Single-pass Wireframe Rendering · Single-pass Wireframe Rendering Andreas Bærentzen 1 Steen L....
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Single-pass Wireframe Rendering Andreas Bærentzen 1 Steen L. Nielsen 1,2 Mikkel Gjøl 3 Bent D. Larsen 1,3 Niels Jørgen Christensen 1 1 Informatics and Mathematical Modelling, Technical University of Denmark, 2 Flux Studios, 3 Dalux The standard procedure for wireframe drawing with hidden line re- moval on a graphics card has not changed for a long time: First the filled polygons are drawn, laying down the depth buffer. Next, the polygon edges are drawn as lines with a small depth offset to ensure that polygons do not occlude their own edges. The depth offset is required because the procedure for rasterizing lines is not exactly the same as the one for rasterizing polygons. Consequently, when rasterizing a polygon edge as a line, a given fragment may have a depth value that is different from when the corresponding polygon itself is rasterized. This leads to stippling artefacts. However, adding an offset is not an ideal solution since this offset can result in disocclusions of lines that should be hidden. Moreover, there is usually stippling in any case near steep slopes in the mesh where a very large offset is sometimes required. The only real fix is a slope dependent offset but that tends to make disocclu- sion problems much worse. A few authors have proposed improved techniques, but either these are not intended for modern graphics hardware [Wang et al.] or they incur a performance hit [Herrel et al.]. Our solution does not use the line primitive at all. Instead polygon edges are drawn directly as a part of polygon rasterization. For each fragment, we compute the shortest distance to the edges of the polygon and map that distance to an intensity value, I , as shown in the figure (right). This mapping is not just a step function but a smooth function, I = exp 2 (-2d 2 ) which amounts to antialiasing by prefiltering. This method works for convex polygons (triangles or quads most likely), and it suffers from none of the artefacts associated with the offset based methods, but it does have one drawback. If a polygon does not have a neighbouring polygon (e.g. near a hole or a silhou- ette) the line is drawn from one side only. This means that silhou- ette lines are thinner and not antialiased. However, in practice the quality is still far better than using the offset based method, and the performance is almost invariably better. On a Geforce 7800 GTX 1 (jab|njc)@imm.dtu.dk 2 steen@flux-studios.com 3 (mig|bdl)@dalux.dk the Happy Buddha mesh was rendered at 25 fps using our method and only 5 fps using the offset based method. Thus, our method seems to be particularly well suited for the rendering of dense trian- gle meshes such as the increasingly common laser scanned models. Furthermore, many variations of the method are possible. In fact, the two images in the figure show the method using attenuation of line intensity (left) and thickness (center). In the center image, al- pha testing was used to remove the interior of the quads. Implementation Observe that the 2D distance from a point to a polygon edge is an affine function. Such functions are reproduced by linear interpola- tion. For this reason, we can compute the distance at each vertex and simply interpolate linearly. Thus, for each vertex of, say, a tri- angle we must send the other two vertices as attributes in order to compute the line distance. The graphics card will do the interpola- tion, but there is one problem: Perspective correct interpolation is currently hardwired into the interpolation used by modern graph- ics cards. It is possible, however, to negate this interpolation by premultiplying the distance (computed in a vertex program) with the w value. The interpolated distance is then postmultiplied in the fragment program by the interpolated 1/w. It is worth mentioning that Direct3D 10 offers an even simpler so- lution: It is possible to switch off perspective correction in D3D 10. Moreover, D3D 10 supports geometry shaders which are executed after vertex shaders but before rasterization. In such shaders, all vertices of a triangle can be accessed making it possible to compute the distance at each vertex without sending additional attributes per vertex. A similar shader type (called primitive shaders) is planned for OpenGL 3.0. References HERRELL, R., BALDWIN, J., AND WILCOX, C. 1995. High- quality polygon edging. IEEE Comput. Graph. Appl. 15, 4, 68–74. WANG, W., CHEN, Y., AND WU, E. 1999. A new method for polygon edging on shaded surfaces. J. Graph. Tools 4, 1, 1–10.
