Hidden Surfaces Dr Scott Schaefer 1 Hidden Surfaces

Hidden Surfaces Dr. Scott Schaefer 1

Hidden Surfaces 2/62

Hidden Surfaces 3/62

Hidden Surfaces 4/62

Backface Culling 5/62

Backface Culling view direction 6/62

Backface Culling view direction 7/62

Backface Culling , draw polygon view direction 8/62

Backface Culling , cull polygon view direction 9/62

Backface Culling 10/62

Backface Culling counter clock-wise orientation, draw polygon 11/62

Backface Culling clock-wise orientation, cull polygon 12/62

Backface Culling Advantages u Improves rendering speed by removing roughly half of polygons from scan conversion n Disadvantages u Assumes closed surface with consistently oriented polygons u NOT a true hidden surface algorithm!!! n 13/62

Backface Culling n Is this all we have to do? 14/62

Backface Culling n Is this all we have to do? No! - Can still have 2 (or more) front faces that map to the same screen pixel 15/62

Backface Culling n 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? 16/62

Painter’s Algorithm Sort polygons according to distance from viewer n Draw from back to front n n How do we sort polygons? 17/62

Painter’s Example z = 0. 7 z = 0. 3 z = 0. 1 Sort by depth: Green rect Red circle Blue tri z=0 18/62

Painter’s Algorithm 19/62

Painter’s Algorithm n Sometimes there is NO ordering that produces correct results!!! 20/62

Painter’s Algorithm 1. Sort all objects’ zmin and zmax 21/62

Painter’s Algorithm 1. Sort all objects’ zmin and zmax 2. If an object is uninterrupted (its zmin and zmax are adjacent in the sorted list), it is fine 22/62

Painter’s Algorithm 1. Sort all objects’ zmin and zmax 2. If an object is uninterrupted (its zmin and zmax 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 23/62

Painter’s Algorithm n The splitting step is the tough one - Need to find a plane to split one polygon by 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 24/62

Painter’s Algorithm n The splitting step is the tough one - Need to find a plane to split one polygon by 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 n After splitting, you can resort the list and should be fine 25/62

Painter’s Algorithm-Summary Advantages u Simple algorithm for ordering polygons n Disadvantages u Sorting criteria difficult to produce u Redraws same pixel many times u Sorting can also be expensive n 26/62

Depth (“Z”) Buffer Simple modification to scan-conversion n Maintain a separate buffer storing the closest “z” value for each pixel n Only draw pixel if depth value is closer than stored “z” value u Update buffer with closest depth value n 27/62

Depth (“Z”) Buffer Advantages u Simple to implement u Allows for a streaming approach to polygon drawing n Disadvantages u Requires extra storage space u Still lots of overdraw n 28/62

Binary Space Partitioning Trees n 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 t Splitting planes can be arbitrarily oriented 29/62

BSP Trees: Objects 9 6 5 1 8 7 4 2 3 30/62

BSP Trees: Objects 9 6 7 5 1 - 8 + 4 2 3 31/62

BSP Trees: Objects Put front objects in the left branch + 9 6 5 1 - 8 7 - + 1 2 3 4 5 6 7 8 9 4 2 3 32/62

BSP Trees: Objects Put front objects in the left branch + 9 6 1 8 7 - + 5 4 2 - 1 2 + 3 4 5 6 7 8 9 3 33/62

BSP Trees: Objects Put front objects in the left branch + 9 6 1 8 7 - + 5 4 2 - 1 3 + 2 4 + - + 3 5 6 - + 7 9 8 34/62

BSP Trees: Objects Put front objects in the left branch + 9 6 1 8 7 - + 5 4 2 - 1 + 3 + 2 2 4 + - + 3 5 - - + 6 6 8 + 7 9 35/62

BSP Trees: Objects Put front objects in the left branch + 9 6 1 8 7 - + 5 - 4 2 1 + 3 + 2 2 4 + - + 3 5 - - + 6 6 8 + 7 9 When to stop the recursion? 36/62

