1 CSCE 441: Computer Graphics Hidden Surface Removal Jinxiang Chai 2 Image space Review: 3D Geometry Pipeline 2 Normalized project space View space World spaceObject space 3 3D Rendering Pipeline Modeling transformation lighting Viewing transformation Project transformation Clipping Scan conversion Image 4 Scan conversion 3D Rendering Pipeline Modeling transformation lighting Viewing transformation Project transformation Clipping Image Transform into 3D world system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 3D normalized project space Clip primitives outside cameras view Draw pixels (includes texturing, hidden surface, etc.) 5 Image space 3D Geometry Pipeline 5 Normalized project space View space World spaceObject space 6 Hidden Surfaces 7 8 9 Polygon Mesh Representation 10 Hidden Surfaces Removal The goal is to determine which surfaces and parts of surfaces are not visible from a certain viewpoint A.K.A occlusion culling or visible surface determination 11 Outline Backface Culling Painters algorithm BSP Scanline Z-buffer Ray casting Required reading: section 16-1 to 16-11 12 Backface Culling Normalized project space 13 Backface Culling view direction Normalized project space 14 Backface Culling view direction Normalized project space 15 Backface Culling view direction 16 Backface Culling view direction, draw polygon 17 Backface Culling view direction, cull polygon 18 Backface Culling Is this all we have to do? 19 Backface Culling Is this all we have to do? No! - Can still have 2 (or more) front faces that map to the same screen pixel 20 Backface Culling Is this all we have to do? No! - Can still have 2 (or more) front faces that map to the same screen pixel - Which actually gets drawn? 21 Backface Culling Advantages Improves rendering speed by removing roughly half of polygons from scan conversion Disadvantages Assumes closed surface with consistently oriented polygons NOT a true hidden surface algorithm!!! 22 Painters Algorithm Basic idea: similar to oil painting - draw background first - then most distant object - then nearer object - and so forth 23 Painters Algorithm Sort polygons according to distance from viewer Draw from back (farthest) to front (nearest) - the entire object Near objects will overwrite farther ones 24 Painters Example z = 0.7 z = 0.3 z = 0.1 Sort by depth: Green rect Red circle Blue tri z = 0 25 Painters Algorithm Does anyone see a problem with this? 26 Painters Algorithm Does anyone see a problem with this? - Objects can have a range of depth, not just a single value - Need to make sure they dont overlap for this algorithm to work 27 Painters Algorithm Does anyone see a problem with this? - Objects can have a range of depth, not just a single value - Need to make sure they dont overlap for this algorithm to work 28 Painters Algorithm 1. Sort all objects z min and z max 29 Painters Algorithm 1. Sort all objects z min and z max 2. If an object is uninterrupted (its z min and z max are adjacent in the sorted list), it is fine 30 Painters Algorithm 1. Sort all objects z min and z max 2. If an object is uninterrupted (its z min and z max are adjacent in the sorted list), it is fine 3. If 2 objects DO overlap 3.1 Check if they overlap in x - If not, they are fine 3.2 Check if they overlap in y - If not, they are fine - If yes, need to split one 31 Painters Algorithm The splitting step is the tough one - Need to find a plane to split one polygon so that each new polygon is entirely in front of or entirely behind the other - Polygons may actually intersect, so then need to split each polygon by the other 32 Painters Algorithm The splitting step is the tough one - Need to find a plane to split one polygon so that each new polygon is entirely in front of or entirely behind the other - Polygons may actually intersect, so then need to split each polygon by the other After splitting, you can resort the list and should be fine 33 Painters Algorithm-Summary Advantages - Simple algorithm for ordering polygons Disadvantages - Splitting is not an easy task - Sorting can also be expensive - Redraws same pixel many times 34 Binary Space Partitioning Trees Basic principle: Objects in the half space opposite of the viewpoint do not obscure objects in the half space containing the viewpoint; thus, one can safely render them without covering foreground objects 35 Binary Space Partitioning Trees Basic principle: Objects in the half space opposite of the viewpoint do not obscure objects in the half space containing the viewpoint; thus, one can safely render them without covering foreground objects 36 Binary Space