Werner Purgathofer - cg.tuwien.ac.at · Visible-Surface Detection identifying visible parts of a scene (also hidden-surface elimination) type of algorithm depends on: complexity of

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Visible Surface DetectionVisible Surface Detection

Werner Purgathofer

Visibility in the Rendering Pipeline

scene objects in object spaceobject capture/creation

modelingviewing vertex stage

( vertex shader“)g

projection(„vertex shader )

transformed vertices in clip spaceclipping + homogenization

transformed vertices in clip space

scene in normalized device coordinates

viewport transformation

rasterizationshading pixel stage

Werner Purgathofer 1raster image in pixel coordinates

shading p g(„fragment shader“)

3D Display: Wireframe Display

© ZwCAD Software Co.,Ltd

Werner Purgathofer / Computergraphik 1 2

3D Display: Depth Cueing

?= or ?

intensity decreases with i i di tincreasing distance


3D Display: Visibility

visible line and surface identification

= or !

© ZwCAD Software Co.,Ltd


3D Display: Visibility

© Snaptu


3D Display: Depth Cueing + Visibility

only visible linesintensity decreasesintensity decreases with increasing distance

© Gerschon Elber


3D Display: Shaded Display

shading + depth cueing:


Visible-Surface Detection

identifying visible parts of a scene (also hidden-surface elimination)( )type of algorithm depends on:

complexity of scenecomplexity of scenetype of objectsavailable equipmentavailable equipmentstatic or animated displays

object space methodsobject-space methodsobjects compared to each other

i th dimage space methodspoint by point at each pixel location


often sorting and coherence used

Visible-Surface Detection Methods

the following algorithms are examples for different classes of methodsdifferent classes of methods

back-face detectiondepth buffer methodscan-line methodscan line methoddepth-sorting methodarea-subdivision methodoctree methodsray-casting method


Back-Face Detection (1)

surfaces (polygons) with a surface normal pointing away from the eye cannot be visiblepointing away from the eye cannot be visible (back faces)

eliminate them before visibility algorithm !

viewing di ti direction


can be eliminated:


eliminating back faces of closed polyhedraview point (x y z) “inside” a polygon surface ifview point (x,y,z) inside a polygon surface if

Ax + By + Cz + D < 0or polygon with normal N=(A, B, C) is a back face if 0NVface if 0NVview

N = (A B C)N = (A, B, C)

VviewVview



object description in viewing coordinates V (0 0 V )Vview=(0,0,Vz) CVNVview z

sufficient condition: if C 0 then back-face

N = (A B C)yv

zv N = (A, B, C)

Vviewx Vviewxv



complete visibility test for non-overlapping convex polyhedraconvex polyhedra

face partially hidden by other faces

preprocessing step for other objects: about 50% of surfaces eliminated


Depth-Buffer Method (1)

z-buffer methodimage-space methodimage space methodhardware implementationno sorting!no sorting!


Depth-Buffer Method (2)

two buffersdepth buffer (distance information)depth buffer (distance information)refresh buffer (intensity information)

size corresponds to screen resolution(for every pixel: r, g, b, z)

draw something =• compare z with z in buffer• if z closer to viewer• then draw and update z in buffer• else nothing!


• else nothing!

Depth-Buffer Algorithm Example

polygons with corresponding .8 .7corresponding z-values .3 .3

.3 .3

.8 .7

.7 .6 .6 .56 5

.44

back-

.3 .3 .6 .5 .4

imagebackground

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1depth-buffer .3 .3

.8 .7

.7 .6 .3 .7 .6.6.8 .7

.3-1 -1 -1 -1-1 -1 -1 -1

-1 -1 -1 -1-1 -1

-1 -1-1

-1 -1


.3 .3 .3 .3 .6 .5 .4 .3-1 -1 -1 -1 -1 -1 -1 -1

Depth-Buffer Algorithm

for all (x,y)depthBuff(x,y) = -1frameBuff(x,y) = backgroundColorframeBuff(x,y) backgroundColor

for each polygon Pf h iti ( ) l Pfor each position (x,y) on polygon Pcalculate depth zif z > depthBuff(x,y) thendepthBuff(x,y) = zdept u ( ,y)frameBuff(x,y) = surfColor(x,y)


Depth-Buffer: Incremental z-Values

depth at (x,y): z =AxByD

C

depth at (x+1 y):

C

z’ =A(x+1)ByD = z Adepth at (x+1,y): z = C = z

CAx B(y 1) D B

depth at (x,y-1): z” =AxB(y1)D

C = z CB

constants !


Depth-Buffer: y-Coordinate Intervals

determine y-coordinate extents of polygon P


Depth-Buffer: Values down an Edge

z =AxByD

CC

z’ =A(x1/m)B(y1)D

Cx’ = x 1/m

’ 1 z Cy’ = y 1

= z C

A/m + BC

constant !constant !


Scan-Line Method

image-space methodextension of scan line algorithm forextension of scan-line algorithm for polygon filling


Scan-Line Method: Edge & Polygon Tables

edge table (all edges, y-sorted)coordinate endpointsinverse slopepointers into polygon table

polygon table (all polygons)coefficients of plane equationp qintensity information(pointers into edge table)(po te s to edge tab e)


Scan-Line Method: Active Edge List

active edge list (all edges crossing current scanline x sorted flag)current scanline, x-sorted, flag)


Scan-Line Method Example

Edge T. 2,3,1,5,1,1,2,2,5,4,3,3,4,4 Poly.T. , , t d / t l

23

act.edges / act.poly.3,2

1 1

31 51,5,2,1,3,1 , ,

12 1

2 4 2,2,5,3,1,5 , ,

5

23

35

3,3,1,5 ,

3 1 Werner Purgathofer / Computergraphik 1 24

44

3,1

Scan-Line Method Details

coherence between adjacent scan linesincremental calculationsincremental calculationsactive edge list very similar(easy sorting, avoid depth calculations)( y g, p )

intersecting or cyclically overlapping surfaces!


