Visible Surface Detection Methods
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1 Visible urface Detection Methods Visible-urface Detection identifying visible parts of a scene (also hidden- elimination) type of algorithm depends on: complexity of scene type of objects available equipment static or animated displays object-space methods objects compared to each other image space methods point by point at each pixel location often sorting and coherence used Werner Purgathofer / omputergraphik Visible-urface Detection Methods the following algorithms are examples for different classes of methods back-face detection depth buffer method scan-line method depth-sorting method area-subdivision method octree methods ray-casting method Werner Purgathofer / omputergraphik Back-Face Detection () s (polygons) with a normal pointing away from the eye cannot be visible (back faces) eliminate them before visibility algorithm! Werner Purgathofer / omputergraphik can be eliminated: Back-Face Detection () eliminating back faces of closed polyhedra view point (x,y,z) inside a polygon if Ax + By + z + D < 0 or polygon with normal N=(A, B, ) is a back face if V view N > 0 N = (A, B, ) Back-Face Detection () object description in coordinates V view =(0,0,V z ) N = V V view sufficient condition: if 0 then back face y v z N = (A, B, ) V view V view Werner Purgathofer / omputergraphik Werner Purgathofer / omputergraphik
2 Back-Face Detection () complete visibility test for non-overlapping convex polyhedra face partially hidden by other faces Depth-Buffer Method () z-buffer method image-space method hardware implementation no sorting! preprocessing step for other objects: about 0% of s eliminated Werner Purgathofer / omputergraphik 6 Werner Purgathofer / omputergraphik 7 Depth-Buffer Method () two buffers depth buffer (distance information) refresh buffer (intensity information) size corresponds to screen resolution (for every pixel: r, g, b, z) draw something = compare z with z in buffer if z closer to viewer then draw and update z in buffer else nothing! Werner Purgathofer / omputergraphik 8 Depth-Buffer Algorithm Example polygons with corresponding z-values image depthbuffer background -infinity Werner Purgathofer / omputergraphik Depth-Buffer Algorithm for all (x,y) depthbuff(x,y) =.0 framebuff(x,y) = backgndolor for each polygon P for each position (x,y) on polygon P calculate depth z if z < > depthbuff(x,y) then depthbuff(x,y) = z framebuff(x,y) = surfolor(x,y) Depth-Buffer: Incremental z-values depth at (x,y): depth at (x+,y): depth at (x,y-): z = Ax By D z = A(x+) By D A = z z = Ax B(y ) D B = z + constants! Werner Purgathofer / omputergraphik 0 Werner Purgathofer / omputergraphik
3 Depth-Buffer: y-oordinate Intervals determine y-coordinate extents of polygon P Depth-Buffer: Values down an Edge z = x = x /m y = y Ax By D z = A(x /m) B(y ) D = z + A/m + B constant! Werner Purgathofer / omputergraphik Werner Purgathofer / omputergraphik can-line Method image-space method extension of scan-line algorithm for polygon filling can-line M.: Edge & Polygon Tables edge table (all edges, y-sorted) coordinate endpoints inverse slope pointers into polygon table polygon table (all polygons) coefficients of plane equation intensity information (pointers into edge table) Werner Purgathofer / omputergraphik Werner Purgathofer / omputergraphik can-line Method: Active Edge List active edge list (all edges crossing current scanline, x-sorted, flag) Werner Purgathofer / omputergraphik 6 can-line Method Example Edge T.,,,,,,,,,,,,, Poly.T.,, act.edges / act.poly.,,,,,,,,,,,,,,, Werner Purgathofer / omputergraphik 7,,,,,
4 can-line Method Details coherence between adjacent scan lines incremental calculations active edge list very similar (easy sorting, avoid depth calculations) intersecting or cyclically overlapping s! Depth-orting Method: Overview s sorted in order of decreasing depth ( in z-) approximate -sorting using smallest z-value (greatest depth) fine-tuning to get correct depth order s scan converted in order sorting both in image and object space scan conversion in image space also called painter s algorithm Werner Purgathofer / omputergraphik 8 Werner Purgathofer / omputergraphik 9 Depth-orting Method: orting () with greatest depth is compared to all other s no depth overlap ordering correct depth overlap z min do further tests in increasing order of complexity z max s with no depth overlap Werner Purgathofer / omputergraphik 0 z min z max Depth-orting Method: orting () bounding rectangles in xy-plane do not overlap check x-,y- separately s with depth overlap but no overlap in the x- Werner Purgathofer / omputergraphik x min x max x min x max Depth-orting Method: orting () completely behind substitute vertices of into equation of is completely behind ( inside ) the overlapping Depth-orting Method: orting () completely in front of substitute vertices of into equation of overlapping is completely in front ( outside ) of, but is not completely behind is not completely behind ( inside ) the overlapping Werner Purgathofer / omputergraphik Werner Purgathofer / omputergraphik
5 Depth-orting Method: orting () projections of, in xy-plane don t overlap Depth-orting Method: orting (6) all five tests fail ordering probably wrong interchange s, repeat process for reordered s s with overlapping bounding rectangles Werner Purgathofer / omputergraphik has greater depth but obscures Werner Purgathofer / omputergraphik sorted list:,, should be reordered:,, Depth-orting: pecial ases avoiding infinite loops due to cyclic overlap reordered s are flagged if would have to be reordered again divide into two parts Area-ubdivision Method () image-space method area coherence exploited area subdivided until visibility decision very easy Werner Purgathofer / omputergraphik 6 Werner Purgathofer / omputergraphik 7 Area-ubdivision Method () relationship polygon rectangular view area surrounding overlapping inside outside Area-ubdivision Method () three easy visibility decisions all s are outside of area checking bounding rectangles only one inside, overlapping, or surrounding is in the area bounding rectangles for initial check one surrounding obscures all other s within the area minimum depth ordering only these four possibilities Werner Purgathofer / omputergraphik 8 Werner Purgathofer / omputergraphik 9
6 Area-ubdivision Method () a surrounding obscuring s ordered according to minimum depth maximum depth of surrounding closest to view plane? test is conservative zv Werner Purgathofer / omputergraphik 0 surrounding area z max z min Area-ubdivision Method () if all three tests fail do subdivision subdivide area into four equal subareas outside and surrounding s will remain in this status for all subareas some inside and overlapping s will be eliminated no further subdivision possible (pixel resolution reached) sort s and take intensity of nearest Werner Purgathofer / omputergraphik Area-ubdivision Method Example finished Octree Methods recursive traversal of octree traversal order depends on processing front-to-back: pixel(x,y) written once completely obscured nodes are not traversed back-to-front: painter s algorithm Werner Purgathofer / omputergraphik Werner Purgathofer / omputergraphik Octree Methods recursive traversal of octree traversal order depends on processing front-to-back: pixel(x,y) written once completely obscured nodes are not traversed back-to-front: painter s algorithm Werner Purgathofer / omputergraphik Ray-asting Method () line-of-sight of each pixel is intersected with all s take closest intersected Werner Purgathofer / omputergraphik closest intersection point 6
7 Ray-asting Method () based on geometric optics, tracing paths of light rays backward tracing of light rays suitable for complex, curved s special case of ray-tracing algorithms efficient ray- intersection techniques necessary intersection point normal vector Werner Purgathofer / omputergraphik 6 7
Werner Purgathofer
Einführung in Visual Computing 186.822 Visible Surface Detection Werner Purgathofer Visibility in the Rendering Pipeline scene objects in object space object capture/creation ti modeling viewing projection
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