High-Speed Display of Graphics Images Utilizing Successively Greater Refinement
Original Publication Date: 1991-Jul-01
Included in the Prior Art Database: 2005-Apr-03
This article describes a method of displaying images calculated from an algorithm in successive degrees of resolution, over time.
High-Speed Display of Graphics Images Utilizing
describes a method of displaying images
calculated from an algorithm in successive degrees of resolution,
resolution of computer graphics images has increased,
the amount of time required to generate these images has also
increased. Some of these images can literally take hours or days to
produce, even using the highest-speed processors.
to produce a realistic image of objects with
reflective surfaces, each point on each visible surface must be
computed by tracing the paths of rays of light reflected from every
other surface in the image. A much simpler, but still dramatic,
example of this problem, is the computation of the members of the
Mandelbrot Set is a mathematical entity which exhibits an
infinite amount of detail at an infinite depth of computation. This
means that more and more detail can be found as the image is
magnified, at the cost of more and more computation.
Mandelbrot Set is a collection of complex numbers. Complex
numbers may be represented as either ordered pairs of real numbers
which can easily be graphed in two dimensions or as numbers of the
form A + Bi, where A and B are real numbers and i is the
square root of -1, for ease of computation.
Mandelbrot Set is defined by the iterative equation Z(n+1)
= Z(n)*Z(n) + Z(O), where Z(n) is the complex number which is the
result of the nth iteration and Z(O) is the starting value, the point
in the complex plane that is being examined.
are typically displayed as a two-dimensional color
image in which the color of each point Z(O) represents the number of
iterations required before the result Z(n) falls outside a circle of
radius 2 centered at the point (O,O).
iteration of this Mandelbrot Set procedure requires
at least four floating-point multiplications of the highest possible
precision, the time required to compute each point of the image can
easily exceed one second as magnification increases, in spite of the
speed of the processor being used or the availability of a high-speed
of new regions of the Mandelbrot Set to be
explored is most easily performed by marking an area on an existing
view of the set. However, the amount of time required to generate
each view of the set is usually too large to allow it to be truly
interactive. This problem is further aggravated by the fact that
images are generated line by line, progressing from one edge of the
image to the opposing edge.
solutions to the problem have either reduced the
overall resolution of the images, failing to fully exploit the
available graphics hardware, or reduced the precision of the
computations, seriously limiting the depth at which the Mandelbrot
Set may be explored.