A List-Priority Rendering Algorithm for Redisplaying Projected Surfaces

摘要: Projected grid surfaces are a particularly interesting subset of bivariate parametric functions. Images generated using three-dimensional computer graphics methods and those resulting from ideal pin-hole cameras fall into this class. Often, range image is provided in addition to the actual image, may be form Z-buffer for synthetic images or stereo-disparity field acquired images. In research I report on an algorithm computing visible projected surface any arbitrary view. This method has several important properties. It determines occlusion-compatible paint order such that closest desired viewpoint drawn last, thus overwriting previously rendered surface. painting determined independent information. Also, facets sequentially, taking advantage local spatial coherency. also describes fast rendering small triangles table driven approach. Introduction A classic problem display functions z = f(x, y). Several special-purpose visibility algorithms have been developed render these specific types surfaces, which often called gridded height fields. The purpose develop related class One earliest solutions was given by Kubert, Szabo, Guilieri [Kubert68]. Later, Wright enhanced Kubert’s familiar floating horizon algorithm, still commonly used today [Wright73]. More recently, improved views suggested [Anderson82] [Wang90]. All displaying compute hidden-line solution instead hidden-surface as common other applications. seems reasonable since representation can provide insights surface’s shape beyond what smooth-shaded do. true when is, average, smooth, case most mathematical surfaces. There are, however, striking similarities between popular hiddenline algorithms, algorithm. Both operate space tightly-coupled with rasterization List-Priority Rendering Algorithm Redisplaying Surfaces Leonard McMillan Comp236 Semester Project 2 process. require comparison operation every pixel potentially displayed determine at sample location column. it more efficient only requires two row-sized buffers, while full screensized array depth values. contrast, Anderson Wang object space. They resolve line segments based unique properties data structure. their approach list-priority techniques, do not involve comparisons each displayed, generate result. major objective adapt object-space techniques different distinguishing characteristic parameterization imposed after projection. three-space coordinates points constrained lie sort lattice grid, are. Furthermore, structure upon valid center projection; point guaranteed grid. Thus, make sense considered conjunction set view parameters. definition viewpoint. equivalent saying defining function, f(x,y), does correspond perspective whereas some question arises: importance surfaces? Consider virtually all naturally imagtry, photographs video images, grids. Most renderings Therefore, obvious application redisplay existing point-of-view. If could found, would allow reuse computed computation new same set. 3 Definitions defined over domain x’0, x’1, ..., x’n y’0, y’1, y’n, where P’ (x’i, y’j), projection real point, P, higher dimensional space, P (x, y, w), x’i x/w, y’j y/w. Projection grids differ typical rather than before. Points P’ij points. region bounded (x’i+1, y’j+1), y’j+1) facet, Fij. Any particular planar view, V, characterized following four parameters: projection, eye position, ; vector origin viewplane, basis vectors sweep out , positive i j directions respectively. formulation slightly general characterization likewise includes position look-at vector, but place uses aspect ratio. proposed capable representing skewed projections (if l, u, v orthogonal) field-of-view symmetrical about direction. original (denoted V0) Vi) described own viewing parameters, . components V shown diagram. locus potential points, project onto Vx, equation: implies associated value, t, part its uniquely identify point. t value analogous stored Z-buffer, ray-length maintained raycasting While element reprojection process, surprisingly, required establish relative facets. e l u V0 e0 l0 u0 v0     Vi ei li ui vi