Digital differential analyzer (graphics algorithm)

Abstract: Two incremental linear interpolation algorithms are derived and analyzed for speed and accuracy. The first is a version of a “simple” digital differential analyzer (DDA) employing fixed-point arithmetic, whereas the second is a new algorithm that uses only integral arithmetic and is a generalization of Bresenham's line-drawing algorithm. The new algorithm is shown to achieve perfect accuracy and, depending on the underlying processor, may be faster than the fixed-point algorithm.

Abstract: A buffered digital differential analyzer (BDDA) algorithm in a computerized numerical controller (CNC) performs milling electric discharge machining (milling EDM'ing) of a curve constructed from a sequence of segments using a traditional computer-aided manufacturing (CAM) system. The proposed algorithm interpolates more than one segment in a sampling interval and supports the effective machining of a parametric curve when the electrode crosses the connection between the short segments. The accuracy of both the speed and the trajectory of motion can be ensured without the time function of the parameter specified by two terms of a Taylor expansion, such as in a real-time parametric curve interpolator. The proposed algorithm is compared with the reference–word interpolation and real-time polynomial interpolation used in a milling EDM to confirm improvements of erosion speed.

Abstract: A system for mapping texture data at high speed with flexibility to different applications wherein texture data is sent to a memory interface (MEMIF) thorough a digital differential analyzer (DDA) and a texture mapping unit (TMAP) and loaded to free areas of a Z coordinatory memory (ZBUF) and a drawing data memory (FBUF). A Z coordinate value or drawing data is read/written through a bidirectional port. The TMAP converts texture coordinates into a physical address, reads texture data from dedicated read ports of the ZBUF and the FBUF with the physical address, and maps the texture data. Each of the ZBUF and the FBUF has a DRAM unit and an auxiliary memory. Data of one row of the DRAM unit can be sent to the auxiliary memory means at a time. When desired texture data is not present in the auxiliary memory, data of the entire row of the desired texture data is sent to the auxiliary memory and then read.

Abstract: VDB[Museth 2013] is a compact data structure and toolset developed at DreamWorks Animation for high-resolution volumetric effects typically encountered in movie production. Since its open source release in 2012, as OpenVDB1, it has been adopted by major third-party renders and VFX tools, including Houdini by SideFX, RenderMan by Pixar, Arnold by Solid Angle, and RealFlow by Next Limit. Thus, it should come as no surprise that it is highly desirable to have efficient algorithms for ray-marching of sparse VDB volumes. The core problem is therefore, how to best utilize the hierarchical data structure of VDB for applications that require efficient ray-marching. As we will demonstrate, the solution is a novel hierarchical digital differential analyzer.