In large-scale construction sites there are constant needs for rapid recognition and accurate measurement of objects so that on-site decisions can be made quickly and safely. Current methods involve full area laser range scanning systems that can produce very detailed models of a scanned scene, however the computational and data acquisition time that is required precludes the methods from being used for real time decision making. This paper presents algorithms to fit objects to sparse point clouds of measured data in a construction scene, that significantly decrease data acquisition time, and computational and modeling time. Two basic fitting and matching algorithms that address construction site material of cuboid and cylindrical shapes are discussed. Experimental results that indicate that the proposed algorithms assist an operator to create models of construction objects rapidly and with sufficient accuracy are also presented.