ITCS 4120-Visible-Surface Detection.ppt

8/14/2019 ITCS 4120-Visible-Surface Detection.ppt

1/38

11/9/2013Zachary Wartell

Visible Surface Detection

Copyright 2006, Zachary Wartell at University of North Carolina. All rights reserved.

Revision 1.3

Textbook:

Chapter 9


2/38


Back-Face Culling

Used to remove unseen polygons from convex, closed

polyhedron (Cube, Sphere)

Does not completely solve hidden surface problem since

one polyhedron may obscure another

, Larry F. Hodges, Drew Kessler


3/38


Back Face Culling

point (x,y,z) is behind planar surface iff:Ax+By+Cz+D 0 If we compute N after transforming to projection

coordinates (so projectors are all perpendicular to viewwindow), just testzN

PRP

View Windo

w

PRP

View Windo

w N=(A,B,C)

yview

xviewzviewPRP=

Nyview

xviewzview


4/38


Depth-Buffer Method

Recall Slide:

ITCS 4120-3D Viewing.ppt# 51-53, 3D3D collineation

on cube
http://www.cs.uncc.edu/~zwartell/ITCS%204120-5120/current/Lectures/Wartell/web%20page/ITCS%204120-3D%20Viewing.ppthttp://www.cs.uncc.edu/~zwartell/ITCS%204120-5120/current/Lectures/Wartell/web%20page/ITCS%204120-3D%20Viewing.ppthttp://www.cs.uncc.edu/~zwartell/ITCS%204120-5120/current/Lectures/Wartell/web%20page/ITCS%204120-3D%20Viewing.ppthttp://www.cs.uncc.edu/~zwartell/ITCS%204120-5120/current/Lectures/Wartell/web%20page/ITCS%204120-3D%20Viewing.ppt


5/38


Depth-Buffer Algorithm

1. Initialize depth buffer and frame buffer for all pixels (x,y)

depthBuffer(x,y) = 1.0; frameBuffer(x,y)=BackgroundColor

2. Process each polygon face, F, in scene

For each projected pixel, P, at location (x,y) in F,

calculate the depthz

Ifz < depthBuffer(x,y), compute surface color, C, at the

pixel P, so set:

depthBuffer(x,y) =z; frameBuffer(x,y)=C

Note: After all surfaces are processed, depth buffer

contains depth for visible surfaces and frame buffer

contains corresponding color values for those surfaces


6/38


(x1,y1,z1)

(x2,y2,z2)

(x3,y3,z3)

(xr

,yr,

zr

)(xl,y

l,z

l)

(x,y,z)

Computingz

After M3dscr{obliquepers,oblique}you have

vertices: {(xi,yi,zi )}

Generally to computez:

Incremental inx:

Incremental iny:

Ax By Dz

C

( 1)/

A x By Dz z A C

C

1/

So:

/ or / , if =

x x m

A m Bz z z z B C m

C


7/38


A-Buffer Method

accumulation bufferbuffer accumulates multiple pieces of

information for each pixel in addition to depth for transparency or

anti-aliasing (high-end movies, etc.). A-buffer element stores: Depth Field : real-number

Surface Data Field (SDF): stores surface data or pointer

When Depth >= 0:

-real-number is depth of surface at pixel

-SDF is surface color and pixel coverage percentage

depth 0RGB & Other

Info Pixel44%48%


8/38


When Depth < 0:

-SDF is pointer to linked list of elements that store:

-RGB intensity

-opacity

-depth

-pixel coverage percentage

-surface ID

-other surface rendering parameters

A-Buffer Method

Depth < 0RGB & Other

Info

RGB & Other

Info

Surface 1 Surface 2


9/3811/9/2013Zachary Wartell

Scan-Line Method

Unlike z-buffer or A-buffer, scan-line method has depth info only for

a single scan-line.