Partitioning Trees Basic principle: Objects in the half space opposite of the viewpoint do not obscure objects in the half space containing the viewpoint; thus, one can safely render them without covering foreground objects If we want to draw 5 correctly - we need draw 6 and 7 first, - then draw 5, - then draw 1,2,3,4 + - 37 Binary Space Partitioning Trees Basic principle: Objects in the half space opposite of the viewpoint do not obscure objects in the half space containing the viewpoint; thus, one can safely render them without covering foreground objects If we want to draw 5 correctly - we need draw 6 and 7 first, - then draw 5, - then draw 1,2,3,4 + - We need to do this for every polygon Can we do this more efficiently? 38 Binary Space Partitioning Trees Basic principle: Objects in the half space opposite of the viewpoint do not obscure objects in the half space containing the viewpoint; thus, one can safely render them without covering foreground objects If we want to draw 5 correctly - we need draw 6 and 7 first, - then draw 5, - then draw 1,2,3,4 + - We need to do this for every polygon Can we do this more efficiently? BSP tree 39 Binary Space Partition Trees BSP tree: organize all of space (hence partition) into a binary tree - Preprocess: overlay a binary tree on objects in the scene - Runtime: correctly traversing this tree enumerates objects from back to front // similar to painters algorithm - Idea: divide space recursively into half-spaces by choosing splitting planes Splitting planes can be arbitrarily oriented 40 Binary Space Partition Trees (1979) BSP tree: organize all of space (hence partition) into a binary tree - Preprocess: overlay a binary tree on objects in the scene - Runtime: correctly traversing this tree enumerates objects from back to front - Idea: divide space recursively into half-spaces by choosing splitting planes Splitting planes can be arbitrarily oriented 41 BSP Trees: Objects 42 BSP Trees: Objects 43 BSP Trees: Objects Put front objects in the left branch 44 BSP Trees: Objects Put front objects in the left branch ? ? - + 45 BSP Trees: Objects Put front objects in the left branch 46 BSP Trees: Objects Put front objects in the left branch ?? -+ 4 47 BSP Trees: Objects Put front objects in the left branch 48 BSP Trees: Objects Put front objects in the left branch 49 BSP Trees: Objects Put front objects in the left branch 50 BSP Trees: Objects Put front objects in the left branch When to stop the recursion? 51 Object Splitting No bunnies were harmed in my example But what if a splitting plane passes through an object? 52 Object Splitting No bunnies were harmed in my example But what if a splitting plane passes through an object? - Split the object; give half to each node: Ouch 53 Polygons: BSP Tree Construction Split along the plane containing any polygon Classify all polygons into positive or negative half-space of the plane If a polygon intersects plane, split it into two Recurse down the negative half-space Recurse down the positive half-space 54 Binary Space Partition Trees (1979) BSP tree: organize all of space (hence partition) into a binary tree - Preprocess: overlay a binary tree on objects in the scene - Runtime: correctly traversing this tree enumerates objects from back to front - Idea: divide space recursively into half-spaces by choosing splitting planes Splitting planes can be arbitrarily oriented 55 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order? 56 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order: 8 57 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order: 8->9 58 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order: 8->9->7 59 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order: 8->9->7->6 60 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order: 8->9->7->6->5 61 BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front Traversal order: 8->9->7->6->5->3->4->2->1 62 Building a BSP Tree for Polygons Choose a splitting polygon Sort all other polygons as Front Behind Crossing On Add front polygons to front child, behind to back child Split crossing polygons with infinite plane Add on polygons to root/current node Recur 63 Building a BSP Tree 64 Building a BSP Tree ,34,5,6,7 1 b 65 Building a BSP Tree ,34,5,6,7 1 b How to divide 2,3,4,5,6,7? 