An Efficient 2.5D Shadow Detection Algorithm for Urban Planning and Design Using a Tensor Based Approach

Abstract

Urbanization is leading us to a more chaotic state where healthy living becomes a prime concern. The high-rise buildings influence the urban setting with a high shadow rate on surroundings that can have no positive impact on the general neighborhood. Nevertheless, shadows are the main factor of defeatist virtual settings, they are expensive to render in real-time. This paper investigates how the amount of sunlight varies by season and how seasons can indicate the time of year to understand how shadows vary in length at different times of the day and how they change over the seasons. We propose a novel efficient (fast and scalable) algorithm to calculate a 2.5D cast-shadow map from a given LiDAR-derived Digital Surface Model (DSM). We present a proof-of-concept demonstration to examine the technical practicability of the introduced algorithm. Tensor-based techniques such as singular value decomposition, tensor unfolding are examined and deployed to represent the multidimensional data. The proposed method exploits horizon mapping ideas and extends the method to a modern graphics algorithm (Bresenham’s line drawing algorithm) to account for the DSM’s underlying surface geometry. A proof-of-concept is developed utilizing Python’s TensorFlow library, exploring data flow graphs and the tensor data structure. The heavy computer graphics algorithm used in this paper is parallelized using PySpark. Results explicate significant enhancements in overall performance while preserving accuracy at negligible variations.