In order to require one scan-line of depth values, we must group andprocess all polygons intersecting a given scan-line at the same time

before process the next scan-line

Build table of edges of all polygons in scene. Maintain active-edge-

table as we visit each scan-line in scene. AET now contains edges

for all polygons at that scanline. Must maintain flag for eachsurface to determine whether pixel on scan-line is inside that

surface.

scan-line



Scan-Line Method Basic Example

Scan Line 1:

(A,B) to (B,C) only inside S1, so color from S1

(E,H) to (F,G) only inside S2, so color from S2

Scan Line 2:

(A,D) to (E,H) only inside S1, so color from S1

(E,H) to (B,C) inside S1 and S2 , so compute & test depth

In this example we color from S1

(B,C) to (F,G) only inside S2, so color from S2B

A

D

C

G

F

E

H

S1 S2Scan Line 1

Scan Line 2Scan Line 3



Scan-Line Method Generalization

This basic approach fails when surfaces cut-through

each other or overlap. To generalize we must divide

surfaces to eliminate overlaps



Depth-Sorting Method

Painters Algorithm

Approach:

sorted surfaces by increasing depth

may require surface splitting

scan-convert surfaces in sorted order (back to front)

Use a sequence of sorting steps and tests of increasing

computational complexity to handle all possible cases of

polygon depth orderings



Sort surfaces by each surfaces smallest z into list:(S1,S2, Si SN)

For all Si,i[2,N]

If farthest surface SFhas no z overlap render it. (easycase)

If there is z overlap with SF we can still avoid reorderingif one of four conditions holds. So we test theseconditions

Depth Sorting Details

z

SF=S1

Si

zmin2

zmax2

zmin1

zmax1

z

SF=S1

Si

zmin2

zmax2

zmin1

zmax1

farther from

PRP !



Depth Sorting: Reorder Avoidance Tests

We can avoid reorder if:

1) Bounding rectangles inxy dont overlap

2) Sfis completely behind overlapping surface relative

to view position

3) Overlapping surface is completely in front of Sf

relative to view position

4) Boundary edges of projections of two surfaces on

projection plane dont overlap

z

Sf

S2

xmin1 xmax1 xmin2 xmax2

1)

Sf

S2

2) 3)

z z

Sf

S2



Depth Sorting: Reorder Avoidance Tests (cont.)

4) Boundary edges of projections of two surfaces on

projection plane dont overlap. (Knowing that bounding

rectangles overlap from (1) doesnt help. We mustcompute expensive polygon/polygon intersection).



Depth Sort: Reordering

If 1-4 fail, we swap Sfand S.

In general further swaps made be needed.

Example:

first swap S S'', but S'' occludes S' so swap S' and S'' to getfinal order S', S'',S

z

S''

S

S'

z

Sf

S



Depth Sort: Surface/Polygon Splitting

It also is possible that there are cyclic occlusion

relationships or surfaces penetrate. To deal with this we

flag a surface when it is put at the end of the depth sortlist and if we ever try to place a surface at the end more

than once, we must split the polygon



BSP-trees

Binary Space Partition is a relatively easy way to sort the polygons relative to theeyepoint

To Build a BSP Tree

1. Choose a polygon, T, and compute the equation of the plane it defines.

2. Test all the vertices of all the other polygons to determine if they are in front of,behind, or in the same plane as T. If the plane intersects a polygon, divide thepolygon at the plane.

3. Polygons are placed into a binary search tree with T as the root.

4. Call the procedure recursively on the left and right subtree.

Larry F. Hodges, Drew Kessler

BSP T E l



BSP-Tree Example

+X -X

C

B

A

D

E

+ZF


T i BSP T



Traversing BSP-Tree

Traverse the BSP tree such that the branch descended

first is the side that is away from the eyepoint. This can

be determined by substituting the eye point into the planeequation for the polygon at the root.

When there is no first branch to descend, or that branch

has been completed then render the polygon at this node.

After the current node's polygon has been rendered,

descend the branch that is closer to the eyepoint.


T i BSP T E l



Traversing BSP-Tree: Example

EYE 1

+X -X

C

B

A

D

E1

+ZF2

E2

F1

EYE 2

A

C

F1 D

E2 F2

B

E1


S litti T i l



Splitting Triangles

If all our polygons are triangles then we

always divide a triangle into moretriangles when it is intersected by theplane.

