of its functionality and parameters:

2.1. Function Overview

The extrude_mesh function transforms a 2D polygonal mesh into a 3D mesh by extruding it along specified directions. This is commonly used to create volumetric elements from 2D shapes, such as converting floor plans into walls.

2.2. Key Parameters

  • Input Mesh: The 2D mesh that will be extruded.

  • Output Mesh: The resulting 3D mesh after extrusion.

  • Bottom Function Object: A callable object or lambda function that specifies how to position the vertices of the bottom face of the extrusion. This function typically moves the vertices along their normal vectors by a given distance.

  • Top Function Object: A callable object or lambda function that specifies how to position the vertices of the top face of the extrusion. This usually involves translating the vertices in a direction defined by the Top function object.

2.3. Function Behavior

  1. Vertex Normal Calculation: Computes the normal vectors for each vertex in the mesh. These normals are used to determine the direction and magnitude of the extrusion.

  2. Vertex Positioning:

    • Bottom Face: Moves the vertices of the bottom face of the input mesh according to the Bottom function object, typically by translating them along their normal vectors.

    • Top Face: Moves the vertices of the top face based on the Top function object, often by applying a transformation defined by the Top function object.

  3. Mesh Construction: Constructs the extruded mesh by connecting corresponding vertices of the bottom and top faces, resulting in a 3D representation of the original 2D mesh.

2.4. Usage Example

Here is a basic example of using the extrude_mesh function:

#include <CGAL/Surface_mesh.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Polygon_mesh_processing/extrude.h>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Surface_mesh<K::Point_3> Mesh;
typedef K::Vector_3 Vector;

Mesh input_mesh; // Initialize with your 2D mesh
Mesh output_mesh; // Mesh to store the extruded result

auto bottom_func = [](const auto& vin, const auto& vout) {
    // Define how to move the bottom vertices
};

auto top_func = [](const auto& vin, const auto& vout) {
    // Define how to move the top vertices
};
CGAL::Polygon_mesh_processing::extrude_mesh(input_mesh, output_mesh, bottom_func, top_func);

Important Considerations:

  • Ensure that the input mesh is well-defined and free of intersecting faces or other issues that might affect the extrusion process.

  • Customize the Bottom and Top function objects to meet the specific requirements of your application and desired extrusion parameters.

3. Other tools:

2D Straight Skeleton and Polygon Offsetting
3d Mesh Generation



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