Visible Surface Detection · 2015. 5. 12. · Ray‐Casting Method (2) based on geometric optics, tracing paths of light rays backward tracing of light rays suitable for complex,

Einführung in Visual ComputingEinführung in Visual Computing186.822

Visible Surface DetectionVisible Surface Detection

W P h fWerner Purgathofer

Visibility in the Rendering PipelineVisibility in the Rendering Pipelinebj t t / tiobject capture/creation

bj t i bj tmodeling

scene objects in object spacemodelingviewing vertex stageviewing

projection

g(„vertex shader“)

projectiont f d ti i li

clipping + homogenizationtransformed vertices in clip space

clipping + homogenizationi li d d i di t

viewport transformationscene in normalized device coordinates

t i tiviewport transformation

rasterizationh di pixel stageshading pixel stage

(„fragment shader“)2raster image in pixel coordinates

(„fragment shader )

3D Display: Wireframe Display3D Display: Wireframe Display

© ZwCAD Software Co.,Ltd

Werner Purgathofer 3

3D Display: Depth Cueing3D Display: Depth Cueing

= or ??

depth cueing = intensity decreasesdepth cueing = intensity decreases with increasing distancewith increasing distance


3D Display: Visibility3D Display: Visibility

visible line and surface identificationvisible line and surface identification

= or != or !

© ZwCAD Software Co.,Ltd,


3D Display: Visibility3D Display: Visibility

© Snaptu© Snaptu


3D Display: Depth Cueing + Visibility3D Display: Depth Cueing + Visibility

only visible linesonly visible linesi t it dintensity decreases ith i i di twith increasing distance

© Gerschon Elber


3D Display: Shaded Display3D Display: Shaded Display

© ZwCAD Software Co.,Ltdshading + depth cueing: ,shading + depth cueing:

8© Ansgar Philippsen

Visible‐Surface DetectionVisible Surface Detectionidentifying visible parts of a scene (also hidden surface elimination)(also hidden‐surface elimination)type of algorithm depends on:type of algorithm depends on:

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

object‐spacemethodsobject spacemethodsobjects compared to each otherobjects compared to each other

image spacemethodsimage spacemethodspoint by point at each pixel locationp y p p

often sorting and coherence usedWerner Purgathofer 9

g

Visible‐Surface Detection MethodsVisible Surface Detection Methods

the following algorithms are examples for different classes of methods

back‐face detectiondepth buffer methoddepth buffer methodscan‐line methodscan line methoddepth sorting methoddepth‐sorting method

bdi i i th darea‐subdivision methodh doctree methods

ray‐casting method


Back‐Face Detection (1)Back Face Detection (1)

surfaces (polygons) with a surface normal pointing away from the eye (p yg ) p g y ycannot be visible (back faces)( )

eliminate them before visibility algorithm ! eliminate them before visibility algorithm !

viewingviewing direction

direction

b li i t dcan be eliminated:Werner Purgathofer 11

Back‐Face Detection (2)Back Face Detection (2)eliminating back faces of closed polyhedraview 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

yor polygon with normal N=(A, B, C) is a back face if

0NV 0 NVviewN = (A, B, C)

VVview



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

CVNV i s ffi ient ondition if C 0 then ba k fa e

CVNVview z

sufficient condition: if C 0 then back‐face negative !

yvz N = (A, B, C)zv

x Vxv Vview



complete visibility test for non‐overlapping convex polyhedra

f i ll hiddface partially hiddenb h fby other faces

preprocessing step for other objects:preprocessing step for other objects:b f f l dabout 50% of surfaces are eliminated


Depth‐Buffer Method (1)Depth Buffer Method (1)z‐buffer methodimage‐space methodhardware implementationno sorting!


Depth‐Buffer Method (2)Depth Buffer Method (2)two buffers

( )refresh buffer (intensity information)d h b ff (di i f i )depth buffer (distance information)

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

d thidraw something =ith i b ff• compare z with z in buffer

if l t i• if z closer to viewerth d d d t i b ff• then draw and update z in bufferl thi !• else nothing!


