Systems and methods perform gridless geological modeling. A system provides an interactive visual model that performs fast modeling of subsurface geological properties without spending processor resources calculating a three-dimensional grid. The system receives structural data, selects points for modeling a property of a subsurface earth volume, and propagates values for the property directly to the points in gridless three-dimensional space. The system then displays the propagated values in an interactive visualization of a structural framework model. The system creates fast interpolation functions and can apply a callback function for acceleration. One technique offloads calculations to a graphics processor or other auxiliary processor for speed. The system provides a myriad of fully interactive volume and dimensional slice probes, with mappable color-coding and a user-selection of rendering styles. Points are quality checked and optimized propagation parameters are stored for accelerated rendering when unavoidable grid production is needed for simulation.