This work presents the implementation of data-parallel perspective volume rendering on a massively parallel SIMD computer, the MasPar MP-1, and shows the benefits of e$icient indirect addressing (an MP-1 feature) which allows individual processing elements to address their local memory independently. Emphasis is put on the geometric transformations required for volume rendering algorithms. TJte data-parallel algorithm separates multi-dimensional spatial transformations into a series of one-dimensional operations that can be performed in parallel on regular data domains, providing performance linear with data size. The rotation andperspective transformation is reduced to four shearlscale passes. The separable approach allows for predictable and regular data handling, independent of data values, allowing optimization of communication between processing elements. The communications required are data axis transpositions, wJtich can be peflormed using the MP-1 's global router, which delivers scalable peflormance. Wrtualization allows graceful scaling in both problem size and architecture size, and a hierarchical design provides a flexible and portable fiamework suitable for different data-parallel SIMD architectures.1 IMAGE-BASED VISUALIZATION Massively data-parallel architectures can realise close to peak performance on regularly structured image processing and viewing operations, allowing in some cases for real-time (or near real-time) interaction with modelling and viewing parameters [17]. A number of special architectures have been used for volume rendering [ 111.Polygon-based graphic algorithms pose problems of scalability, discretization independent of problem domain, and dependence on special purpose hardware for high performance [9]. Image-or pixel-based algorithms can be scalable with problem size, need not introduce geometrical artifacts and can be implemented on general purpose data-parallel computers. As a result, increases in model complexity (e.g. molecular modelling), empirical data generated from sensors (e.g. remote sensing and medical imaging) and inter-* action impose requirements that polygon-based systems often cannot satisfy. Image-based approaches are particularly well-suited to handling large multidimensional empirical data and the integration of computer vision, computer graphics and image processing 131.2 DATA-PARALLEL VOLUME RENDERING The data-parallel algorithm achieves data access regularization by following the approach taken by Drebin&al.[4], which is a source for better efficiency in data access. Data-parallel geometrical transformations, including rotation and perspective, are applied to the data to localize projection rays within individual processing element memories. Once localization is completed, iso-surface rendering is computed using Levoy's technique [12]. This consists of computing voxel opacities for iso-surface classification, computing Phong shading, and compositing along the viewing rays for the final view (See also [21] for an extensive discussion on volume rendering iss...
