Principles and applications of pencil tracing

Abstract

Pencil tracing, a new approach to ray tracing, is introduced for faster image synthesis with more physical fidelity. The paraxial approximation theory for efficiently tracing a pencil of rays is described and analysis of its errors is conducted to insure the accuracy required for pencil tracing. The paraxial approximation is formulated from a 4x4 matrix (a system matrix) that provides the basis for pencil tracing and a variety of ray tracing techniques, such as beam tracing, ray tracing with cones, ray-object intersection tolerance, and a lighting model for reflection and refraction. In the error analysis, functions that estimate approximation errors and determine a constraint on the spread angle of a pencil are given.The theory results in the following fast ray tracing algorithms; ray tracing using a system matrix, ray interpolation, and extended 'beam tracing' using a 'generalized perspective transform'. Some experiments are described to show their advantages. A lighting model is also developed to calculate the illuminance for refracted and reflected light.

Right-triangular subdivision for texture mapping ray-traced objects

“…Ray tracing with beam [9], cone [2], and pencil [14] rays are methods for area sampling, but they require complex intersection and clipping calculations. Whitted [16] suggests using a pyramid instead of a linear eye ray that is defined by the four corners of a pixel.…”

Prefiltered Cross-Section Occluders

“…The introduction of distributed ray tracing [5] achieved soft shadowing effects by stochastically sampling rays and averaging their results. This implicit visibility shaft between area lights and sample points is made explicit in variants of ray tracing that attempt to leverage the spatial coherence of nearby rays, including shadow volumes [6], cone tracing [7], pencil tracing [8], beam tracing [9] [10], and packet tracing [11] [12].…”

A beam tracing method with precise antialiasing for polyhedral scenes

“…So, refracted rays are supposed to converge to a certain point called virtual eye. A more precise, but more complicated refraction determination is developed in [10]. We use a different approach in order to avoid these approximations and complex computations.…”

“…Beam tracing [7][8][9][10][11] can be considered as an alternative to ray tracing. The antialiasing property of beam tracing is very interesting because it is probably the only approach that can produce a general antialiasing.…”

“…Refractions are free from linear approximation or complex computations usually used in similar beam tracers [8,10]. Soft shadows due to non-punctual light sources can be produced with no stochastic sampling.…”