Visible Surface Detection (Chapt. 15 in FVD, Chapt. 13 in Hearn - - PowerPoint PPT Presentation

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Visible Surface Detection

(Chapt. 15 in FVD, Chapt. 13 in Hearn & Baker)

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• Given a set of 3D objects and a viewing specifications, determine which

lines or surfaces of the objects should be visible.

• A surface might be occluded by other objects or by the same object

(self occlusion)

• Two main approaches:

– Image-precision algorithms: determine what is visible at each pixel. – Object-precision algorithms: determine which parts of each object are visible.

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Hidden Lines Removal

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Coherence

• Most methods use coherence features in the surface:

– Object coherence. – Face coherence. – Edge coherence. – Scan-line coherence. – Depth coherence. – Frame coherence.

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Back-face Culling

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Back-face Culling

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Back-face Culling

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Back-face Culling

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Depth Sort (Painter Algorithm)

• Sort all of the polygons in the scene by their depth.
• Draw them back to front.
• Question: Does a depth ordering always exist?
• Answer: Unfortunately, no!
• For polygons with constant Z value, this sorting clearly works.

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Z x x x

• Given two polygons P and Q, an order may

be determined between them, if at least

• ne of the following holds:
• Z values of P and Q do not overlap.
• The bounding rectangle in the x,y plane

for P and Q do not overlap.

• P is totally on one side of Q’s plane.
• Q is totally on one side of P’s plane.

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P is totally on one side of Q’s plane

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• How to quickly determine which polygon to draw

first?

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• How to quickly determine which polygon to draw

first?

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• How to quickly determine which polygon to draw

first? Simply sorting back-to-front all polygons based

• n their mid-points doesn’t always work

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• In addition to the frame buffer (keeping the pixel values), keep a Z-

buffer containing the depth value of each pixel.

• Surfaces are scan-converted in an arbitrary order. For each pixel

(x,y), the Z-value is computed as well. The (x,y) pixel is overwritten

• nly if its Z-values is closer to the viewing plane than the one

already written at this location.

Z-buffer Algorithm

Penetrating Triangle

Z-buffer Algorithm

Incremental Scanline

         C C D By Ax z D Cz By Ax , ) (

x C A z z C x x A z z C D Bj Ax C D Bj Ax z z                ) ( ) ( ) ( ) (

1 1 1 1 1

, since x = 1,

C A z z  

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Scan-line Algorithm

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Scan-line Algorithm

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BSP-Tree Algorithm

Virtual Reality Applications

 The user “walks” interactively in a virtual polygonal environment.

Examples: model of a city, museum, mall, architectural design

 Large and complex - hundreds thousands or even millions of

polygons The goal: to render an updated image for each view point and for each view direction in interactive frame rate

The Visibility Problem

Selecting the (exact?) set

• f polygons from the

model which are visible from a given viewpoint

The Visibility Problem is important

Average number of polygons, visible from a viewpoint, is much smaller than the model size

Indoor scene

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Oil-tanker ship

Copying Machine

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Outdoor scenes

The Visibility Problem is not easy... A small change of the viewpoint might causes large changes in the visibility

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The Visibility Problem is not easy...

A small change of the viewpoint might causes large changes in the visibility

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Close details Far details

Culling

A primitive can be culled by: View Frustum Culling Occlusion Culling Back Face Culling

Avoid processing polygons which contribute nothing to the rendered image

View Frustum Culling

Remove primitives entirely

• utside the

field of view Modify remaining primitives so as to pass through only the portion inside view frustum Pass through scene primitives entirely inside frustum

Backface Culling

N N N

> 90 > 90 < 90

cull away polygons whose front sides face away from the viewer

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Occlusion Culling

Cull the polygons occluded by other objects in the scene Very effective in densely

• ccluded scenes

Global: involves interrelation between the polygons

Visibility Culling

View-frustum culling Back-face culling Occlusion culling

View Frustum

Hidden Surface Removal

Polygons overlap, so somehow, we must determine which portion of each polygon to draw (is visible to the eye)

Output sensitive algorithms

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Visibility in real-time rendering

• interactively walk through a large model
• large model  millions of polygons  acceleration

necessary (e.g., visibility)

Exact Visibility Approximate Visibility

Includes all the polygons which are at least partially visible and only these polygons. Includes most of the visible polygons plus maybe some hidden ones.

May classify invisible object as visible but may never classify visible object as invisible

Conservative Visibility

Includes at least all the visible objects plus maybe some additional invisible objects

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What is visible? What is Occluded?

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From this point only the red objects are visible

Point Visibility

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From this cell the red objects are visible as well as orange ones

Cell Visibility

Compute the set of all polygons visible from every possible viewpoint from a region (view-cell)

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The Aspect Graph

Isomorphic graphs

The Aspect Graph

 ISG – Image Structure graph

The planner graph, defined by the outlines

• f an image, created by projection of a

polyhedral object, in a certain view direction

The Aspect Graph (Cont.)

 Aspect

Two different view directions of an object have the same aspect iff the corresponding Image Structure graphs are isomorphic

The Aspect Graph (Cont.)

 VSP – Visibility Space Partition

 Partitioning the viewspace into maximal connected

regions in which the viewpoints have the same view

• r aspect

 Visual Event

A boundary of a VSP region called a VE for it marks a change in visibility

The Aspect Graph (Cont.)

 Aspect Graph

A vertex for each region of the VSP An edge connecting adjacent regions

Regions of the VSP are not maximal but maximal connected regions.

Aspect graph (Cont.)

2 polygons - 12 aspect regions

Aspect graph (Cont.)

3 polygons - “many” aspect regions

Different aspect regions can have equal sets of visible polygons

Supporting & Separating Planes

3 2 2 1 1 Supporting Separating Supporting Separating A T is not occluded in region 1 T is partially occluded in region 2 T is completely occluded in region 3 A - occluder T - occludee T

Visibility from the light source

The Art Gallery Problem

See: ftp://ftp.math.tau.ac.il/pub/~daniel/pg99.pdf

Classification of visibility algorithms

• Exact vs. Approximated
• Conservative vs. Exact
• Precomputed vs. Online
• Point vs. Region
• Image space vs. Object space
• Software vs. Hardware
• Dynamic vs. Static scenes