Three-Dimensional Graphics IV - University of Oulujiechen/Course/Lecture9/CG_3d_4-C8.pdf ·...

C O M P U T E R G R A P H I C SC O M P U T E R G R A P H I C S

Computer GraphicsComputer Graphics

Three-Dimensional Graphics IV

Guoying Zhao 1 / 61Guoying Zhao 1 / 61


• Hidden Surface Removal• Hidden Surface Removal

• Polygon Clipping



S fHidden Surface Removal


C O M P U T E R G R A P H I C S

Vi ibl S f D t i tiVisible Surface Determination

• DefinitionDefinition– Given a set of 3-D objects and a view

specification (camera) determine whichspecification (camera), determine which lines or surfaces of the object are visible

’ l d VSD t ti• you’ve already seen a VSD step…computing smallest non-negative depth value along a ray

• why might objects not be visible? occlusion vs• why might objects not be visible? occlusion vs. clipping

• clipping is one object at a time while occlusion• clipping is one object at a time while occlusion is global

– Also called Hidden Surface Removal (HSR)Guoying Zhao 4 / 61

– Also called Hidden Surface Removal (HSR)

C O M P U T E R G R A P H I C S

Photorealistic Image

Guoying Zhao 5 / 61


GraphicsGraphics Pipeline

3D d l i ld di t

Visible surface detection and rendering process also take place in the pipeline

Geometric transformation in 3D space

3D model in world coordinates

Rasterization

P j i

3D model in world coordinates

2D i iProjection

2D graphics in projection coordinates

2D image in viewport coordinates

Window clipping

Clipped 2D graphics in window coordinates

Transformation from window to viewport

pp g p

Guoying Zhao 6 / 61Guoying Zhao 6 / 612D graphics in viewport coordinates


Visible Surface Determination

• Why to do it?• Why to do it?– Avoiding ambiguity– Improving rendering rates



A idi bi itAvoiding ambiguity



I i d i tImproving rendering rates



Hidden Surface Removal Methods• Object space algorithms• Object-space algorithms

Area-Subdivision MethodDepth Sorting Method

• Image-space algorithmsRay Casting MethodZ-buffer



Hidden Surface Removal

Obj t h i i t ti• Object-space approach: use pairwise testing between polygons (objects)

partially obscuring can draw independently

• Worst case complexity O(n2) for n polygons

p y obscu g c d w depe de y


Worst case complexity O(n ) for n polygons


Area-Subdivision Method

• It’s applied by successively dividing the total viewing area into smaller and smaller rectangles until each small area is the projection of part of a single visible


small area is the projection of part of a single visible surface or no surface at all.





Possible relationships between polygon surfaces and a rectangular

areaarea– surrounding– overlapping– inside

t id– outside2

4

1

3

1




• No further subdivisions until:• No further subdivisions until:– All polygons are outside the area– Only one inside, overlapping, or

surrounding polygon is in the area– A surrounding polygon obscures all other

surfaces within the area boundariessu aces t t e a ea bou da es




F i d ith l ti 2N*2N ft N• For a window with resolution 2N*2N，after N divisions, the obtained sub-window is same to one pixel


one pixel.


Depth Sorting Method


Painter’s Method


Painter’s Algorithm

• Render polygons a back to front order so that• Render polygons a back to front order so that polygons behind others are simply painted overover

B behind A as seen by viewer Fill B then A



Depth Sort

• Requires ordering of polygons first• Requires ordering of polygons first – O(n log n) calculation for ordering– Not every polygon is either in front or

behind all other polygons

• Order polygons and deal withOrder polygons and deal with easy cases first, harder later

Polygons sorted by distance from COP



Easy Cases

• A lies behind all other polygons– Can render

• Polygons overlap in z but not in either x or y– Can render independently



Hard Cases

Overlap in all directionscyclic overlap

But one is fully on one side of the other

penetration


p


Back-Face Removal (Culling)Back Face Removal (Culling)

θ•face is visible iff 90 ≥ θ ≥ -90equivalently cos θ ≥ 0equivalently cos θ ≥ 0or v • n ≥ 0

I O GL i l bl lli•In OpenGL we can simply enable cullingbut may not work correctly if we have nonconvex objects



Image Space Approach

• Look at each projector (nm for an n x m• Look at each projector (nm for an n x mframe buffer) and find closest of k

lpolygons• Complexity O(nmk)Complexity O(nmk)• Ray tracing • z-buffer



Ray Casting Method

• Cast a ray along the line of sight from a y g gpixel position through a scene

PixelPixel



z-Buffer Algorithm

• Use a buffer called the z or depth buffer to• Use a buffer called the z or depth buffer to store the depth of the closest object at each pixel found so farpixel found so far

• As we render each polygon, compare the depth of each pixel to depth in z bufferof each pixel to depth in z buffer

• If less, place shade of pixel in color buffer and update z bufferupdate z buffer



