- How to improve realism - Gouraud and Phong Shading - Texturing - Phong Lighting - More advanced lighting models - Shadows

Transcription

1 Computer Graphics Visibility & Shadows Rendering pipeline How to accelerate rendering Use fewer primitives to approximate complex models Clipping Discard occluded (nonvisible) objects How to improve realism Gouraud and Phong Shading Texturing Phong Lighting More advanced lighting models Shadows Visibility Multiple objects are mapped to the same pixel Which one is visible? image precision techniques O(#pixel x #polygons) Which part of an object is visible from a given viewpoint object precision techniques O(#polygons) Visibility Object space techniques Painter s algorithm Culling Image space techniques Area subdivision Zbuffer Mixed techniques Scanline algorithms Ray casting Painter s algorithm Painter s algorithm Sort all polygons with respect to z min Paint polygons from back to front Disambiguate visibility if zranges of polygons are overlapping Disambiguate visibility z min (A)<z min (B)<z max (A) [x,y]ranges not overlapping? A behind supporting plane of B? B in front supporting plane of A? Nonoverlapping projections? paint A B behind supporting plane of A? A in front supporting plane of B? swap A & B

2 Painter s algorithm Repeated swap cyclic overlap Split A at supporting plane of B or vice versa Sorting becomes dominant when rendering a scene from many viewpoints Presort (partition) the scene to exploit clustering Tree traversal instead of sorting Also good for raytracing Octree (scene independent) BSP (scene dependent) Octrees/Quadtrees Recursive regular subdivision of space into 8/4 subspaces One node is split into 8/4 child nodes Sorting criterion is distance of node 023 center to view point 2 y x 023 BspTrees (Binary Space Partitioning) Computational representation of space Search structure and representation of geometry Generalization of binary search trees for dim> Search complexity to find spatial relationships between n polygons within O() to O(n log n) Recursive space partitioning by means of arbitrarily positioned partitioning planes Quadtree BSP and Visibility P A B P 2 P 3 A C B D P 2 D P 3 C C D B A P BSP and Visibility 2

3 Occlusion Determine visible part of surface Image space (zbuffer) (image precision) Occluding lines (haloeffect) Compare pixel depth Object space (depth sort) (object precision) Compare polygons and intersect Collective term Culling View frustrum culling (Clipping) Occlusion culling Backface culling Remove invisible surfaces (approx. half of the faces for sufficiently convex objects) Determine normal, dot product with direction of projection Culling Predetermine object visibility View frustum culling / clipping Backface culling Bounding box hierarchies (cluster objects) Cell visibility (cluster viewpoints) Virtual occluders (contour polygons) Backface culling Solid polyhedron Frontfacing sides block backfacing sides Culling backfacing sides ( N V ) > 0 Vertex ordering in view space switched Discards about half of the faces Depth sort Depth sort List Priority algorithms.sort all polygons for the smallest (farthest) z 2.If zextent does not overlap Use the Painter algorithm (draw opaque backtofront) 3.If zextent overlaps perform additional tests (bounding box) and split 3

4 ZBuffer Store current minimum zvalue for each pixel Additional memory requirements Testing during fragment processing Frustum transform preserves zordering Incremental zvalue update (if fragment is closer to near plane than current one) Fastest method (hardware support) Today s standard approach ZBuffer Determine zvalue for every pixel and compare with saved zvalue of pixels drawn previously need additional zbuffer (632 bit) ZBuffer ZBuffer Holds z values after Frustum map (perspective division) Windowtoview port map (scaling) Resulting z [0;] Algorithm: Framebuffer BackgroundColor zbuffer Accuracy problems Depth values: nonlinear in [Z near, Z far ] due to perspective projection z foreach polygon (arbitrary sequence) foreach Pixel(x, y) in projected polygon z = z(x, y) from interpolation if z >= zbuffer(x,y) then zbuffer(x,y) = z Framebuffer(x,y) = Pixel(x, y) 0 ZBuffer Scanline algorithms Drawbacks Memory requirements zaliasing for small zextent Using transparency requires sorting Much work if depth complexity is high For each scanline: solve D visibility problem Active / passive polygons (per frame) Sweepline events (per scanline) Activate Deactivate Intersect Exploit scanline coherence 4

5 Hidden line removal Shadows Visibility Which objects can be seen from the Wireframe representation view point? (historically: vector displays) Shadows Draw solid polygons in background Which objects can be seen from the color (fills the zbuffer) Draw wireframes with small zoffset (shift light source? towards the view point) Shadows Reminder: rendering equation S Shadows Shadow algorithms Lo ( x, ωo ) = Le ( x, ωo ) + f r ( x, ωi ωo ) s( x, l ) Ls ( x, ωi ) cos(n, ωi ) New term s(x,l) that is 0 if light vector l is blocked Projected geometry Shadow volumes Shadow textures Shadow maps Perspective shadow maps (Global illumination) at point x, otherwise Projected geometry Project objects along light rays onto ground plane (4x4 projection matrix) Draw projected object Shadow volumes Polygonal representation of regions in shadow Precomputed for static scenes Spanned by light source and object silhouettes: O(n*m) In shadow color With alphablending Suitable for few shadow receivers 5

6 Shadow volumes Ray casting Count intersections of shadow volume Intersect more frontfacing than backfacing shadow volume polygons in shadow Special case: view point in shadow Efficient OpenGL implementation Draw polygon setting the stencil buffer using stencil buffer zero zero 2 3 Shadow maps TwoPass Algorithm: Pass : All objects that can be rasterized Self shadowing + Independent of scene complexity Save zbuffer (= distance to light) This buffer is called the Shadow Map Needs hardware extension Render scene from view point Slower, more complicated implementation using alpha Project object points into shadow map test, projective textures, multitexturing Get zvalue at projection point Compute distance of object point to light source In shadow, if distance pointlight > zvalue from map + General method for computing shadows Pass 2: Shadow maps Render scene as seen from the light source Draw shadows where stencil is set Use stencil as mask 2 Shadow textures Object A casts shadow on object B Render A as seen from the light source Use the resulting image as a texture for B Discrete sampling, shadow map resolution Aliasing artifacts at shadow boundaries Perspective shadow maps 6