66 3 Building a BSP Tree , 6,5-22,4,5-1, b bf 67 3 Building a BSP Tree , 6,5-22,4,5-1, b bf 68 b Building a BSP Tree , , 6, b b f f 69 Building a BSP Tree , 6, b b b b f f 70 Building a BSP Tree , 6, b b b b f f 71 Building a BSP Tree , 6, b b b b f f Building a BSP Tree , b b b b b f f 73 6 Building a BSP Tree b b b b bf f f Building a BSP Tree b b b b bf f f Building a BSP Tree b b b b bf f f Rendering with a BSP Tree b b b b bf f f How to traverse the tree? Rendering with a BSP Tree b b b b bf f f How to traverse the tree? - draw back polygons - draw on polygons - draw front polygons Rendering with a BSP Tree Traversal order: b b b b bf f f 79 f Rendering with a BSP Tree Traversal order: 6 b b b b b f f 80 f Rendering with a BSP Tree Traversal order: 6->(5-2) b b b b b f f 81 4 f Rendering with a BSP Tree Traversal order: 6->(5-2)->(7-2) b b b b b f f 82 3 f 4 f Rendering with a BSP Tree Traversal order: 6->(5-2)->(7-2)->3 b b b b b f 83 3 f 4 f Rendering with a BSP Tree Traversal order: 6->(5-2)->(7-2)->3->(5-1) b b b b b f bf 3 f 4 f Rendering with a BSP Tree Traversal order: 6->(5-2)->(7-2)->3->(5-1)->4->(7-1)->2->1 b b b b 85 Rendering with a BSP Tree Interpret the tree relative the position of the viewpoint How to traverse the tree Draw back polygons Draw on polygons Draw front polygons bf 3 f 4 f b b b b Different View Points? b b b b bf f f Do we need to build a new tree? Different View Points? b b b b bf f f Do we need to build a new tree? - No, we use the same tree if objects are static Different View Points? b b b b bf f f Do we need to build a new tree? - No, we use the same tree if objects are static How can we traverse the tree? 89 Rendering with a BSP Tree If eye is in front of plane Draw back polygons Draw on polygons Draw front polygons If eye is behind plane Draw front polygons Draw on polygons Draw back polygons Else eye is on plane Draw front polygons Draw back polygons ,7 5 bf 1,2,3,4 90 Rendering with a BSP Tree If eye is in front of plane Draw back polygons Draw on polygons Draw front polygons If eye is behind plane Draw front polygons Draw on polygons Draw back polygons Else eye is on plane Draw front polygons Draw back polygons ,7 5 bf 1,2,3,4 91 Rendering with a BSP Tree If eye is in front of plane Draw back polygons Draw on polygons Draw front polygons If eye is behind plane Draw front polygons Draw on polygons Draw back polygons Else eye is on plane Draw front polygons Draw back polygons ,7 5 bf 1,2,3,4 92 1 Different View Points? Traversal order: 7-1 bf 3 f 4 f b b b b + - 93 1 Different View Points? Traversal order: bf 3 f 4 f b b b b 94 1 Different View Points? Traversal order: bf 3 f 4 f b b b b + - 95 1 Different View Points? Traversal order: bf 3 f 4 f b b b b + - 96 1 Different View Points? Traversal order: 1->2 7-1 bf 3 f 4 f b b b b + - 97 1 Different View Points? Traversal order: 1->2->(7-1) 7-1 bf 3 f 4 f b b b b + - 98 1 Different View Points? Traversal order: 1->2->(7-1)->4 7-1 bf 3 f 4 f b b b b + - 99 1 Different View Points? Traversal order: 1->2->(7-1)->4->(5-1) 7-1 bf 3 f 4 f b b b b + - 100 1 Different View Points? Traversal order: 1->2->(7-1)->4->(5-1)->3 7-1 bf 3 f 4 f b b b b 101 1 Different View Points? Traversal order: 1->2->(7-1)->4->(5-1)->3->(7-2)->(5-2)->6 7-1 bf 3 f 4 f b b b b Rendering with a BSP Tree Traversal order? b b bf f f b b Rendering with a BSP Tree Traversal order? b b bf f f b b + - 1 Rendering with a BSP Tree Traversal order? b b bf f f b b >? Rendering with a BSP Tree Traversal order? b b bf f f b b 1->? + - Rendering with a BSP Tree Traversal order? b b bf f f b b 1->? + - Rendering with a BSP Tree Traversal order? b b bf f f b b 1->? + - Rendering with a BSP Tree Traversal order? b b bf f f b b 1->6 + - Rendering with a BSP Tree Traversal order? b b bf f f b b 1->6->? Rendering with a BSP Tree Traversal order? 1->6->5-2 b b bf f f b b Rendering with a BSP Tree Traversal order? 1->6->(5-2)->(7-2)->3->4->(5-1)->(7-1)->2 b b bf f f b b 112 Improved BSP Rendering Take advantage of view direction to cull away polygons behind viewer 113 Improved BSP Rendering Take advantage of view direction to cull away polygons behind viewer View frustum 114 Improved BSP Rendering Take advantage of view direction to cull away polygons behind viewer 115 Summary: BSP Trees Pros: Simple, elegant scheme No depth comparisons needed Polygons split and ordered automatically Works for moving cameras Only writes to framebuffer (i.e., painters algorithm) 116 Summary: BSP Trees Cons: Computationally intense preprocess stage restricts algorithm to static scenes Worst-case time to construct tree: O(n 3 ) Splitting increases polygon count Again, O(n 3 ) worst case Redraws same pixel many times Choosing splitting plane not an exact science Not suitable for moving objects 117 Outline Backface Culling Painters algorithm BSP Scan line Z-buffer Ray casting Reading: section 16-1 to 16-11