Frame Buffer and Depth Buffer

Screen Frame buffer Depth Buffer

Color value Depth valueGuoying Zhao 26 / 61Guoying Zhao 26 / 61

Color value Depth value


Z-buffer Method

y

x

Guoying Zhao 27 / 61Guoying Zhao 27 / 61Z


Z-buffer Method

yy

x

x ZGuoying Zhao 28 / 61Guoying Zhao 28 / 61

x Z


Z-buffer Method

y

x



Z b ff M h dZ-buffer Method

Framebuffer Depth Buffer

-5 -5 -5 -5 -5 -5 -5 -55 5 5 5 5 5 5 5-5 -5 -5 -5 -5 -5 -5 -5

-5 -5 -5 -5 -5 -5 -5 -5-5 -5 -5 -5 -5 -5 -5 -5-5 -5 -5 -5 -5 -5 -5 -55 5 5 5 5 5 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 5 5 5 5 5 5-5 -5 -5 -5 -5 -5 -5 -5

-5 -5 -5 -5 -5 -5 -5 -5-5 -5 -5 -5 -5 -5 -5 -5-5 -5 -5 -5 -5 -5 -5 -55 5 5 5 5 5 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5



Z-buffer Method

y

x



Z-buffer Method

yy

x

x ZGuoying Zhao 34 / 61Guoying Zhao 34 / 61

x Zv



Frame buffer Depth Buffer

-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 0 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 0 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 0 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 0 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 0 -1 -2 -5-5 -5 -1 -1 -1 -1 -5 -5-5 -5 -1 -1 -1 -1 -5 -55 5 1 1 1 1 5 5-5 -5 -5 -5 -5 -5 -5 -5





-5 -5 -5 -5 -5 -5 -5 -55 5 11 1 1 5 5-5 -5 -1-1 -1 -1 -5 -5

-5 -5 2 1 0 -1 -2 -5-5 -5 -1 -5-5 -5 -1 -1 -1 -1 -5 -5

2 1 0 -25 5 1 1 1 1 5 5

-5 -5 -5 -5 -5 -5 -5 -5




y

x



Efficiency

• If we work scan line by scan line as we• If we work scan line by scan line as we move across a scan line, the depth h i fchanges satisfy aΔx+bΔy+cΔz=0

Along scan line Δy = 0Δz = - Δxa

c

In screen space Δx = 1Guoying Zhao 47 / 61Guoying Zhao 47 / 61

47

p


Scan-Line Algorithm

• Can combine shading and hsr through• Can combine shading and hsr through scan line algorithm

scan line i: no need for depth information, can only be in noyor one polygon

scan line j: need depth information only when ininformation only when inmore than one polygon



Implementation

• Need a data structure to store• Need a data structure to store– Flag for each polygon (inside/outside)– Incremental structure for scan lines that

stores which edges are encountered – Parameters for planes



Visibility Testing

• In many realtime applications such as games we• In many realtime applications, such as games, we want to eliminate as many objects as possible within the applicationpp– Reduce burden on pipeline– Reduce traffic on bus

• Partition space with Binary Spatial Partition (BSP) Tree



Simple Example

consider 6 parallel polygons

top view

The plane of A separates B and C from D, E and F



BSP Tree

• Can continue recursively• Can continue recursively – Plane of C separates B from A– Plane of D separates E and F

• Can put this information in a BSP treeCan put this information in a BSP tree– Use for visibility and occlusion testing



Clipping



Polygon Clipping

• Not as simple as line segment clipping• Not as simple as line segment clipping– Clipping a line segment yields at most one

li tline segment– Clipping a polygon can yield multiple

polygons

• However, clipping a convex polygon can yield at most one other pol gon


at most one other polygon


Tessellation and ConvexityTessellation and Convexity

• One strategy is to replace nonconvex• One strategy is to replace nonconvex (concave) polygons with a set of triangular polygons (a tessellation)polygons (a tessellation)

• Also makes fill easierT ll ti d i GLU lib• Tessellation code in GLU library



Clipping as a Black Box

• Can consider line segment clipping as a• Can consider line segment clipping as a process that takes in two vertices and

d i h i hproduces either no vertices or the vertices of a clipped line segmentg



Pipeline Clipping of Line SegmentsPipeline Clipping of Line Segments

• Clipping against each side of window is• Clipping against each side of window is independent of other sides– Can use four independent clippers in a

pipeline



Pipeline Clipping of PolygonsPipeline Clipping of Polygons

• Three dimensions: add front and back clippersThree dimensions: add front and back clippers• Strategy used in SGI Geometry Engine• Small increase in latency• Small increase in latency



Bounding Boxes

• Rather than doing clipping on a complex• Rather than doing clipping on a complex polygon, we can use an axis-aligned bounding box or extentbox or extent– Smallest rectangle aligned with axes that

encloses the polygonencloses the polygon– Simple to compute: max and min of x and y



Bounding boxes

Can usually determine accept/rejectCan usually determine accept/reject based only on bounding box

reject

accept

requires detailedclipping



Clipping and Visibility

• Clipping has much in common with• Clipping has much in common with hidden-surface removal

• In both cases, we are trying to remove objects that are not visible to theobjects that are not visible to the cameraOft i ibilit l i• Often we can use visibility or occlusion testing early in the process to eliminate as many polygons as possible before going through the entire pipeline


g g g p p

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