Discontinuity Edge Overdraw

Discontinuity Edge Overdraw

• Pedro V. Sander1

• Hugues Hoppe2

• John Snyder2

• Steven J. Gortler1

Aliasing in meshes

• Within triangles interiors (solved by mipmapping)
• Among triangles (‘small object problem’)
• At triangle edges (‘crawling jaggies’)

Our approach: only attack jaggies

• Basic algorithm:

• Render mesh.
• Identify ‘troublesome’ edges.
• Render troublesome edges as antialiased lines.

Edge overdraw demo

Previous work: Supersampling

• In the limit, solves all aliasing artifacts.

• However, higher rendering cost.

• e.g. 2x2:

Previous work: Edge Antialiasing

• Crow ‘77 Scanline renderer

• Bloomenthal ‘83 Image post-process

• OpenGL “polygon antialiasing” Requires special hardware & front-to-back rendering

Previous work: edge overdraw

• Sauer et al ‘99 2-pass software rendering. Requires polygon sorting. Only silhouettes & brute-force search.

• Wimmer ‘97 Requires polygon sorting.

• Donovan ‘99 framebuffer-to-texture copy

Our contribution

• Use ordinary line antialiasing.

• Reduce crawling jaggies, while maintaining:

• Temporal smoothness
• Spatial consistency
• Spatial sharpness

• Fast detection of discontinuity edges

Discontinuity edges

• Dynamic discontinuity edges

• Silhouette edges

• Static discontinuity edges (“sharp edges”)

• Surface boundaries
• Material boundaries
• Creases

Discontinuity edges

• Dynamic discontinuity edges

• Silhouette edges

• Static discontinuity edges (“sharp edges”)

• Surface boundaries
• Material boundaries
• Creases

Discontinuity edges

• Dynamic discontinuity edges

• Silhouette edges

• Static discontinuity edges (“sharp edges”)

• Surface boundaries
• Material boundaries
• Creases

Silhouette extraction

• [Sander et al 2000] Build silhouette tree during preprocess. Each node contains:

• Set of edges.
• Conservative test.

• If test passes, then sub-tree is skipped.

Silhouette extraction tree

• Leave out:

• Sharp edges (~10%)
• Concave edges (~40%)

• Reduces silhouette extraction cost by half.

Shading the edges

• Silhouette edge: Use the frontface shading attributes.

• Frontfacing edge: Combine between the two face shading attributes (avoids popping).

Temporal smoothness: sharp edge combining

• d1 = dot(e.f1,viewdir)

• d2 = dot(e.f2,viewdir)

• β = d1 / (d1 + d2)

How to combine

• Two approaches:

• Edge blended-draw

• Blend face attributes and render once.
• Catches occasional highlight.
• Requires multitexturing.

• Edge double-draw

• Render twice (once for each face’s attributes).
• Requires rendering more edges.
• Causes slight discontinuity at β==0.5

Drawbacks of combining

• Slower.

• Blurs discontinuities too much.

Spatial sharpness: asymmetric edge combining

• We combine as little as possible.

• We use an asymmetric ramp.

• Most of the time use “default” face.

Sharp edge orientation

• For each edge, determine a default face.

• Consistent through sharp edge paths.

Spatial consistency: sharp edge orientation

• Traverse sharp edge paths setting consistent edge orientation. Stops at:

• Dead ends
• Loop
• Multiple sharp edge “crossings”

Discontinuity edge sorting

• For best results, sort edges from back to front.

• No need to sort edges that are far from the silhouette.

Sorting demo

Final algorithm (Preprocess)

• Collect sharp edges in mesh.

• Assign them consistent orientation.

• Construct silhouette extraction tree (exclude sharp and concave edges).

Final algorithm (Runtime)

• render mesh;

• extract silhouette;

• for silhouette edge e

• render e using frontface shading attributes

• for sharp edge e

• compute e.β;

• if e.β < 0.9 then

• render e using default face shading attributes

• else

• render e by combining shading attributes

Final algorithm (modifications for sorting)

• Render sharp edges for which 0.1 < e.β < 0.9

• Place other sharp edges in a set S.

• Place silhouette edges in S.

• Sort S back-to-front.

• Render edges in S.

Rendering Details

• Render triangles:

• standard z-buffer settings.
• GL_POLYGON_OFFSET_FILL.

• Render edges (as antialiased lines):

• OVER operation.
• z-buffer writes disabled.

Timings

Timings

Timings

Comparison with Supersampling

Demos

Limitations

• It ‘thickens’ the model a bit (mostly visible at low resolutions).

• Memory overhead.

Summary

• Edge overdraw is a simple, efficient alternative for eliminating jaggies.

• Designed to reduce spatial aliasing.

• But, also reduces crawling jaggies.

• Future work: Extracting silhouettes on dynamic meshes.

The end