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Parameterization Quantities

A parameterization is a set of 2D coordinates associated with a mesh, often referred to as “UV coordinates”. This sections details several functions for visualizing such parameterizations.

param_demo

Example: 

import numpy as np
import polyscope as ps
ps.init()

N_vert = 100
N_face = 250
vertices = np.random.rand(N_vert, 3) # (V,3) vertex position array
faces = np.random.randint(0, N_vert, size=(N_face,3)) # (F,3) array of indices 
                                                      # for triangular faces
ps_mesh = ps.register_surface_mesh("my mesh", vertices, faces)

# parameterization per vertex
param_vert = np.random.rand(N_vert,2)
ps_mesh.add_parameterization_quantity("rand param", param_vert, enabled=True)

# parameterization per corner
param_corner = np.random.rand(ps_mesh.n_corners(),2)
ps_mesh.add_parameterization_quantity("rand param corner", param_corner, defined_on='corners')

# use options to customize visualization
ps_mesh.add_parameterization_quantity("rand param corner2", param_corner, defined_on='corners',
                                       coords_type='world', viz_style='local_rad')


# with custom checker/grid color
cA = (0.1, 0.2, 0.3)
cB = (0.4, 0.5, 0.6)
ps_mesh.add_parameterization_quantity("rand param corner3", param_corner, defined_on='corners',
                                       coords_type='unit', viz_style='grid', grid_colors=(cA, cB))

# view the mesh with all of these quantities
ps.show()

SurfaceMesh.add_parameterization_quantity(name, values, defined_on='vertices', coords_type='unit', enabled=None, viz_style=None, grid_colors=None, checker_colors=None, checker_size=None, cmap=None, island_labels=None, create_curve_network_from_seams=None)

Add a parameterization quantity to the mesh.

  • name string, a name for the quantity
  • values an Nx2 numpy array, coordinates at vertices/corners
  • defined_on one of 'vertices','corners', is this a coordinate per vertex or per corner?

This function also accepts optional keyword arguments listed below, which customize the appearance and behavior of the quantity.

Visualizing islands and seams

For parameterizations on surface meshes, additional features are available to visualize UV island and seams. The term islands refers to connected components of faces in the 2D parameterization, and the term seams refers to the subset of edges separating adjacent faces which are not connected.

UV islands can be colored per-island with the viz_style="checker_islands" style. Each face should have a distinct integer indicating which island it is a part of, which the caller must compute and pass via the optional argument below (Polyscope does not compute it automatically).

SurfaceMesh.add_parameterization_quantity(..., island_labels=island_labels)

island_labels

Set an integer value per-face of the mesh, which can be used to color islands distinctly in the "checker_islands" style. Each face should have an integer indicating which island it is a part of, numbered however you like.

Technically this can be any integer per-face, although it is generally useful for visualizing islands.

  • island_labels is the array of face labels, an Fx1 numpy array of integers per-face

This will have no effect unless you also set viz_style="checker_islands".

Additionally, the seams of a parameterization can be visualized as a curve network. These seams are computed automatically by Polyscope, the curve network is created by calling the function below, and is otherwise an ordinary curve network.

SurfaceMesh.add_parameterization_quantity(..., create_curve_network_from_seams="seam_curves")

createCurveNetworkFromSeams

Create a curve network from the seams of a UV map.

  • create_curve_network_from_seams is the string name of the the curve network quantity that will be created. Passing "" generates a default fname

Styles

Several styles are available for how a parameterization is displayed.

The viz_style option determines how parameterizations are visualized:

  • checker: a two-color checker pattern
  • grid: a two-color grid with thin lines
  • local_check: a checkerboard over a radial colormap, centered around (0,0)
  • local_rad: distance stripes over a radial colormap, centered around (0,0)

Types

The coords_type options determines how parameter coordinates are interpreted for scaling:

  • unit: UV coords are assumed to lie on the [0,1] interval
  • world: UV coords are assumed to be scaled like the world-space positions of the mesh

Parameterization Quantity Options

When adding a parameterization quantity, the following keyword options can be set. These are available for all kinds of parameterization quantities on all structures.

Keyword arguments:

  • enabled boolean, whether the quantity is initially enabled (note that generally only one quantity can be shown at a time; the most recent will be used)
  • coords_type string, one of 'unit', 'world' (see above)
  • viz_style string, one of 'checker', 'grid', 'local_check', 'local_rad' (see above)
  • grid_colors 2-tuple of rgb colors, used to color the grid visualization
  • checker_colors 2-tuple of rgb colors, used to color the checkerboard visualization
  • checker_size float, the size of checkers/grid/stripes
  • cmap string, which colormap to use

If not specified, these optional parameters will assume a reasonable default value, or a persistent value if previously set.