Transcript of Single-pass Wireframe Rendering · Single-pass Wireframe Rendering Andreas Bærentzen 1 Steen L....
Single-pass Wireframe Rendering
Andreas Bærentzen1 Steen L. Nielsen1,2 Mikkel Gjøl3 Bent D. Larsen1,3 Niels Jørgen Christensen1
1 Informatics and Mathematical Modelling, Technical University of Denmark, 2 Flux Studios, 3 Dalux
The standard procedure for wireframe drawing with hidden line re-moval on a graphics card has not changed for a long time: First thefilled polygons are drawn, laying down the depth buffer. Next, thepolygon edges are drawn as lines with a small depth offset to ensurethat polygons do not occlude their own edges.
The depth offset is required because the procedure for rasterizinglines is not exactly the same as the one for rasterizing polygons.Consequently, when rasterizing a polygon edge as a line, a givenfragment may have a depth value that is different from when thecorresponding polygon itself is rasterized. This leads to stipplingartefacts. However, adding an offset is not an ideal solution sincethis offset can result in disocclusions of lines that should be hidden.Moreover, there is usually stippling in any case near steep slopes inthe mesh where a very large offset is sometimes required. The onlyreal fix is a slope dependent offset but that tends to make disocclu-sion problems much worse. A few authors have proposed improvedtechniques, but either these are not intended for modern graphicshardware [Wang et al.] or they incur a performance hit [Herrel etal.].
Our solution does not use the line primitive at all. Instead polygonedges are drawn directly as a part of polygon rasterization. Foreach fragment, we compute the shortest distance to the edges of thepolygon and map that distance to an intensity value, I, as shownin the figure (right). This mapping is not just a step function but asmooth function, I = exp2(−2d2) which amounts to antialiasing byprefiltering.
This method works for convex polygons (triangles or quads mostlikely), and it suffers from none of the artefacts associated with theoffset based methods, but it does have one drawback. If a polygondoes not have a neighbouring polygon (e.g. near a hole or a silhou-ette) the line is drawn from one side only. This means that silhou-ette lines are thinner and not antialiased. However, in practice thequality is still far better than using the offset based method, and theperformance is almost invariably better. On a Geforce 7800 GTX
1(jab|njc)@[email protected](mig|bdl)@dalux.dk
the Happy Buddha mesh was rendered at 25 fps using our methodand only 5 fps using the offset based method. Thus, our methodseems to be particularly well suited for the rendering of dense trian-gle meshes such as the increasingly common laser scanned models.Furthermore, many variations of the method are possible. In fact,the two images in the figure show the method using attenuation ofline intensity (left) and thickness (center). In the center image, al-pha testing was used to remove the interior of the quads.
Implementation
Observe that the 2D distance from a point to a polygon edge is anaffine function. Such functions are reproduced by linear interpola-tion. For this reason, we can compute the distance at each vertexand simply interpolate linearly. Thus, for each vertex of, say, a tri-angle we must send the other two vertices as attributes in order tocompute the line distance. The graphics card will do the interpola-tion, but there is one problem: Perspective correct interpolation iscurrently hardwired into the interpolation used by modern graph-ics cards. It is possible, however, to negate this interpolation bypremultiplying the distance (computed in a vertex program) withthe w value. The interpolated distance is then postmultiplied in thefragment program by the interpolated 1/w.
It is worth mentioning that Direct3D 10 offers an even simpler so-lution: It is possible to switch off perspective correction in D3D 10.Moreover, D3D 10 supports geometry shaders which are executedafter vertex shaders but before rasterization. In such shaders, allvertices of a triangle can be accessed making it possible to computethe distance at each vertex without sending additional attributes pervertex. A similar shader type (called primitive shaders) is plannedfor OpenGL 3.0.
References
HERRELL, R., BALDWIN, J., AND WILCOX, C. 1995. High-quality polygon edging. IEEE Comput. Graph. Appl. 15, 4, 68–74.
WANG, W., CHEN, Y., AND WU, E. 1999. A new method forpolygon edging on shaded surfaces. J. Graph. Tools 4, 1, 1–10.
