The most fundamental linkages in ecosystem dynamics are trophodynamic. A trophodynamic theory requires a framework based upon inter-organism or interparticle distance, a metric important in its own right, and an essential component relating trophodynamics and the kinetic environment. It is typically assumed that interparticle distances are drawn from a random distribution, even though particles are known to be distributed in patches. Both random and patch-structure interparticle distance are analysed using the theory of stochastic geometry. Aspects of stochastic geometry - point processes and random closed sets (RCS) - useful for studying plankton ecology are presented. For point-process theory, the interparticle distances, random-distribution order statistics, transitions from random to patch structures, and second-order-moment functions are described. For RCS-theory, the volume fractions, contact distributions, and covariance functions are given. Applications of stochastic-geometry theory relate to nutrient flux among organisms, grazing, and coupling between turbulent flow and biological processes. The theory shows that particles are statistically closer than implied by the literature, substantially resolving the troublesome issues of autotroph-heterotroph nutrient exchange; that the microzone notion can be extended by RCS; that patch structure can substantially modify predator-prey encounter rates, even though the number of prey is fixed; and that interparticle distances and the RCS covariance function provide a fundamental coupling with physical processes. In addition to contributing to the understanding of plankton ecology, stochastic geometry is a potentially useful for improving the design of acoustic and optical sensors.