【正文】 s throughout the entire period of construction. For example, if the user selects a time increment as large as 1 day, visualizing construction operations of a project with a total duration of 5 months can take approximately 1 min on the same puter. However, with such a coarse time increment, it is likely that some potential spatial conflicts can be missed since a crane can perform multiple operations on a given day.These all suggest that the accuracy of detected spatial conflicts be not rely mainly on a userselected time increment of discrete event simulation. This paper focuses on this need to model and identify possible spatial conflicts during an equipment operation without the reliance on a userselected time increment. It presents an automated approach for generating workspace requirements of mobile cranes to enable automatic identification of spatial conflicts related to Crane operations. It also describes the validation performed to assess the effectiveness of such an approach in detecting spatial conflicts related to mobile crane operations.2. ApproachIn this research, we represented an equipment workspace as a collection of threedimensional geometric objects enclosing spaces occupied by a piece of equipment and materials attached to it during an operation. The developed approach takes a 4D product and process model, and information about equipment operations, which is a sequence of geometric transformations describing the motion of pieces of equipment and materials used in the operations. Using this approach, it is expected that it will be possible to generate a collection of workspaces correspondin to motion of each equipment part and materials. By aggregating such collections of workspaces, it is then possible to create the equipment workspace requirement of an operation.Based on the workspaces generated, spatial conflicts can be identified between workspaces and building ponents that are expected to be in place during a given time frame. The detailed discussion of the approach is divided into four parts including (1) a kinematic representation of a piece of equipment, (2) a representation of equipment operations and motions, (3) a representation of equipment workspaces, and (4) reasoning mechanisms for generating equipment workspaces.3. Implementation and validationIn this research, we developed a prototypical visualization environment that allows a user to model and view dynamic motion of a crane, and identify spatial conflicts related to crane operations. Once a sequence of geometric transformations of a crane is modeled, the system automatically generates workspaces corresponding to geometric transformation of parts of a crane and materials. In the prototype, we also implemented two collision detection approaches for identifying spatial conflicts. The first approach detects collision between equipment workspaces and building structures. The other approach is a conventional approach that detects collision between pieces of equipment and building structures at every time step throughout the course of equipment motion. The time steps for detecting collision are determined by a time increment specified by the user. Later, these two approaches will be called workspacebased and time stepbased approaches, respectively.To assess the effectiveness of using equipment workspaces for spatial conflict detection, we created a construction scenario demonstrating installation of a set of steel beams. During the installation, a telescopicboom truck crane is used to lift one m WF 2462beam at a time from a laydown area, and then place it on existing building structures. We modeled the building ponents, the truck crane, and a sequence of geometric transformation of the truck crane during lifting operation, based on the information collected from an actual construction site. However, we modeled only the building ponents that are in close proximity with the crane to avoid excessive tests in spatial conflict detection. In the scene, a building is posed of fiftyfour ponents including floors, beams, and columns, which are totally represented by 2120 triangles. The truck crane modeled in this scene has eight parts. For simplicity, we modeled each part of the crane as a rectangular box. Since the operation of the truck crane involves both rotation and translation of equipment parts of the crane, the workspaces of the truck crane are posed of all types of the polyhedrons . Therefore, we can assess the effectiveness of different types of the representations of equipment workspaces in one construction scenario. In this assessment, we pared the time spent in detecting spatial conflicts and the accuracy of spatial conflicts detected by the approach discussed in this paper against those used by the time stepbased approach. The two spatial conflict detection approaches are based on the same type of a spatial data structure and use the same algorithms for performing intersection tests. Comparing the effectiveness of the two approaches using the same collision detection algorithms allows us to assess how well equipment workspaces can support identification of equipment related spatial conflicts.4. ConclusionsThis paper addresses the need for modeling equipment workspace requirements and identifying spatial conflicts related to mobile crane operations prior to the execution of the actual operations. The approach presented accounts for dynamic behavior of mobile cranes during their operation in representing and reasoning about their workspace requirements in 3D and over time. The equipment workspaces were geometrically represented by a set of polyhedrons, each of which encloses a space occupied by an equipment part or an attached material moving during an operation.Equipment workspaces provide a basis to identify possible spatial conflict without needing to define time increments for simulation. They enable the detection of spatial conflicts between a piece of equipment