Object Splitting No bunnies were harmed in my example n But what if a splitting plane passes through an object? n - Split the object; give half to each node: - Worst case: can create up to O(n 3) objects! Ouch 37/62

Building a BSP Tree n n n Choose a splitting polygon Sort all other polygons as u Front u Behind u Crossing u On Add “front” polygons to front child, “behind” to back child Split “crossing” polygons with infinite plane Add “on” polygons to root Recur 38/62

Building a BSP Tree 6 7 3 1 2 5 4 39/62

Building a BSP Tree 6 7 3 1 2 5 4 1 b 2, 3, 4, 5, 6, 7 40/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b f 7 -2, 6, 5 -2 3 b 2, 4, 5 -1, 7 -1 41/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b f 7 -2, 6, 5 -2 3 f 2 b 7 -1 b 4, 5 -1 42/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b f 7 -2, 6, 5 -2 3 f 2 b 7 -1 b 4 b 5 -1 43/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b f 7 -2, 6, 5 -2 3 f 2 b 7 -1 b 4 b 5 -1 44/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b f 7 -2, 6, 5 -2 3 f 2 b 7 -1 b 4 b 5 -1 45/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 f b 3 f 6, 5 -2 2 b 7 -1 b 4 b 5 -1 46/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 47/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 48/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 49/62

Rendering with a BSP Tree n n n If eye is in front of plane u Draw “back” polygons u Draw “on” polygons u Draw “front” polygons If eye is behind plane u Draw “front” polygons u Draw “on” polygons u Draw “back” polygons Else eye is on plane u Draw “front” polygons u Draw “back” polygons 50/62

BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front + 9 6 1 8 7 - + 5 - 4 2 1 + 3 + 2 2 4 + - + 3 5 - - + 6 6 8 + 7 9 Traversal order? 51/62

BSP Trees: Objects Correctly traversing this tree enumerates objects from back to front + 9 6 1 8 7 - + 5 4 2 - 1 + 3 + 2 2 4 + - + 3 5 - - + 6 6 8 + 7 9 Traversal order: 8 ->9 ->7 ->6 ->5 ->3 ->4 ->2 ->1 52/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 Traversal order: 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 53/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 Traversal order: 6 ->(5 -2)->(7 -2)->3 ->(5 -1)->4 ->(7 -1)->2 ->1 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 54/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 Traversal order: 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 55/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 Traversal order: 1 ->2 ->(7 -1)->4 ->(5 -1)->3 ->(7 -2)->(5 -2)->6 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 56/62

Building a BSP Tree 6 7 -2 5 -2 7 -1 5 -1 3 1 2 4 1 b 7 -2 Traversal order? 3 f b 6 b 5 -2 f 2 b 7 -1 b 4 b 5 -1 57/62

Rendering with a BSP Tree n n Advantages u No depth comparisons needed u Polygons split and ordered automatically Disadvantages u Computationally intense preprocess stage restricts algorithm to static scenes u Splitting increases polygon count u Redraws same pixel many times u Choosing splitting plane not an exact science 58/62

Improved BSP Rendering n Take advantage of view direction to cull away polygons behind viewer 59/62

Improved BSP Rendering n Take advantage of view direction to cull away polygons behind viewer View frustum 60/62

Improved BSP Rendering n Take advantage of view direction to cull away polygons behind viewer 61/62

Open. GL and Hidden Surfaces gl. Enable(GL_DEPTH_TEST); gl. Enable(GL_CULL_FACE); gl. Clear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); gl. Cull. Face ( GL_BACK ); 62/62

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Scan Line Algorithm Assume for each line of screen, we have scan -lines for all polygons intersecting that line n For each polygon, keep track of extents of scan line n Whenever the x-extents of two scan lines overlap, determine ordering of two polygons n 64/62

Scan Line Algorithm 65/62

Scan Line Algorithm 66/62

Scan Line Algorithm 67/62

Scan Line Algorithm Advantages u Takes advantage of coherence resulting in fast algorithm u Does not require as much storage as depth buffer n Disadvantages u More complex algorithm u Requires all polygons sent to GPU before drawing n 68/62