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PMR: Point to Mesh Rendering, A Feature-Based Approach. Tamal K. Dey and James Hudson {tamaldey,jhudson}@cis.ohio-state.edu http://www.cis.ohio-state.edu/~tamaldey October 30, 2002 Department of Computer and Information Science The Ohio State University. Overview. Introduction

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slide1

PMR: Point to Mesh Rendering,

A Feature-Based Approach

Tamal K. Dey and James Hudson

{tamaldey,jhudson}@cis.ohio-state.edu

http://www.cis.ohio-state.edu/~tamaldey

October 30, 2002

Department of Computer and Information Science

The Ohio State University

overview
Overview
  • Introduction
  • Algorithm: Two Stages
    • Preprocessing
    • Viewing
  • Results
  • Conclusion
hierarchy construction
Hierarchy Construction
  • Points and triangles displayed
  • Feature-dependent, not screen-space
  • Advantageous for large, flat areas
  • Goals:
    • Quality at all viewing distances
    • Adaptive display
    • Adjustable speed vs. quality setting
    • No input mesh needed
motivation
Motivation
  • Triangles good for quality; points for speed
  • Difference is subtle when far away

Point-based splatting

PMR

Zoom in on the nose...

splatting vs pmr
Splatting vs. PMR

PMR

Point Splatting

When zoomed-in, differences are more noticeable,

especially at upper left edge of nose.

our approach
Our Approach
  • Utilizes hierarchy
    • Contains Points and Triangles
  • Hierarchy: scale independent
    • Depends on model\'s features
  • No surface mesh required
    • More flexibility
    • Simpler data structure
preprocessing
Preprocessing
  • Decimate input where "redundant" points exist
    • Use features to determine this
  • Threshold guides levels of hierarchy
  • No new points added; only removal

t = 0.2

t = 0.3

t = 0.4

feature detection
Feature Detection
  • We use Voronoi diagram to detect features
    • Can be costly: time + memory
    • Solution: Use octree decomposition of space
    • Maximum of 12000 points per node useful
feature detection1
Feature Detection
  • Dense point set: long, skinny Voronoi cells
  • Capture this via height and radius values
    • Pole vector = estimated normal (AB98)
    • Height estimates distance to medial axis
    • Radius estimates distance between neighbors
feature detection2
Feature Detection
  • Decimation is based on ratio
  • Remove all points with ratio <  (threshold)
    • Point with small ratio must have close neighbors
    • Repeat for several values of  to give hierarchy
  • We use values from =0.1 to =1.0
  • Each leaf node N is processed individually

radius

height

point hierarchy
Point Hierarchy
  • The final point hierarchy contains progressively fewer points

t = 0.2

t = 0.3

t = 0.4

triangle hierarchy
Triangle Hierarchy
  • For point p: We define umbrella of p
    • Umbrella = set of triangles incident on p and are dual to Voronoi edges intersecting tangent polygon
triangle hierarchy1
Triangle Hierarchy
  • Result: progressively sparser triangle sets

t = 0.2

t = 0.3

t = 0.4

disk file
Disk File
  • For each leaf, store to disk:
    • Points, estimated normals, hierarchy levels
      • Umbrella triangles per vertex
      • Umbrella radii per vertex
      • Average umbrella radius for all points
  • Map file to memory when viewing
viewing
Viewing
  • Must determine pixel size
  • Done once per leaf node only
    • Closest corner point = the one to use
    • Project two world space points to screen
    • Gives ratio of world space to screen space
    • Conservative estimate
choice of hierarchy
Choice of Hierarchy
  • Choice of hierarchy level made once per leaf
    • Metric: Use average umbrella size
    • Try to match umbrella size to pixel size
      • If too dense: more points to process
      • If too sparse: detail lost
    • User can trade speed for quality via scale factor

Too dense

Just right

Too sparse

pixel vs umbrella
Pixel vs. Umbrella
  • For each point: choose: Pixel vs. Umbrella
    • Compare umbrella radius to (pixel size)  (scale factor)
      • scale factor allows trade-off of quality vs. speed
    • Choose umbrella only if size too big; else choose pixel
    • Conservative estimation performed

Can draw as pixel

Must draw as triangles

scale factor
Scale Factor
  • Scale factor allows modification of calculation
    • If scale factor larger, calculations treat pixels as larger
    • Selects sparser hierarchy level
    • Can modify scale factor to selectively slow transition between levels, especially at high levels of decimation
scale factor transition
Scale Factor Transition
  • Need to slow transition between sparser levels
  • Differences invisible when far away

t=0.1 t=0.3 t=0.8 t=1.0

results
Results
  • System used:
    • Pentium 4, 1.7 Ghz, 2 GB RAM
    • Matrox Millenium G450 graphics card
    • Software-only OpenGL rendering
results1
Results
  • We varied  from 0.1 to 1.0, steps of 0.1
    • If  is large (1.0), features are lost
    • Varying the scale factor
      • If pixel size is 2 world space units, begin altering
      • Reduce factor linearly until pixel is 4 world space units
      • If pixel is 4 or more units: factor is equal to 1
      • Net effect: as decimation becomes sparser, slow the transition between levels.
results2
Results

Varying distances; Blue=triangles, Red=points

0.11 FPS, 4.5M tris, 0 points (Full detail)

0.65 FPS, 650K tris, 377K points (PMR)

0.77 FPS, 670K tris,48K points (PMR)

1.65 FPS, 215K tris, 204K points (PMR)

results3
Results

Sparse level

Dense level

results4
Results
  • Comparison of full-detail (t=0) vs PMR

Full detail, 0.54 FPS

PMR, 3.85 FPS

results5
Results
  • Comparison of full-detail vs PMR

Full detail, 0.25 FPS

PMR, 0.71 FPS

results6
Results
  • Comparison of full-detail vs PMR

Full detail, 0.11 FPS

PMR, 0.61 FPS

results7
Results

Sparse level

Dense level

Factor=1

0.16 FPS

Factor=3

0.74 FPS

Factor=5

0.96 FPS

results8
Results

Vertices

Full

PMR

Object

Dragon

Happy

Blade

DavidHead

StMatthew

437645

542557

882954

2000646

3382855

0.54

0.43

0.25

0.11

0.072

3.85

3.44

0.71

0.78

0.67

Frames per second. Full denotes the full

(t=0) mesh; PMR denotes the adaptive

hierarchy scheme with a factor of 5.

preprocessing times

Vertices

Time

Size (MB)

Object

Dragon

Happy

Blade

DavidHead

StMatthew

437645

542557

882954

2000646

3382855

03:53

04:36

09:02

06:36

26:38

97

150

238

512

479

Preprocessing Times

Note: Times are in Hours:Minutes.

conclusions
Conclusions
  • A hybrid rendering scheme
    • Points and triangles employed
    • User-adjustable error tolerance
    • No input surface required
  • Future work
    • Applications to volume rendering
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