Initalize objects for parameterization -- done once on program startup

* Create dual 1-form visualization, since Polyscope's 1-form visualization function only takes triangles. Adapted from * JS version of this assignmen

* Instead of using Polyscope's addOneFormIntrinsicVectorQuantity(), for better control of the visualization. */

* Check if mesh is planar. */

* Convert map to mesh positions. */

* Compute the midpoint of a halfedge. */

* Helper function for interpolateWachspressWhitney(). Computes the distance from a point <p> to the segment with * endpoint <a> and direction <u>. *

* Determine if a mesh satisfies Gauss-Bonnet. * * Input: A vector where the ith entry is the the index of the singularity at the ith vertex. * Retu

Set mesh color.

Set mesh color.

* Display the operator diagram. */

* Display isolines. */

* Show selected vertices. * This function gets called every time an element is selected on-screen. */

* Show selected vertices. * This function gets called every time an element is selected on-screen. */

* Display the selected simplices. * TODO: Use SurfaceVertexCountQuantity* SurfaceMesh::addVertexCountQuantity, etc. instead of SurfaceGraphQuantity f

* Show selected vertices. * This function gets called every time an element is selected on-screen. */

* Shift φ such that its minimum value is zero. */

* Compute the total surface area of the mesh. * * Input: * Returns: The surface area of the mesh. */

* Given an initial angle αi in face i, this function computes the new angle αj in the neighboring face j as * αj = αi - θij + θji, where θij and θji

Solve and update mesh colors.

* Computes the normal at a vertex using the "equally weighted" method. * * Input: The vertex on which the normal is to be computed. * Returns: The

Constructor

constructor

Constructor * Input: The surface mesh <surfaceMesh> and geometry <geo>. */

* Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

* Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

constructors

Initialize an empty MeshSubset. */

Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

constructors

Constructors

* Load in the bunny mesh to test on. */

Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

Some sanity checks for the Laplace matrix and mass matrix.

Some sanity checks for the Laplace matrix (same as from poisson-problem)

* Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

* Constructor * Input: The surface mesh <inputMesh> and geometry <inputGeo>. */

Add an edge to this subset. */

Add a face to this subset. */

Adds a subset's vertices, edges, and faces to this subset. */

Add a vertex to this subset. */

* Assign a unique index to each vertex, edge, and face of a mesh. * All elements are 0-indexed. * * Input: None. Access geometry via the member var

* Build a closed, but not exact, primal 1-form ω. * * Input: A std::vector of Halfedges representing a homology generator of the mesh. * Returns: A

* Build a dual spanning tree on a mesh without boundary. More specificially, populate the member variable <faceParent>, * which is a std::map that ma

* Build the mean curvature flow operator. * * Input: The mass matrix <M> of the mesh, and the timestep <h>. * Returns: A sparse matrix representing

* Build the mean curvature flow operator. * * Input: The mass matrix <M> of the mesh, and the timestep <h>. * Returns: A sparse matrix representing

* Build a primal spanning tree on a mesh without boundary. More specifically, populate the member variable * <vertexParent>, which is a std::map that

* Builds the sparse complex POSITIVE DEFINITE Laplace matrix. Do this by building the negative semidefinite Laplace * matrix, multiplying by -1, and

* Compute the area scaling of the given face. * * Input: A Face in the original mesh, and the parameterization. * Returns: The area scaling of the

* Compute the dual 0-form potential β by solving the system d𝛿β = -K + 2π * singularity. * * Input: A vector where the ith entry is the the index of

* Compute the harmonic component γ = ∑_{i = 1, ..., 2g} zi ξi by solving the system Pz = v - ∑𝛿β. * v - ∑𝛿β should be normalized to lie between -π an

* Compute the area-weighted quasi-conformal error of the given face. * See "geometric stretch metric" in http://hhoppe.com/ssp.pdf for more details.

* Computes the cotangent of the angle opposite to a halfedge. (Do NOT use built-in function for this) * * Input: The halfedge whose cotan weight is

Make a deep copy of the input MeshSubset and return it as a new * MeshSubset. */

Delete an edge from this subset. */

Delete a face from this subset. */

Removes a subset's vertices, edges, and faces from this subset. */

Delete a vertex from this subset. */

* User-defined buttons */

* User-defined buttons */

* User-defined buttons */

* Buttons for the simplicial operators. */

* User-defined buttons */

* Check whether a halfedge is in the dual spanning tree. * * Input: A halfedge <he> * Returns: True if <he> is in the dual spanning tree, false oth

* Check whether a halfedge is in the primal spanning tree. * * Input: A halfedge <he> * Returns: True if <he> is in the primal spanning tree, false