Chapter 9. Somsak Walairacht, Computer Engineering, KMITL

Transcription

1 Computer Graphics Chapter 9 Visible Surface Detection Methods Somsak Walairacht, Computer Engineering, KMITL

2 Outline Classification of Visible-Surface Detection Algorithms Back-Face Detection Depth-Buffer Method A-Buffer Method Scan-Line Method Depth-Sorting Method BSP-Tree Method Area-Subdivision Method Octree Methods Ray-Casting Method Comparison of Visibility-Detection Methods Wire-Frame Visibility Methods OpenGL Visibility-Detection Functions / Computer Graphics 2

3 Classification of Visible- Surface Detection Algorithms 2 approaches Object-Space Method Compares objects and parts of objects to each other within the scene Determine ee esurface aceasaas a whole oe Image-Space Method Visibility is decided point by point at each pixel position on the projection plane Most visibility-surface algorithms use image-space methods / Computer Graphics 3

4 Back-Face Detection A fast and simple object-space method Find the faces on the backs of polyhedral and discard them A point is behind a polygon surface if Ax + By + Cz + D < 0 Back-face test by considering the direction of the normal vector for a polygon surface A polygon is a back face if V view. N > / Computer Graphics 4

5 Back-Face Detection (2) Right-handed viewing system If object is converted to projection coordinates and viewing direction is parallel to z v axis, Only consider the z component of the normal vector N N = (A, B, C) A polygon is back face if C<=0 Similarly, left-handed system, back face if C >= / Computer Graphics 5

6 Ex. Back-Face Detection y y view x view N(3,2,6) B(0,3,0) z view 3x+2y+6z +6-6=0 C(0,0,1) 0 z A(2,0,0) x / Computer Graphics 6

7 Back-Face Detection (3) Complete visibility test for nonoverlapping convex polyhedra For concave polygon, more test must be carried out to determine whether there are additional faces that are totally or partially obscured by other faces For a general scene, back-face removal can be expected to eliminate about half of the polygon surfaces in a scene from further visibility tests / Computer Graphics 7

8 Depth-Buffer Method Image-space approach Compares surface depth values throughout a scene from each pixel position on the projection plane Also called the z-buffer method Depth is measured along the z-axis / Computer Graphics 8

9 Depth-Buffer Method (2) 2 buffer areas are required A depth buffer Stores depth values for each (x, y) position Frame buffer (Refresh buffer) Stores the surface-color values for each pixel position Calculated depth is compared with the stored value, if it is less than value in the depth buffer, the new value is stored Algorithm 1. Initialize the depth and frame buffer depthbuff(x, y) = 1.0, framebuff(x, y) = backgndcolor 2. Process each polygon in a scene For each projected (x, y) pixel, calculate the depth z If z < depthbuff(x, y), compute the surface color depthbuff(x, y) = z, framebuff(x, y) = surfcolor(x, y) / Computer Graphics 9

10 Depth-Buffer Method (3) Calculate the depth of any point on the plane containing the polygon A surface position (x, y) from plane equation z = (-Ax-By-D)/C Depth z of (x+1,,y) z = [-A(x+1)-By-D]/C, z = z-a/c Depth z of (x-1/m, y-1) z = [-A(x-1/m)-B(y-1)-D]/C, z = z+(a/m+b)/c Depth z of (x, y-1) z = [-Ax-B(y-1)-D]/C, z = z+b/c / Computer Graphics 10

11 Scan-Line Method Image-space method Across each scan line, depth calculations are performed to determine which surface is nearest to the view plane at each position An active list of edges is formed for each scan line Contains only edges that cross the current scan line Sorting in order of increasing x A flag for each surface to indicate whether a position along scan line is inside or outside the surface Process pixel position from left to right At left intersection, flag is on At right intersection, flag is off / Computer Graphics 11

12 Scan-Line Method (2) Scan line 1, active edges: AB,BC,EH,FG AB-BC, flag S1 on EH-FG, flag S2 on Scan line 2, active edges: AD,EH,BC,FG AD-EH EH, flag S1 on EH-BC, flag S1,S2 on Calculate depth After BC, flag S1 off Flag S2 on until FG Scan line 3 is same as scan line 2 Coherence along scan lines Same active edges list / Computer Graphics 12

13 Scan-Line Method (3) / Computer Graphics 13

14 Depth-Sorting Method Using both image-space and object-space operations Basic functions Surfaces are sorted in order of decreasing depth Surface are scan-converted in order, starting with the surface of greatest depth This method is often referred to painter s algorithm Each color layer covers up the previous layer / Computer Graphics 14

15 Depth-Sorting Method (2) Compare surfaces whether there are any depth overlaps No overlaps, each surface is processed in depth order until all have been scan-converted If depth overlap is detected, need addition comparisons to determine z z z max S z max S z max z min S S z max z min z min z min No Depth Overlap x Depth Overlap x / Computer Graphics 15

16 Depth-Sorting Method (3) Tests for each surface that has a depth overlap with S 1. The bounding rectangles (coordinate extents) in xy directions do not overlap 2. Surface S completely behind the overlapping surface 3. The overlapping surface is completely in front of S 4. The boundary-edge projections on the view plane do not overlap If one of these test is true, no reordering for S S is the most distant surface S is scan-converted / Computer Graphics 16

17 Depth-Sorting Method (4) Two surfaces with depth Surface S is completely Overlapping surface S is overlap but no overlap in the x direction behind the overlapping surface S completely in front of surface S, but S is not completely behind S 4 Two polygon surfaces with overlapping bounding rectangles in the xy plane / Computer Graphics 17