Depth-Sorting Method: Overview

surfaces sorted in order of decreasing depth (viewing in z direction)(viewing in z-direction)

“approximate”-sorting using smallest z-value (greatest depth)fine-tuning to get correct depth orderg g p

surfaces scan converted in orderti b th i i d bj tsorting both in image and object space

scan conversion in image spacescan conversion in image spacealso called “painter’s algorithm”


Depth-Sorting Method: Sorting (1)

surface S with greatest depth is compared to all other surfaces S’compared to all other surfaces S

no depth overlap ordering correctdepth overlap do further tests in

zminS

increasing order of complexity zmaxof complexity max

z´min S´

z´max2 surfaces with no d th l


viewing direction xz

depth overlap


ordering correct ifbounding rectangles in xy plane do notbounding rectangles in xy-plane do not overlapcheck x-,y-direction separately

viewing direction

S´2 surfaces with depth

overlap but no overlap S

S´

overlap but no overlap in the x-direction


xmin xmax x´min x´maxxz


ordering correct ifS completely behind S’S completely behind S’substitute vertices of S into equation of S’

overlap in x- and z-directionS

viewing directionS is completely

behind (“inside”) S´behind ( inside )the overlapping S’

S


xz


ordering correct ifS’ completely in front of SS’ completely in front of Ssubstitute vertices of S’ into equation of S

overlap in x- and z-direction

SS is not completely

viewing direction

S is not completely behind (“inside”) the

overlapping S’S´

overlapping S’


xz


ordering correct ifS’ completely in front of SS’ completely in front of Ssubstitute vertices of S’ into equation of S

Soverlapping S’ is l t l i f t viewing

directioncompletely in front

(“outside”) of S, but S i t l t l

S´is not completely

behind S’


xz


ordering correct ifprojections of S S’ in xy plane don’t overlapprojections of S,S’ in xy-plane don’t overlap

surfaces with overlapping bounding rectangles


surfaces with overlapping bounding rectangles


all five tests fail ordering probably wrongordering probably wronginterchange surfaces S, S’repeat process for reordered surfacesrepeat process for reordered surfaces

SSS´

viewing direction

S´S”

S

xzxz


sorted surface list: S, S’, S” should be reordered: S’, S”, S

surface S has greater depth but obscures S’

Depth-Sorting: Special Cases

avoiding infinite loops due to cyclic overlapreordered surfaces S’ are flaggedreordered surfaces S’ are flaggedif S’ would have to be reordered again

divide S’ into two parts


Area-Subdivision Method (1)

image-space methodarea coherence exploitedarea coherence exploitedviewing area subdivided until visibility d i idecision very easy



relationship polygon rectangular view area

inside f

outside f

surrounding f

overlapping f surface surfacesurface surface

only these four possibilities


only these four possibilities


all surfaces are outside of viewing areathree easy visibility decisions

all surfaces are outside of viewing areachecking bounding rectangles

only one inside overlapping oronly one inside, overlapping, or surrounding surface is in the area

bounding rectangles for initial checkbounding rectangles for initial checkone surrounding surface obscures all other surfaces within the viewing areasu aces e e g a ea

minimum depth ordering



a surrounding obscuring surfacesurfaces ordered according to minimum depthsurfaces ordered according to minimum depthmaximum depth of surrounding surface closest to view plane?test is conservativetest is conservative

viewing direction

zmax

zmin

x

surroundingsurface


xz area


if all three tests fail do subdivisionsubdivide area into four equal subareassubdivide area into four equal subareasoutside and surrounding surfaces will remain in this status for all subareassome inside and overlapping surfaces will besome inside and overlapping surfaces will be eliminated

no f rther s bdi ision possible (pi elno further subdivision possible (pixel resolution reached)

sort surfaces and take intensity of nearest surface


su ace

Area-Subdivision Method Example

1 21 23 4


Octree Methods

recursive traversal of octreetraversal order depends on processingtraversal order depends on processing direction

front-to-back: pixel(x y) written oncepixel(x,y) written oncecompletely obscured

d t t dnodes are not traversedback-to-front:

painter’s algorithm viewing direction


Octree Methods

recursive traversal of octreetraversal order depends on processingtraversal order depends on processing direction

viewingfront-to-back:

pixel(x y) written once

viewing direction

pixel(x,y) written oncecompletely obscured

d t t dnodes are not traversedback-to-front:

painter’s algorithm


Ray-Casting Method (1)

line-of-sight of each pixel is intersected with all surfacesall surfacestake closest intersected surface

closest intersectionviewing


intersectionpoint

viewing direction

Ray-Casting Method (2)

based on geometric optics, tracing paths of light rayslight raysbackward tracing of light rayssuitable for complex, curved surfacesspecial case of ray tracing algorithmsspecial case of ray-tracing algorithmsefficient ray-surface intersection techniques necessary

intersection pointintersection pointnormal vector


Documents

Werner Purgathofer - cg.tuwien.ac.at · Visible-Surface Detection identifying visible parts of a scene (also hidden-surface elimination) type of algorithm depends on: complexity of