Lecture09-VisibleSurfaceDetection (1)

8/10/2019 Lecture09-VisibleSurfaceDetection (1)

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Chapter 9

Somsak Walairacht, Computer Engineering, KMITL


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Outline

Classification of Visible-Surface Detection Algorithms Back-Face Detection Depth-Buffer Method A-Buffer Method Scan-Line Method Depth-Sorting Method - ree e o Area-Subdivision Method Octree Methods

- Comparison of Visibility-Detection Methods Wire-Frame Visibility Methods

-

01074410 / 13016218 Computer Graphics 2


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Classification of Visible-Surface Detection Algorithms

2 approaches Object-Space Method

Compares objects and parts of objects to each otherwithin the scene

Determine surface as a whole

Image-Space Method

Visibility is decided point by point at each pixel position

Most visibility-surface algorithms use image-spacemethods



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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

Vview . N > 0



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Back-Face Detection (2)

Right-handed viewing system If object is converted to projection coordinates and

v , Only consider the z component of the normal vector N

N = (A, B, C) A po ygon is ac ace i = 0


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Ex. Back-Face Detection

y xviewyview

B(0,3,0)N(3,2,6)

x+ y+ z - =

x

A(2,0,0), ,



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Back-Face Detection (3)

Complete visibility test for nonoverlappingconvex polyhedra

For concave polygon, more test must be

carried out to determine whether thereare additional faces that are totall orpartially obscured by other faces

-can be expected to eliminate about half ofthe polygon surfaces in a scene fromfurther visibility tests



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Depth-Buffer Method

Image-space approach Compares surface depth

scene from each pixel

position on the projection

Also called the z-buffermethod

Depth is measured alongthe z-axis



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Depth-Buffer Method (2)

2 buffer areas are required A depth buffer

Stores depth values for each (x, y) position

Stores the surface-color values for each pixel position

Calculated depth is compared with the stored value, if it is lessthan 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) = backgndColor

. 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)



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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

De th z of x+1z = [-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



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Scan-Line Method

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

the view plane at each position

An active list of edges is formed for each scan line Contains onl ed es 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



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Scan-Line Method (2)

Scan line 1, active edges:AB,BC,EH,FG

AB-BC, flag S1 on -

Scan line 2, active edges:

AD,EH,BC,FG- ,

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 ed es list



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Scan-Line Method (3)



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Depth-Sorting Method

Using both image-space and object-spaceoperations

Basic functions

Surfaces are sorted in order of decreasing depth Surface are scan-converted in order, starting with

the surface of greatest depth

s me o s o en re erre o pa n er salgorithm



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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

Szmax

S

zmax

zmax

Szmax

zmin

zmin

zmin

zmin


x xNo Depth Overlap Depth Overlap


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Tests for each surface that has a depth overlap with S1. The bounding rectangles (coordinate extents) in xy directions

2. Surface S completely behind the overlapping surface

3. The overlapping surface is completely in front of S

-. overlap

If one of these test is true, no reordering for S

S is scan-converted



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1 2 3

Two surfaces with depth Surface S is completely Overlapping surface Sisoverlap but no overlap in

the x direction

behind the overlapping

surface Scompletely in front of

surface S, but S is not

completely behind S

Two polygon surfaces with

overlapping bounding4


rectangles in the xy plane


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Should all four tests fail for an overlappingsurface S

Interchange surfaces S and S in the sorted list

Surface S extends to a

greater depth, but it

Three surfaces that have

been entered into the

sorted surface list in the


order S, S, Sshould be

reordered as S, S, S


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BSP- ree Method

Painting surfaces into frame buffer from backto front painters algorithm

Useful when the view reference point

changes, but the objects in a scene are atfixed positions

Visibility testing involves identifying surfaces

e n or n ront o t e part t on ng p ane ateach step of the space subdivision



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BSP- ree Method

When BSP tree is complete, process the tree from theright nodes to the left nodes



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BSP- ree Method

25a

5b

front back

1

3 4

5b

2front back

4 15a



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BSP- ree Method

25a

5b

front back

1

3 2front back

4back

4 15a 5b



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Area-Subdivision Method

Image-space method Take advantage of coherence, by locating

single surface

By successively dividing the total view-p ane area nto sma er an sma errectangular An easy way is to successively divide the area

n o equa par s a eac s ep Each rectangular contains the projection of

part of a single visible surface



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Area-Subdivision Method (2)

First, test if the view is sufficientlycomplexYes, subdivide it

est to each smaller areas subdividinif a single surface is still uncertain

Continue until subdivisions are easil

analyzed as belonging to a singlesurface or reached the resolution limit



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Relationship between a surface and an area of the subdividedview plane Surrounding surface

Overlapping surface Partly inside and partly outside the area

Inside surface omp ete y ns e t e area

Outside surface Completely outside the area



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Test for determining surface visibility within arectangular 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,

, Condition 3: An area has one surrounding surface

that obscures all other surfaces



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Condition 1 test by comparing coordinate extents ofeach surface

Condition 3 test by sorting surfaces according to minimum depth from

v ew p ane

Use plane equation to calculate depth values at four verticesof the area for all surrounding, inside, overlapping surfaces

nce a sur ace as een en e as an ou s e orsurrounding, it will remain in that category for allsubdivisions of the area



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As a variation

boundaries instead of dividingthem in half

,subdivisions are required,but more rocessin is

needed to subdivide and toanalyze the relation of



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Octree Method

When an octree representation is used,visibility testing is done by searching octreenodes in a front-to-back order

Front octants 0,1,2,3 are visible

, , ,

When a color value is encountered, it issaved only if no previously saved value

n y ron co ors are save



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Octree Method (2)

Visibility testing is carried outwith recursive processing ofoctree nodes and createquadtree representation

Depth-first traversal of the

octree, octant 0 is visitede ore

Completely obscured nodes arenot traversed

Different views of objects,octants are renumbered so that0,1,2,3 are front nodes



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Ray-Casting Method

Along the line of sight, can determinedwhich objects intersect this line

Method is based on eometric-o ticsmethods, 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

Only follow a ray out from each pixel to thenearest object



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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 can- ne or area-su v s on s a as way

Several thousand surfaces Scan-line, depth-sorting, or BSP-tree

Few thousand surfaces - 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 ctree

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


Parallel processing


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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 displayederent y rom t e v s e e ges

Methods are also called visible-line detection

me o s or en- ne e ec on me o s



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Wire-Frame Surface-VisibilityAlgorithms

Compare edge position with the positions of the surfaces in a

scene Same methods used in line-clipping algorithms

If both projected edge endpoints are behind the surface, edge ishidden

Calculate intersection positions and determine the depth values at



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Wire-frame Depth-CueingAlgorithm

Displaying visibility information by vary thebrightness of objects as a function of distance

Fdepth = (dmaxd) / (dmaxdmin)where d is the distance of a point form the viewing

osition dmin, dmax can be set to the normalized depth

range 0.0~1.0 ,

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



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OpenGL Visibility-DetectionFunctions



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Lecture09-VisibleSurfaceDetection (1)

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