Tim Burke, Computer Science major Class of 2025, presented his research entitled, “Redefining Velocity in Discrete Spaces using Quantized Motion Sequences (QMS)“, at the Northeastern Section of the Mathematical Association of America (MAA) conference held at Boston College on November 19th.
Burke’s research explores a new approach to conceptualizing velocity in grid-based environments. His abstract states:
In the study of motion, conceptualizing velocity as a continuous vector is straightforward in continuous spaces but poses challenges in discrete environments, such as those defined by integer lattice points. Traditional methods for approximating the path of an object in discrete space, like Bresenham’s line algorithm, focus on incremental error correction to mimic continuous motion. However, this research takes a fundamentally different approach by returning to the drawing board to formalize how velocity might be inherently conceptualized in discrete space. The Quantized Motion Sequence (QMS) methodology is an innovative solution. QMS enables the translation of an object’s velocity directly into the associated path, a sequence of $x$ and $y$ unit steps that encodes analogs of the directionality and magnitude of the continuous vector. This sequence is generated through a recursive process, resulting in a discrete approximation of the vector demonstrating maximum scale and directional invariance. By redefining velocity through QMS, this research offers a novel perspective for understanding motion in discrete spaces, potentially enhancing movement analysis in theoretical and practical applications, including simulation environments and computational algorithms.