Depth‐Buffer Algorithm ExampleDepth Buffer Algorithm Example

polygons withp ygcorresponding

3 3.8 .7p g

z-values .3 .33 3

.7 .6 .6 .56 5

.44.3 .3 .6 .5 .4

backimage

back-groundimage ground

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1depth- 8 7 8 7

-1 -1 -1 -11 1 1 1

-1 -1 -1 -11 1 1 1

-1 -1 -1 -11 1

-1 -1 -1 -11 1depth

buffer 3 3.8 .77 6 3 7 66

.8 .73

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

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

-1 -1-1

-1 -1buffer .3 .3

.3 .3.7 .6 .3

.3 .3.7 .6.6

.6 .5 .4.3.3

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

1 1-1 -1

1-1 -1


3 3 3 3 6 5 3

Depth‐Buffer AlgorithmDepth Buffer Algorithm

for all (x,y)frameBuff(x,y) = backgroundColor( ,y) gdepthBuff(x,y) = -1 p ( ,y)

for each polygon Pfor each polygon Pfor each position (x y) on polygon Pfor each position (x,y) on polygon Pcalculate depth zcalculate depth zif z > depthBuff(x y) thenif z > depthBuff(x,y) thend thB ff( )depthBuff(x,y) = zframeBuff(x,y) = surfColor(x,y)


Depth‐Buffer: Incremental z‐ValuesDepth Buffer: Incremental z Values

depth at (x,y): z = AxByDdepth at (x,y): z = C

d th t ( 1 ) A(x+1)ByD Adepth at (x+1,y): z' = A(x 1) By DC = z C

AC C

Ax B(y 1) D Bdepth at (x,y‐1): z" = AxB(y1)DC = z C

BC C

constants !y constants !y

y–1y 1

x x+1


Depth‐Buffer: y‐Coordinate IntervalsDepth Buffer: y Coordinate Intervals

determine y‐coordinate extents of polygon Pdetermine y coordinate extents of polygon P

top scan line

y scan linel ft d

yleft edge i t tiintersection

bottom scan linebotto sca e


Depth‐Buffer: Values down an EdgeA B D

Depth Buffer: Values down an Edge

z = AxByDCz C

z' A(x1/m)B(y1)Dy' = y 1 z' = ( ) (y )

Cx' = x 1/m

A/m + B= z Cli Cy scan line(y – 1) scan line constant !(y 1) scan line

x x'Werner Purgathofer 2121

x x

Scan‐Line MethodScan Line Method

image‐space methodextension of scan‐line algorithm for polygon filling


Scan‐Line Method: Edge & Polygon TablesScan Line Method: Edge & Polygon Tables

edge table (all edges y‐sorted)edge table (all edges, y sorted)coordinate endpointscoordinate endpointsinverse slopeinverse slopepointers into polygon tablep p yg

polygon table (all polygons)coefficients of plane equationintensity information( i i d bl )(pointers into edge table)


Scan‐Line Method: Active Edge ListScan Line Method: Active Edge List

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


Scan‐Line Method ExampleScan Line Method ExampleEdge Table: 2,3,1,5,1,1,2,2,5,4,3,3,4,4 Polygon Table: , ,

active edges active polygons2 3,2

31 51 2 1 3 1

1 11 5

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

2 122 4 2,2,5,3,1,5 , ,

533

533,3,1,5 , 3 3,3,1,5 ,

4 3,1 Werner Purgathofer / Computergraphik 1 254

Scan‐Line Method ‐ CoherenceScan Line Method Coherencecoherence between adjacent scan lines

incremental calculationsi d li i ilactive edge lists very similar

(easy sorting avoid depth calculations)(easy sorting, avoid depth calculations)

26Werner Purgathofer / Einführung in Visual Computing

Depth‐Sorting Method: OverviewDepth Sorting Method: Overview

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

“approximate”‐sorting using smallest z‐value (greatest depth)pp g g (g p )fine‐tuning to get correct depth orderfine tuning to get correct depth order

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

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


Depth‐Sorting Method: Sorting (1)Depth Sorting Method: Sorting (1)

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

no depth overlap ordering correctp p gdepth overlap z idepth overlap do further tests in

zminS

increasing order gof complexity zmax

z'min S'min S

2 surfaces with no depth overlap z'maxf p pviewing x


viewing direction

xz


ordering correct ifbounding rectangles in xy‐plane do not overlapg g y p pcheck x‐,y‐direction separatelycheck x ,y direction separately

viewing2 surfaces with depth

viewingdirection S'2 surfaces with depth

overlap but no overlap SS

overlap but no overlap in the x‐direction

Sin the x‐direction

x x x' x' xzWerner Purgathofer 29

xmin xmax x min x max xz


ordering correct ifS completely behind S'p ysubstitute vertices of S into equation of S'substitute vertices of S into equation of S

