We have developed a new numerical approach to the dynamics of minor bodies and dust particles, which enables us to increase, without using a supercomputer, the number of employed particle positions in each model up to 10(exp 10) - 10(exp 11), a factor of 10(exp 6) - 10(exp 7) higher than existing numerical simulations. We apply this powerful approach to the high-resolution modeling of the structure and emission of circumstellar dust disks, incorporating all relevant physical processes. In this Letter, we examine the resonant structure of a dusty disk induced by the presence of one planet of mass in the range of (5 x 10(exp -5) - 5 x 10(exp -3))M. It is shown that the planet, via resonances and gravitational scattering, produces (i) a central cavity void of dust; (ii) a trailing (sometimes leading) off-center cavity; and (iii) an asymmetric resonant dust belt with one, two, or more clumps. These features can serve as indicators of planet(s) embedded in the circumstellar dust disk and, moreover, can be used to determine the mass of the planet and even some of its orbital parameters. The results of our study reveal a remarkable similarity with various types of highly asymmetric circumstellar disks observed with the JCMT around Epsilon Eridani and Vega.