### **Parameterization** * * * * * **Description**： Parameterizing a surface amounts to finding a one-to-one mapping from a suitable domain to the surface. A good mapping is the one which minimizes either angle distortions (conformal parameterization) or area distortions (equiareal parameterization) in some sense. In this component, we focus on parameterizing triangulated surfaces which are homeomorphic to a disk or a sphere, and on piecewise linear mappings onto a planar domain. Although the main motivation behind the first parameterization methods was the application to texture mapping, it is now frequently used for mapping more sophisticated modulation signals (such as normal, transparency, reflection or light modulation maps), fitting scattered data, re-parameterizing spline surfaces, repairing CAD models, approximating surfaces and remeshing. **Input**： * Geometry: Input a Geometry. * Method: Parameterization methods. '0' = Tutte Barycentric Mapping; '1' = Discrete Authalic Parameterization; '2' = Discrete Conformal Map; '3' = Floater Mean Value Coordinates; '4' = Least Squares Conformal Maps; '5' = As Rigid As Possible Parameterization. If you wanna learn more about these algorithms please click [**CGAL_Parameterization**]([https://doc.cgal.org/latest/Surface\_mesh\_parameterization/index.html#Chapter\_Planar\_Parameterization\_of\_Triangulated\_Surface\_Meshes](https://doc.cgal.org/latest/Surface_mesh_parameterization/index.html#Chapter_Planar_Parameterization_of_Triangulated_Surface_Meshes)) * BorderType：Border Types. '0' = Circular_border_arc_length: It is able to parameterize the border of a 3D surface onto a circle, with an arc-length parameterization: the (u,v) values are proportional to the length of border edges; '1' = Circular_border_uniform: It is able to parameterize the border of a 3D surface onto a circle in a uniform manner: points are equally spaced; '2' = Square_border_arc_length: It is able to parameterize the border of a 3D surface onto a square, with an arc-length parameterization: (u,v) values are proportional to the length of border edges; '3' = Square_border_uniform: It is able to parameterize the border of a 3D surface onto a square in a uniform manner: points are equally spaced." **Output**： Mesh: Output the mesh. UVPosition: Output UV Positions.