overlap in z‐directionoverlap in x‐directionS

viewing directionS is completely directionp y

behind (“inside”) S'( )the overlapping S'pp g

xzWerner Purgathofer 30

z


ordering correct ifS' completely in front of Sp ysubstitute vertices of S' into equation of Ssubstitute vertices of S into equation of S

overlap in x‐ and z‐direction

l i S' i l t l i Soverlapping S' is completely in f t (“ t id ”) f S b t S i viewing

directionfront (“outside”) of S, but S is

t l t l b hi d S’ directionnot completely behind S’S'


z


ordering correct ifS' completely in front of Sp ysubstitute vertices of S' into equation of Ssubstitute vertices of S into equation of S

SS is not completely behind

viewing direction

S is not completely behind (“inside”) the overlapping S' direction( inside ) the overlapping S

S'


z


ordering correct ifprojections of S, S' in xy‐plane don’t overlapp j , y p p

surfaces with overlapping bounding rectanglesWerner Purgathofer 33

Depth‐Sorting Method: Sorting (6)Depth Sorting Method: Sorting (6)all five tests fail

ordering probably wrongi h f S S'interchange surfaces S, S'

t f d d frepeat process for reordered surfaces

SSS'

viewingS

S'S

viewing direction

SS"

xz xzxz

sorted surface list: S, S', S" should be surface S has greater depth Werner Purgathofer / Computergraphik 1 34 reordered: S', S", Sbut obscures S'

Depth‐Sorting: Special CasesDepth Sorting: Special Cases

avoiding infinite loops due to cyclic overlapreordered surfaces S' are flaggedggif S' would have to be reordered again divide S' into two partsif S would have to be reordered again divide S into two parts

intersecting or cyclically overlapping surfaces!

35Werner Purgathofer / Einführung in Visual Computing

Area‐Subdivision Method (1)Area Subdivision Method (1)

image‐space methodarea coherence exploitedviewing area subdivided until visibility decision very easyg y y y



relationship polygon rectangular view area

inside outside surrounding overlapping surfacesurface surfacesurface

only these four possibilitiesonly these four possibilities


Area‐Subdivision Method (3)

th i ibilit d i iArea Subdivision Method (3)three easy visibility decisions

ll f t id f i iall surfaces are outside of viewing area

only one inside, overlapping, or surrounding surface is in y , pp g, gthe area

one surrounding surface obscures all other surfaces withinone surrounding surface obscures all other surfaces within the viewing areathe viewing area



a surrounding obscuring surfacesurfaces ordered according to minimum depthg pmaximum depth of surrounding surface closest to view plane?maximum depth of surrounding surface closest to view plane?test is conservativetest is conservative

viewingzmax

viewing direction

dizmin

surroundingsurface

xz area



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

if no further subdivision possible (pixel resolution reached)if no further subdivision possible (pixel resolution reached)t f d t k i t it f t fsort surfaces and take intensity of nearest surface


Area‐Subdivision Method ExampleArea Subdivision Method Example

1 21 23 43 4

finishedfinished

Werner Purgathofer

Octree MethodsOctree Methods

recursive traversal of octreetraversal order depends on processing direction p p g

front‐to‐back:front to back: pixel(x y) written oncepixel(x,y) written oncecompletely obscuredcompletely obscured nodes are not traversednodes are not traversed

b k t f tback‐to‐front:i ipainter’s algorithm viewing

direction


Octree MethodsOctree Methods

recursive traversal of octreetraversal order depends on processing direction p p g

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

viewing directioncompletely obscured

nodes are not traverseddirection

nodes are not traversedb k t f tback‐to‐front:

painter’s algorithm


Ray‐Casting Method (1)Ray Casting Method (1)

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

closestclosest intersectionviewing

di ti intersectionpointdirection


p

Ray‐Casting Method (2)Ray Casting Method (2)

based on geometric optics, tracing paths of light raysbackward tracing of light raysg g ysuitable for complex curved surfacessuitable for complex, curved surfacesspecial case of ray tracing algorithmsspecial case of ray‐tracing algorithmsff f hefficient ray‐surface intersection techniques necessaryintersection pointnormal vector


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Visible Surface Detection · 2015. 5. 12. · Ray‐Casting Method (2) based on geometric optics, tracing paths of light rays backward tracing of light rays suitable for complex,