Flattening

Table of Contents

• Flattening algorithms
• Measuring flattening error

Flattening algorithms

Coming soon.

Measuring flattening error

A common way to measure flattening error is to observe the L2 and LInf stretch metrics introduced by Sander et al. [sander2001texture] . Volume Cartographer provides a method for calculating these metrics in the Texturing module. Once calculated, these metrics can also be plotted to an image:

#include <iostream>
 
#include <vc/texturing/FlatteningError.hpp> // LStretch
#include <vc/texturing/PPMGenerator.hpp> // GenerateCellMap
 
using namespace volcart;
using namespace volcart::texturing;
 
// Calculate error metrics
auto metrics = LStretch(mesh3D, mesh2D);
 
// Report the inverted global metrics (see note below)
metrics = InvertLStretchMetrics(metrics);
std::cout << "Global L2 stretch: " << metrics.l2 << "\n";
std::cout << "Global LInf stretch: " << metrics.lInf << "\n";
 
// Plot the per-face error
auto cellMap = GenerateCellMap(mesh2D, uvMap, height, width);
auto plots = PlotLStretchError(metrics, cellMap, ColorMap::Plasma);

Flattening error can also be plotted when running vc_render:

$ vc_render ... --uv-plot-error error_plots.png

This will generate two images, error_plots_l2.png and error_plots_lInf.png, plotting the per-face L2 and LInf metrics respectively.

Note

The L2 and LInf stretch metrics represent the stretch from the 2D domain to the 3D domain. Thus, an LInf value of 0.5 indicates a flattening where a 3D unit vector is half the length of its corresponding 2D unit vector. This is the inverse of how stretch is generally considered in most of Volume Cartographer, where we are interested in the stretch introduced relative to the 3D domain. The VC applications dealing with these metrics will often invert the returned values to make reporting more intuitive.