Trace - An experiment in rendering point fields

Written by Paul Bourke
April 2002


"TRACE" was an experimental rendering program written in an attempt to render point fields.....in more interesting ways than with just points. In many scientific simulations while points are used for practical computational reasons, they are intended to be approximations to continuous distributions and so it makes sense to render them as such. Some initial examples from this rendering experiment are shown on the right, they are mostly from astronomy based simulations based upon points that represent stars, gas, and dark matter.

The overall flow of the program is as follows:
  • Initialise internal state, read the data file, set up internal optimisations, get camera state and other options from either the command line or sefault settings file.

  • For each pixel in the destination image create a ray from the camera into the scene. The way this ray passes through the scene will dictate how the pixel in question is shaded.

  • For each point in the scene calculate the closest distance to the ray. It is this closest distance that acts as an approximation on how much influence the point has on the ray.

  • Evaluate a function of the ray-point distance to determine how the colour of the ray should change. The different functions are listed near the end of thie document. They are all monotonically decreasing function of the distance from the origin (data point position).

  • Save the resulting image as well as statistical and performance information.

Data file format

A very simple data format was chosen, it was an ascii file where each line represents one point. The first character of the line identifies the line data type, this could be "#" for a comment or "p" for a point. The next three items on the line are the x,y,z coordinates of the point. The next item is the point type (see table below), this is an integer from 0 upwards. The next item is the spread of the distribution, the interpretation depends somewhat on the point type. The last three items on the line are the r,g,b colour of the point. An example data file might be as follows

# Tests all the datatypes

p -1.4 3  0.5  0  0.1  1 1 1
p -1.0 3  0.5  1  0.1  1 1 1
p -0.6 3  0.5  2  0.1  1 1 1
p -0.2 3  0.5  3  0.1  1 1 1
p  0.2 3  0.5  4  0.1  1 1 1
p  0.6 3  0.5  5  0.1  1 1 1
p  1.0 3  0.5  6  0.1  1 1 1
p  1.4 3  0.5  7  0.1  1 1 1

p -1.4 3 0.0  0  0.075  1 0 0
p -1.0 3 0.0  1  0.075  1 0 0
p -0.6 3 0.0  2  0.075  1 0 0
p -0.2 3 0.0  3  0.075  1 0 0
p  0.2 3 0.0  4  0.075  1 0 0
p  0.6 3 0.0  5  0.075  1 0 0
p  1.0 3 0.0  6  0.075  1 0 0
p  1.4 3 0.0  7  0.075  1 0 0

p -1.4 3 -0.5  0  0.05  1 0 1
p -1.0 3 -0.5  1  0.05  1 0 1
p -0.6 3 -0.5  2  0.05  1 0 1
p -0.2 3 -0.5  3  0.05  1 0 1
p  0.2 3 -0.5  4  0.05  1 0 1
p  0.6 3 -0.5  5  0.05  1 0 1
p  1.0 3 -0.5  6  0.05  1 0 1
p  1.4 3 -0.5  7  0.05  1 0 1
Gives the rendered image below

Optimisation

A brute force approach means that every point is compared and contributes to every ray. This is obviously wasteful because all point distributions only affect a local region and if the ray passes further than a points maximum influence it never contributes or changed the ray. The subset of points that need to be considered for a ray was reduced by dividing up the view frustum into an n by n grid and tagging which points can possibly influence a ray in each grid cell. So when a ray is passing through a particular cell only those points whose distribution affects that cell are considered.

  















Point distribution types

The following table gives the different point distributions that were implemented. The choice for a particular application depends mostly on the type of falloff, in practice only types 0, 1, 2, and 6 were used.

Number Name Formula Example
0 Rectangle W(r) = 1 for r<d
1 Gaussian W(r) = exp(-r*r/(d*d))
2 Inverse W(r) = 1 / (1 + r / d)
3 Inverse squared W(r) = 1 / (1 + r*r/(d*d))
4 Cosine W(r) = (1 + cos(r*pi/(2*d))) / 2
5 Exponential cosine W(r) = exp(-r/d) (1 + cos(r*pi/(2*d))) / 2
6 Exponential W(r) = exp(-r/d)
7 Linear W(r) = (d*2 - r) / (2*d)