www.elsevier.com/locate/jvlc Journal of Visual Languages & Computing Journal of Visual Languages and Computing 14 (2003) 233–254 A differential volume rendering method with second-order difference for time-varying volume data Shih-Kuan Liao, Chin-Feng Lin, Yeh-Ching Chung*, Jim Z.C. Lai Department of Information Engineering, Feng Chia University, Taichung, Taiwan 407, ROC Received 13 June 2002; received in revised form 9 January 2003; accepted 19 January 2003 Abstract The differential volume rendering method is a ray casting based method for time-varying volume data. In the differential volume rendering method, the changed voxels between consecutivetimestepsareextractedtoformdifferentialfilesinadvance.Whenthedatasetisto be rendered, changed voxels are projected onto the image plane to determine the positions of changed pixels. Only the changed pixels, instead of all pixels on the image, are updated by casting new rays in each time step. The main overhead of the differential volume rendering method is the determination of changed pixels. In this paper, we propose a two-level differential volume rendering method, in which the determination of changed pixels is accelerated by the aid of the second-order difference. Since changed voxels in two consecutive differential files may partially overlap in the space, the projection computation spent on the overlappedareaisredundant.Weusethispropertytoextractthedifferenceofchangedvoxels between consecutive differential files to form the second-order difference. Based on the second-order difference, the changed pixels can be determined more efficiently. The experimental results show that the proposed method outperforms the comparative methods for all test datasets in most cases. In addition, the rendering time can be predicted once the data files are loaded in each time step. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Ray casting; Differential volume rendering; Second-order difference; Time-varying volume data; Flow animation; CFD *Corresponding author. Tel.: +886-424517250x3765; fax: +886-424516101. E-mail address: ychung@fcu.edu.tw (Y.-C. Chung). 1045-926X/03/$-see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1045-926X(03)00020-X