pmr: point to mesh rendering, a feature-based approach tamal k. dey and james hudson...

PMR: Point to Mesh Rendering,PMR: Point to Mesh Rendering,A Feature-Based ApproachA Feature-Based Approach

Tamal K. Dey and James Hudson

{tamaldey,jhudson}@cis.ohio-state.eduhttp://www.cis.ohio-state.edu/~tamaldey

October 30, 2002

Department of Computer and Information ScienceThe Ohio State University

Department of Computer and Information Science

OverviewOverview

IntroductionAlgorithm: Two Stages

Preprocessing Viewing

ResultsConclusion


Hierarchy ConstructionHierarchy Construction

Points and triangles displayedFeature-dependent, not screen-spaceAdvantageous for large, flat areasGoals:

Quality at all viewing distances Adaptive display Adjustable speed vs. quality setting No input mesh needed


MotivationMotivationTriangles good for quality; points for speedDifference is subtle when far away

Point-based splatting

PMR

Zoom in on the nose...


Splatting vs. PMRSplatting vs. PMR

Point Splatting PMR

When zoomed-in, differences are more noticeable, especially at upper left edge of nose.


Our ApproachOur Approach

Utilizes hierarchy Contains Points and Triangles

Hierarchy: scale independent Depends on model's features

No surface mesh required More flexibility Simpler data structure


PreprocessingPreprocessingDecimate input where "redundant" points exist

Use features to determine thisThreshold guides levels of hierarchyNo new points added; only removal

= 0.2 = 0.3 = 0.4


Feature DetectionFeature DetectionWe 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 DetectionFeature DetectionDense point set: long, skinny Voronoi cellsCapture this via height and radius values

Pole vector = estimated normal (AB98) Height estimates distance to medial axis Radius estimates distance between neighbors


Feature DetectionFeature 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

radiusheight


Point HierarchyPoint HierarchyThe final point hierarchy contains

progressively fewer points

= 0.2 = 0.3 = 0.4


Triangle HierarchyTriangle HierarchyFor point p: We define umbrella of p

Umbrella = set of triangles incident on p and are dual to Voronoi edges intersecting tangent polygon


Triangle HierarchyTriangle Hierarchy

Result: progressively sparser triangle sets

= 0.2 = 0.3 = 0.4


Disk FileDisk FileFor each leaf, store to disk:

Points, estimated normals, hierarchy levelsUmbrella triangles per vertexUmbrella radii per vertexAverage umbrella radius for all points

Map file to memory when viewing


ViewingViewingMust 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 HierarchyChoice of HierarchyChoice 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 processIf too sparse: detail lost

User can trade speed for quality via scale factor

Just right Too sparseToo dense


Pixel vs. UmbrellaPixel 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 FactorScale FactorScale 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 TransitionScale Factor Transition

Need to slow transition between sparser levelsDifferences invisible when far away

=0.1 =0.3 =0.8 =1.0


ResultsResults

System used: Pentium 4, 1.7 Ghz, 2 GB RAM Matrox Millenium G450 graphics card Software-only OpenGL rendering


ResultsResults

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.


ResultsResults

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

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

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

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

Varying distances; Blue=triangles, Red=points


ResultsResultsDense level Sparse level


ResultsResults

Comparison of full-detail (=0) vs PMR

Full detail, 0.54 FPS PMR, 3.85 FPS


ResultsResultsComparison of full-detail vs PMR



ResultsResults

Dense level Sparse level

Factor=10.16 FPS

Factor=30.74 FPS

Factor=50.96 FPS


ResultsResults

DragonHappyBlade

DavidHeadStMatthew

437645542557882954

20006463382855

0.540.430.250.11

0.072

3.853.440.710.780.67

Object Vertices Full PMR

Frames per second. Full denotes the full(=0) mesh; PMR denotes the adaptive

hierarchy scheme with a factor of 5.


Preprocessing TimesPreprocessing Times

DragonHappyBlade

DavidHeadStMatthew

437645542557882954

20006463382855

03:5304:3609:0206:3626:38

97150238512479

Object Vertices Time Size (MB)

Note: Times are in Hours:Minutes.


ConclusionsConclusions

A hybrid rendering scheme Points and triangles employed User-adjustable error tolerance No input surface required

Future work Applications to volume rendering

pmr: point to mesh rendering, a feature-based approach tamal k. dey and james hudson...

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