Abstract: The relationships between graphics and geometry are discussed in this paper. From the
view that shape is the source of the graph, the drawing/image are fundamentally constructed by
geometric elements, thus the process of generation, representation, processing and propagation of
drawing/image could be regarded as some operations of definition, transformation and interrelation of
geometric elements. Therefore, it can be concluded that geometry is the basis of graphics and its
theory, and meanwhile geometric computing is also the basis of graphics computing. Then, based on
the analysis of graphics and its computing fundamentally, the essence, contradiction and key
technologies of graphics computing are presented. The respective roles and advantages/disadvantages
of algebra and geometry, emphasizing the leading status of human in the design of algorithms are also
discussed. Moreover, the generation of a drawing or a model depends more on the relations between
their elements than the elements themselves. Since the drawing/images have become the major
objects and representation in graphics computing, a geometry-based shape calculation mechanism is
introduced to fix the shortage of normal numerical calculation mechanism, so as to pursuit a new
mode of geometric computing as thinking by shape while computing by number.

Key words: graphics, geometry, geometric computing, numerical computing, shape computing