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Chapter 9Visible Surface Detection MethodsVisible Surface Detection Methods

Somsak Walairacht, Computer Engineering, KMITL

Outline Classification of Visible-Surface Detection Algorithms Back-Face Detection Depth-Buffer Method A-Buffer Method Scan-Line Method Depth-Sorting Method

BSP T M th d BSP-Tree Method Area-Subdivision Method Octree Methods

Ray Casting Method Ray-Casting Method Comparison of Visibility-Detection Methods Wire-Frame Visibility Methods OpenGL Visibility-Detection Functions

01074410 / 13016218 Computer Graphics 2

OpenGL Visibility Detection Functions

Classification of Visible-Surface Detection Algorithms

2 approaches Object-Space Method

Compares objects and parts of objects to each other within the scene

Determine surface as a wholee e e su ace as a o e

Image-Space Method Visibility is decided point by point at each pixel position

on the projection planeon the projection plane

Most visibility-surface algorithms use image-space methods


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 surfaceA polygon is a back face if A polygon is a back face if

Vview . N > 0


Back-Face Detection (2) Right-handed viewing system If object is converted to projection coordinates and

viewing direction is parallel to z axisviewing direction is parallel to zv axis, Only consider the z component of the normal vector N N = (A, B, C)

A l i b k f if C 0 A polygon is back face if C<=0


Similarly, left-handed system, back face if C >= 0

Ex. Back-Face Detection

y xviewyview

zview

B(0,3,0)

3 +2 +6 6 0

view

N(3,2,6)

C(0 0 1)

3x+2y+6z -6=0

xz

A(2,0,0)C(0,0,1)


z

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 ypartially obscured by other faces

For a general scene, back-face removal 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


Depth-Buffer Method Image-space approach

Compares surface depth values throughout avalues throughout a scene from each pixel position on the projection planeplane

Also called the z-buffer method Depth is measured along

the z-axis


Depth-Buffer Method (2) 2 buffer areas are required

A depth buffer Stores depth values for each (x, y) position

Frame buffer (Refresh buffer) 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

Algorithm1. Initialize the depth and frame buffer

depthBuff(x, y) = 1.0, frameBuff(x, y) = backgndColor2. Process each polygon in a scene2. 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)


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) p ( , 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


Scan-Line Method Image-space method Across each scan line, depth calculations are

performed to determine which surface is nearest toperformed 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 lineContains 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


Scan-Line Method (2) Scan line 1, active edges:

AB,BC,EH,FG AB-BC, flag S1 on EH-FG, flag S2 on EH FG, flag S2 on

Scan line 2, active edges: AD,EH,BC,FG AD-EH flag S1 on AD 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


Same active edges list

Scan-Line Method (3)


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

Thi th d i ft f d t i t ’ This method is often referred to painter’s algorithm

Each color layer covers up the previous layer


Each color layer covers up the previous layer

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

determinez z

Szmax

S

S’z’max

zmax

S’z’max

z’min

zmin S’

z’min

zmin


x xNo Depth Overlap Depth Overlap

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 overlapdo not overlap

2. Surface S completely behind the overlapping surface3. The overlapping surface is completely in front of S4 The boundary-edge projections on the view plane do not4. 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 the most distant surface S is scan-converted


Depth-Sorting Method (4)

12 3

Two surfaces with depth Surface S is completely Overlapping surface S’ is poverlap but no overlap in the x direction

p ybehind the overlapping surface S’

pp gcompletely in front of surface S, but S is not completely behind S’

Two polygon surfaces with overlapping bounding

4


rectangles in the xy plane

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


obscures surface Sorder S, S’, S’’ should be reordered as S’, S’’, S

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 b hi d i f f h i i i lbehind or in front of the partitioning plane at each step of the space subdivision


BSP-Tree Method When BSP tree is complete, process the tree from the

right nodes to the left nodes


BSP-Tree Method

5 32

5a5

5b

3

13 1

245b

4 25a

5b


BSP-Tree Method

5 32

5a5

5b

3front back

13 4

5b2

front back

45b

15a


BSP-Tree Method

5 32

5a5

5b

3front back

13 2

front back4

back

415a 5b


Area-Subdivision Method Image-space method Take advantage of coherence, by locating

projection areas that represent part of aprojection areas that represent part of a single surface

By successively dividing the total view-l i t ll d llplane area into smaller and smaller

rectangular An easy way is to successively divide the area

i t 4 l t t h tinto 4 equal parts at each step Each rectangular contains the projection of

part of a single visible surface


Area-Subdivision Method (2)

First, test if the view is sufficiently complexp Yes, subdivide it

Test to each smaller areas, subdividing , gif a single surface is still uncertain

Continue until subdivisions are easily yanalyzed as belonging to a single surface or reached the resolution limit


Area-Subdivision Method (3) Relationship between a surface and an area of the subdivided

view plane Surrounding surface

Completely encloses the area Completely encloses the area Overlapping surface

Partly inside and partly outside the area Inside surface

C l l i id h Completely inside the area Outside surface

Completely outside the area



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 surroundingoverlapping, or surrounding Condition 3: An area has one surrounding surface

that obscures all other surfaces


Area-Subdivision Method (5) Condition 1 test by comparing coordinate extents of

each surfaceCondition 2 usually require intersection tests Condition 2 usually require intersection tests

Condition 3 test by sorting surfaces according to minimum depth from

i lview plane Use plane equation to calculate depth values at four vertices

of the area for all surrounding, inside, overlapping surfacesO f h b id tifi d t id Once a surface has been identified as an outside or surrounding, it will remain in that category for all subdivisions of the area



As a variation Subdivision along surface Subdivision along surface

boundaries instead of dividing them in half

In general fewer In general, fewer subdivisions are required, but more processing is p gneeded to subdivide and to analyze the relation of surfaces


surfaces

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 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 valueO l f t l d Only front colors are saved


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 b fbefore

Completely obscured nodes are not traversed

Different views of objects, octants are renumbered so that 0,1,2,3 are front nodes


Ray-Casting Method Along the line of sight, can determined

which objects intersect this line Method is based on geometric-optics g p

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

algorithmsalgorithms Only follow a ray out from each pixel to the

nearest object


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 surfacesScan line or area subdivision is a fast way 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 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

O 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


Implemented in hardware Parallel processing

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 diff tl f th i ibl ddifferently from the visible edges

Methods are also called visible-line detection th d hidd li d t ti th dmethods or hidden-line detection methods


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 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 pointsthose intersection points


Wire-frame Depth-Cueing Algorithm Displaying visibility information by vary the

brightness of objects as a function of distance form the viewing positionform the viewing position

Fdepth = (dmax–d) / (dmax–dmin)where d is the distance of a point form the viewing

positionp dmin, dmax can be set to the normalized depth

range 0.0~1.0 Each pixel its color is multiplied by f (d) Each pixel, its color is multiplied by fdepth(d)

Nearer points are displayed with higher intensities Points at maximum depth have intensity = 0


OpenGL Visibility-Detection Functions


End of Chapter 9End of Chapter 9


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