PSC Maps

This repository includes code for two maps and a tool to visualize those maps. It can be easily integrated in any renderer just by including the corresponding header library. It is the accompanying code for this paper:

Stratified Sampling of Projected Spherical Caps
Carlos Ureña and Iliyan Georgiev.
EG Symposium on Rendering 2018 (CGF Track), Karlsruhe, July 2018.
PDF available at: http://iliyan.com/publications/ProjectedSphericalCaps

Prerequisites

The code for light-source sampling (file PSCMap.h) has no prerequisites, as it can be compiled as is. However file MapViewer.cpp (which implements a tool which visualizes the maps) requires AntTweakBar library, which can be obtained here: http://anttweakbar.sourceforge.net/doc/

Maps viewer tool build and usage

You can build the maps viewer tool just by typing make. The corresponding makefile file has been tested on macOS and Linux (not yet on MS Windows), by using both GNU g++ and LLVM clang++ compilers. Probably you'll need to set the AntTweakBar source folder in the makefile.

When running, the map viewer tool visualizes iso-curves for both maps, and the partial area curve. You can adjust the values of alpha and beta by using the sliders. You can switch between radial and parallel maps by pressing M key. You can also run numerical integration tests by pressing T key.

Using the maps code in a renderer

If you want to use the maps in your renderer, you just need to include PSCMaps.h, as this is a header only, single file, templatized library (see example usage below). The map evaluates the sample position in the disc (see paper), thus, in order to obtain a sample direction, this position must be converted to world coordinates.

Here is an example code using a map instance. This computation produces sample_dir_wc (sample direction in world coordinates) and area (area of the projected spherical cap). The sample direction should be used to evaluate visibility to the light source, while the area weights the resulting radiance.

#include "PSCMaps.H"

....
using namespace PSCM ;

// object which stores map evaluation status
PSCMaps<float> pscm ;

// get the orthonormal reference frame aligned with the shading point normal
// and the spherical cap

vec3  vz  = ......., // Z axis (unit-length normal vector at shading point)
      vx = ....... , // X axis (unit-length, perp. to 'vz', in the plane of 'n' and the vector to cap center)
      vy = ....... ; // Y axis (unit length, perpendicular to 'vx' and 'vz')

// compute angle alpha and beta
const float alpha = ....... , // spherical cap aperture angle
            beta  = ....... , // spherical center's angle with local X axis

// initialize the map evaluator
// (once per each (spherical cap,shading point) pair)
pscm.initialize( alpha, beta, true );

// check if the spherical cap is visible over the horizon
if ( pscm.is_invisible() )
   return ;  

// get the area
const float area = pscm.get_area();

// evaluate the map (once per sample vector)
float s  = ....... , // s- coordinate of sample point (in [0,1])
      t  = ....... , // t-coordinate of sample point (in [0,1])
      x ,            // x- coordinate of resulting vector (in the local frame)
      y ;            // y- coordinate of resulting vector (in the local frame)
pscm.eval_map( s, t, x, y );

// convert from coordinates in the shading point reference frame to world coordinates
const vec3 sample_dir_wc = x*vx + y*vy + sqrt(1.0-x*x-y*y)*vz ;