Jitter is one popular way of generating samples for stochastic sampling in computer graphics. The Poisson disk distribution better approximates that of the human photomosaic. In this paper we examine the spatial and frequency space behaviour of a number of existing algorithms for generating stochastic samples and propose a new algorithm based on low pass filtering a jittered set of displacements. The distribution is at least as much like that of the human photomosaic as any existing algorithm, while being fast to compute.

Forward differencing is widely used to generate rapidly large numbers of points at equally space parameter values along a curve. A failing of forward differencing is the tendency to generate many extraneous points for curves with highly nonuniform parameterizations. A key result is presented and proven, namely, that a few levels of subdivision, prior to initialization for forward differencing, can improve substantially the quality of the step size estimate, resulting in very few extra points. The initial subdivisions can be done without loss of the exact integer precision available in forward differencing. For small numbers of points—a common occurrence in fonts—exact subdivision is even faster than exact forward differencing. When exact subdivision is used in conjunction with a previously presented exact forward-differencing algorithm, arbitrary cubic curves may be rendered with 32-bit arithmetic and guaranteed single-pixel accuracy, in a grid with an address space as large as 0…7281, with no two generated points greater than one pixel apart. This is more steps than previously possible. Previous discussions of rendering using subdivision have concentrated not on distance but on straightness estimates, whereby subdivision can be stopped once a subcurve can be drawn safely using its polygonal approximation. In this article, bounds are also derived on the size of the control polygon after multiple levels of subdivision: these are used to determine bounds on the number of steps required for differencing. It is shown that any curve whose rasterization fits in a space of ω pixels requires no more than 9ω steps.

Most graphical output devices exhibit what has been termed spatial non-linearity: the effect of setting two adjacent pixels to a given value is not the same as the sum of the effects of setting those two pixels to the same value in isolation: checkerboards of different frequencies do not have the same apparent luminance.We present a method applicable to bit-mapped devices for compensating for short-range spatial non-linearity in error-diffused images.The modification to error diffusion is such that it can be used with any error diffusion technique.In essence, it consists of finding the influence of the neighbouring (output) pixels when making the decision of whether to turn on a given pixel, and passing errors computed accordingly.

The technique of placing directed line segments at grid points, known as hedgehogging, which has been used for visualizing 2D vector fields, is considered. A means of rapidly rendering a slice of a 3D field, suitable for a bilevel display, is provided. Shape and shadowing are used to disambiguate orientation. Liberal use of lookup tables makes the technique very fast.>

Cubic spline curves have many nice properties that make them desirable for use in comptuer graphics, and the advantages of antialiasing have been known for some years. Yet, only recently has there been any attempt at directly antialiasing spline curves. Parametric spline curves have resisted antialiasing in several ways: single segments may cross or become tangent to themselves. Cusps and small loops are easily missed entirely. Thus, short pieces of the curve cannot necessarily be rendered in isolation. Finding the distance from a pixel center to the curve accurately and efficiently—usually an essential part of antialiasing—is an unsolved problem. The method presented by Lien, Shantz, and Pratt [21] is a good start, although it considers pixel-length pieces of the curve in isolation and lacks robustness in the handling of certain curves. This paper provides an improved method that is more robust, and is able to handle intersections and tangency.

Two incremental cubic interpolation algorithms are derived and analysed. Each is based on a known linear interpolation algorithm and modified for third order forward differencing. The tradeoff between overflow avoidance and loss of precision has made forward differencing a method which, although known to be fast, can be difficult to implement. It is shown that there is one particular family of curves which represents the worst case, in the sense that if a member of this family can be accurately drawn without overflow, then any curve which fits in the bounding box of that curve can be. From this the limitations in terms of step count and screen resolution are found for each of the two algorithms.

The interaction of light with particles suspended in the air is the cause of some beautiful effects. Among these effects are the colors of the sunset, the blue of the sky, and the appearance of a scene in fog. A lighting model that takes into account the effects of scattering by suspended particles is presented. A method of computing the colors of the sun and sky, for any sun position above the horizon, is derived from the lighting model. The model is also suitable for rendering fog under general lighting conditions. As an example of the use of the model for rendering fog, the special case of fog lit by the sun, without shadows, is considered.