18 Depth-Sorting Method (5) Should all four tests fail for an overlapping surface S Interchange surfaces S and S in the sorted list Surface S extends to a greater depth, but it obscures surface S Three surfaces that have been entered into the sorted surface list in the order S, S, S should be reordered as S, S, S / Computer Graphics 18

19 BSP-Tree Method Painting surfaces into frame buffer from back to front painter s algorithm Useful when the view reference point changes, but the objects in a scene are at fixed positions Visibility testing involves identifying surfaces behind or in front of the partitioning i i plane at each step of the space subdivision / Computer Graphics 19

20 BSP-Tree Method When BSP tree is complete, process the tree from the right nodes to the left nodes / Computer Graphics 20

21 BSP-Tree Method 2 5a 5 3 5b a 4 5b / Computer Graphics 21

22 BSP-Tree Method 2 5a 5 3 front 5b back front back 4 2 5a 1 5b / Computer Graphics 22

23 BSP-Tree Method front 5a 5 5b back front back 4 back 4 5a 1 5b / Computer Graphics 23

24 Area-Subdivision Method Image-space method Take advantage of coherence, by locating projection areas that represent part of a single surface By successively dividing the total view- plane area into smaller and smaller rectangular An easy way is to successively divide the area into 4 equal parts at each step Each rectangular contains the projection of part of a single visible surface / Computer Graphics 24

25 Area-Subdivision Method (2) First, test if the view is sufficiently complex Yes, subdivide it Test to each smaller areas, subdividing if a single surface is still uncertain Continue until subdivisions are easily analyzed as belonging to a single surface or reached the resolution limit / Computer Graphics 25

26 Area-Subdivision Method (3) Relationship between a surface and an area of the subdivided view plane Surrounding surface Completely encloses the area Overlapping surface Partly inside and partly outside the area Inside surface Completely l inside id the area Outside surface Completely outside the area / Computer Graphics 26

27 Area-Subdivision Method (4) Test for determining surface visibility within a rectangular area No further subdivisions if one of the following conditions is true Condition 1: All surfaces are outside the area Condition 2: An area has only one inside, overlapping, or surrounding Condition 3: An area has one surrounding surface that obscures all other surfaces / Computer Graphics 27

28 Area-Subdivision Method (5) Condition 1 test by comparing coordinate extents of each surface Condition 2 usually require intersection tests Condition 3 test by sorting surfaces according to minimum depth from view plane Use plane equation to calculate depth values at four vertices of the area for all surrounding, inside, overlapping surfaces Once a surface has been identified d as an outside or surrounding, it will remain in that category for all subdivisions of the area / Computer Graphics 28

29 Area-Subdivision Method (6) As a variation Subdivision along surface boundaries instead of dividing them in half In general, fewer subdivisions are required, but more processing is needed to subdivide and to analyze the relation of surfaces / Computer Graphics 29

30 Octree Method When an octree representation is used, visibility testing is done by searching octree nodes in a front-to-back order Front octants 0,1,2,3 are visible Rear octants 4,5,6,7 are hidden by the front When a color value is encountered, it is saved only if no previously saved value O l f t l d Only front colors are saved / Computer Graphics 30

31 Octree Method (2) Visibility testing is carried out with recursive processing of octree nodes and create quadtree representation Depth-first traversal of the octree, octant 0 is visited before Completely obscured nodes are not traversed Different views of objects, octants are renumbered so that 0,1,2,3 are front nodes / Computer Graphics 31

32 Ray-Casting Method Along the line of sight, can determined which objects intersect this line Method is based on geometric-optics methods, which trace the parts of light rays Trace the light-ray paths backward from the pixels through the scene Effective method for scenes with curved surfaces, particularly, spheres Ray casting is a special case of ray-tracing algorithms Only follow a ray out from each pixel to the nearest object / Computer Graphics 32

33 Comparison of Visibility- Detection Methods Surfaces are widely distributed Very little depth overlap, few surfaces Depth-sorting or BSP-tree is most efficient Few overlaps, small number of surfaces Scan-line or area-subdivision is a fast way Several thousand surfaces Scan-line, depth-sorting, or BSP-tree Few thousand surfaces Depth-sorting or Octree Nearly constant with processing time, and independent to number of surfaces Depth-buffer low performance with simple scenes but high performance for complex scenes Curved surface representations Ray-casting or Octree Octree is fast and simple Only integer additions and subtractions, no sorting or intersection calculations Possible to combine and implement different visible-surface detection methods Implemented in hardware Parallel processing / Computer Graphics 33

34 Wire-Frame Visibility Methods Apply depth cueing Displayed intensity of a line is a function of its distance from the viewer Hidden edges are eliminated or displayed differently from the visible ibl edges Methods are also called visible-line detection methods or hidden-line detection ti methods / Computer Graphics 34

35 Wire-Frame Surface-Visibility Algorithms Compare edge position with the positions of the surfaces in a scene Same methods used in line-clipping algorithms Compare edge and surface depth values If both projected edge endpoints are behind the surface, edge is hidden Calculate intersection positions and determine the depth values at those intersection points / Computer Graphics 35

36 Wire-frame Depth-Cueing Algorithm Displaying visibility information by vary the brightness of objects as a function of distance form the viewing position F depth = (d max d) / (d max d min ) where d is the distance of a point form the viewing position d min, d max can be set to the normalized depth range 0.0~1.0 Each pixel, its color is multiplied by f depth (d) Nearer points are displayed with higher intensities Points at maximum depth have intensity = / Computer Graphics 36

37 OpenGL Visibility-Detection Functions / Computer Graphics 37

38 End of Chapter / Computer Graphics 38