Rings around exoplanets (exorings) are one of the most expected discoveries in exoplanetary research. There is an increasing number of theoretical and observational efforts for detecting exorings, but none of them have succeeded yet. Most of those methods focus on the photometric signatures of exorings during transits, whereas less attention has been paid to light diffusely reflected: what we denote here as the bright side of the light curve. This is particularly important when we cannot detect the typical stellar flux drop produced by transiting exoplanets. Here, we endeavour to develop a general method to model the variations on the light curves of both ringed non-transiting and transiting exoplanets. Our model (dubbed as Pryngles) simulates the complex interaction of luminous, opaque, and semitransparent objects in planetary systems, discretizing their surface with small circular plane discs that resemble sequins or spangles. We perform several numerical experiments with this model, and show its incredible potential to describe the light curve of complex systems under various orbital, planetary, and observational configurations of planets, moons, rings, or discs. As our model uses a very general approach, we can capture effects like shadows or planetary/ring shine, and since the model is also modular we can easily integrate arbitrarily complex physics of planetary light scattering. A comparison against existing tools and analytical models of reflected light reveals that our model, despite its novel features, reliably reproduces light curves under common circumstances. Pryngles source code is written in PYTHON and made publicly available. (C) 2022 Elsevier B.V. All rights reserved.