Abstract: We have briefly introduced the principal theory of the aspect graph representation. The theory and method for calculating and drawing the chart of a cylinder intersecting with a sphere have been proposed based on the computing theory and method of the aspect graph. The geometrical and mathematical models of the cylinder intersecting with the sphere are established. We analyzed the projective space of the aspect graph of the cylinder intersecting with the sphere. The dimension of the projective space is 4. The representation of the projective space is given. The types of the visual events in the front, top and left views of the cylinder intersecting with the sphere are analyzed. There are 4 types of visual events. The characteristic views are computed. The chart of the cylinder intersecting with the sphere is obtained.