It is possible for the number of triangles to increase

exponentially but in practice it is found that the increase

may be as small as two fold.

A heuristic to help minimize the number of fractures is to

enter the triangles into the tree in order from largest to

smallest.


A S bdi i i M th d



Area-Subdivision Method

Recursively subdivide viewplane into quadrants until:

rectangle contains part of 1 projected surface

rectangle contains part of no surface

rectangle is size of pixel

A S bdi i i M th d



Area-Subdivision Method

We need tests that can quickly determine tell if current area is part

of one surface or if further subdivision is needed.

Four cases for relation between surface and rectangular area:

surroundingsurface

overlappingsurface

insidesurface

outside

surface

A S bdi i i St i C diti



Area-Subdivision: Stopping Conditions

Recursive subdivision can stop when either:

1) a rectangle has all surfaces outside

2) a rectangle has exactly one inside, overlapping, or

surrounding surface

3) a rectangle has one surrounding surface and the

surface occludes all other surfaces in the area

For efficiency:

compare rectangle to projected surface bounding

rectangle first. Only perform exact interaction test ifnecessary. If single bounding rect. intersects

rectangle, test for exact intersection and color the

framebuffer for the intersection of surface & rectangle.

T ti C diti 3



Testing Condition 3

sort surfaces on minimum depth from view plane

for each surrounding surface for current rectangle

compute maximum depth within rectangle subsection

If maximum depth of a surrounding surface is closer to

view plane than the minimum depths of all other surfaces

within the area, condition 3 is achieved (i.e. surrounding

surface occludes all others).

zarea

zmax

Condition 3 Test need not be e ha sti e



Condition 3 Test need not be exhaustive

There are cases that this computation will miss. Rather than

performing further more expensive testing, we just subdivide the

rectangle (i.e. dont stop recursion). This choice is conservative: we may recurse when we dont need (to

avoid complex geometric computation), but as we continue recursive

subdivision we will eventually compute exact answer because in

limiting case rectangle is one pixel and in this case we simply

calculate depth of each intersecting surface at that single point andset the framebuffer to the nearest surfaces color.

Ray Casting Method


28/38


Ray-Casting Method

based geometric optics method that trace rays of light

backwards light path tracing

compare to depth buffer (surfaces to pixels versus pixel to surfaces)

special case of ray-tracing

COP

pixel

view plane

Octrees


29/38


Octrees

Octree:

partitions 3-space by a regular, recursive subdivision of 3-space

into axis-aligned boxes 3D objects are stored in the octree node that contains them.

Recursively subdivide until each octree node is either empty, a

homogeneous volume, or contains single object thats easy to

compute visibility (example can use back-face culling alone).

3 2

0 1

4 5

67

0 1 2 3 4 5 6 7

Any of these octants could then be

recursively subdivide

Octrees: Rendering


30/38


Octrees: Rendering

Given a particular view, the octants can be ordered in view depth

order. The order is the same for octants at all levels in the

recursive subdivision. For general perspective viewing, traverse the octree in back-to-front

order and render contents of each node (nearer objects pixels

overwrite farther objects pixels).

3 2

0 1

4 5

67

view frustum For parallel projections withview planes parallel to octant

faces, render front-to-back

using a quadtree subdivision of

the display window to record

when a object has been drawnonto a region of the window.

Comparison of visibility detection methods


31/38


Comparison of visibility-detection methods

effectiveness of method depends on surface distribution

wide distribution along view depth implies little depth overlap.

This is ideal for depth-sorting and BSP-trees few overlaps in surface view plane projections is ideal for scan-

line or area-subdivision

more generally

few surfaces implies few depth overlaps which is ideal for depth-

sort or BSP-tree

scan-line also good for a few thousand polygon surfaces

for large number of surfaces octree or depth-buffer is better

depth-buffertends to have constant computation cost as #

of surfaces increases because more surfaces tends to implyindividual surfaces are small (but beware of depth-

complexity). Relative performance best for complex scenes.

Octreefor parallel projection of volume data only need

integer add/sub. operations

Visibility Detection of Curve Surfaces


32/38


Visibility Detection of Curve Surfaces

ray-castingcompute ray surface intersections

scan-linecompute intersection of scan-lines extruded

plane with surfaces

octreeschop up surfaces into pieces at octant

boundaries

depth-bufferapproximate surface with polygons

surfaces represented as parametric, explicit or implicit

equations

use efficient numerical approximation methods forcomputing surface intersections with parallel

calculations or hardware implementation for common

surfaces (quadrics, bezier-surfaces, etc.)

Surface contour plots


33/38


Surface contour plots

given some surface representation write it in view coordinate system

(z is depth):

y=f(x,z) plot curves each at fixedzin front-to-back order and eliminate

hidden sections. Incrementzby z over surfaces visiblezrange.

For each curve, iterate overxcoordinate in screen coordinates,

compute correspondingyand plot point (x,y). To eliminate hidden

surfaces record (ymin,ymax) of plotted points for eachxscreencoordinate. Only plot point (x,y) ifyis outside (ymin,ymax) atx.

Wire frame visibility methods


34/38


Wire-frame visibility methods

wire-frame rendering of 3D object can be fast (fewer pixels to fill) and

can emphasize various 3D features, but it becomes visually

ambiguous as to what parts are in front/back of others

Direct approach requires testing each line segment against eachsurface. Must work with projected coordinates of segment and

surface boundaries. Hidden edges can be removed or drawn with

dashes

end points inside

& behind

end points inside

& infront

end points inside

& infront & behind

end points outside

& behind at boundary

end points outside

& behind & infrontat boundary

Wire Frame Depth Cueing


35/38


Wire-Frame Depth Cueing

Vary brightness of objects in scene as function of depth:

Color of point is multiplied byfdepth(d)

Additionally we could simulate atmospheric effects (smog/haze)

where farther pixels are paler in color

max

max min

max min

( )

is distance of point from view position

, application dependent. Often [0.0,1.0] in normalized coordinates

depthd df d

d d

d

d d

OpenGL Visibility


36/38


OpenGL Visibility

Back-face removalglFrontFace(ff); // ff {GL_CW,GL_CCW}

glEnable(GL_CULL_FACE);glCullFace(mode); // mode {GL_BACK,GL_FRONT,

GL_FRONT_AND_BACK}

Depth-Buffer

- tell GUI library to allocated depth-buffer for

graphics windows- glClear (GL_DEPTH_BUFFER_BIT)

-glEnabled (GL_DEPTH_TEST)

-glClearDepth (maxDepth); // maxDepth [0.0,1.0]

-glDepthRange (nearNormDepth,farNormDepth)//nearNormDepth [0.0,1.0], farNormDepth [0.0,1.0]

-glDepthFunc (testCondition)

//testCondition{GL_LESS,GL_GREATER,GL_EQUAL,GL_NOTEQUAL,

// GL_LEQUAL,GLGEQUAL,GL_NEVER,GL_ALWAYS}

OpenGL Visibility (cont )


37/38


OpenGL Visibility (cont.)

Depth-Buffer

glDepthMask (writeStatus);// writeStatus {GL_TRUE,GL_FALSE}

use for displaying single animated foreground object over static background

object (disable write when drawing foreground object)

use for approximate transparency (disable write when drawing transparent

surface)

Wire-frame Surface-Visibility Methods

glPolygonMode(GL_FRONT_AND_BACK,GL_LINE) shows polygons as outlines

draw polygon twice. Once as outline using foreground color and once as filled

polygon in background color. To prevent filled polygon pixels from interfering

with outline pixels use glPolygonOffset

Depth-Cueing

glEnable (GL_FOG)

glFogi (GL_FOG_MODE,GL_LINEAR)

glFogf (GL_FOG_START, minDepth)

glFogf (GL_FOG_END, maxDepth)

Revisions


38/38

Revisions

Revision 1.2

Integrated BSP and Depth Buffer slides from Hodges and Kessler

Revision 1.3 - typos

Documents

ITCS 4120-Visible-Surface Detection.ppt