Real-Time Rendering POLYGONAL TECHNIQUES Lecture 05 Marina Gavrilova

Brief Outline Surface Geometry Tessellation Shading Problem Edge Crack Consolidation Mesh Simplification

Geometric Representation 3D objects are usually represented as geometric simplices (i.e. Triangles) Set of vertices (0-simplices) Set of Edges (1-simplices) Set of Triangles (2-simplices) Surface normal for each triangle Texture component and associated UV coordinate Shading and lighting parameters Object surface properties

Object representation 3D

Tessellation The process of splitting a polygon into smaller pieces (usually triangles) Types: Regular tessellation Convex tessallation Triangle fan tessalation Regular triangle tessallation

Smooth Shading Problem Occur during triangulation Choice of diagonal can effect shading Fixed diagonal division creates visual artifact Triangulation may create incorrect texture Quad CorrectIncorrect Visual Artifact Correct

Solution to Smooth Shading Problem Carefully choose diagonal Choose shortest diagonal Lit-quads: choose shortest color difference diagonal Terrain models: Maximize minimum angle Texture problem: Further tessellate the object Use different Texture Coordinate interpolation

Edge Cracking and Repair Occurs in NURBS, Multiple LOD When SPLINE surfaces meet, border mismatch and cracks are apparent ROAM and PM with multiple LOD: Occurs between primitives of different LOD T-vertices creates cracks Solution: Edge-stitching  add aditional edges Potential side-effect: Thin triangles (visual artifact) Solution: Use more sophisticated split and crack repair scheme Repairing cracks

Consolidation Processed after the tessellation phase Consolidation: Finding and adjusting links between tessellated objects Form a polygonal mesh (i.e. triangle mesh) Perform triangle stripping Solid objects or manifolds can facilitate culling techniques Face Orientation and normal  adjust all face-vertex order to either of CW or CCW, Normal in the right direction

General Approach to Consolidation Form Vertex-edge-face for all polygons and sort them Compute intersection and seam and determine solidity Correct orientation (direction of normal) of each face Normal must point Outward direction for a solid object Find smoothing groups and compute vertex normal Find boundaries Create Polygonal meshes

Mesh Simplification Use less number of triangles to render an object Mesh simplification Multiple LOD Progressive meshes: Error metric or Energy function Two operations: vertex split or edge collapse Apply refinements to minimize energy function

View-Dependent Refinement of Progressive Meshes Hugues Hoppe Microsoft Research SIGGRAPH 97

View-dependent LOD 29,400 faces different LOD’s coexist over surface

base mesh original mesh 150 M0M0M0M0 M1M1M1M1 152 Review of progressive meshes … M 175 … 50013,546 MnMnMnMn vlvlvlvl vrvrvrvr vuvuvuvu vtvtvtvt vsvsvsvs vlvlvlvl vrvrvrvr edge collapse vertex split

150 M0M0M0M0 M1M1M1M1 vspl The PM representation M … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 M0M0M0M0 MnMnMnMn MiMiMiMi MnMnMnMn

v2v2v2v2 Vertex hierarchy vspl 0 M0M0M0M0 vspl 1 vspl 2 vspl 3 vspl 4 vspl 5 v1v1v1v1 v3v3v3v3 M0M0M0M0 v 10 v 11 vspl 3 v1v1v1v1 v2v2v2v2 v4v4v4v4 v5v5v5v5 vspl 0 v8v8v8v8 v9v9v9v9 vspl 2 v3v3v3v3 v6v6v6v6 v7v7v7v7 vspl 1 v5v5v5v5 v 12 v 13 vspl 4 v 10 vspl 5 v 14 v 15 v6v6v6v6 PM: MnMnMnMn [Xia & Varshney 96] M0M0M0M0

ICCSA 2004 GTVIS: Fast and Efficient Rendering System for Real- Time Terrain Visualization Russel A. Apu, Marina L. Gavrilova Department of Computer Science University of Calgary

Understanding Height Fields DEM: Digital Elevation Model Contains only relative Height Regular interval Pixel color determine height Discrete resolution

ROAM: Real-time Optimally Adapting Mesh Quad Tree Triangle BIN Tree No cracks Reversible Efficient Adaptive Developed by Mark Duchaineau, Lawrence Livermore National Laboratory

Improvements over Original ROAM Scheme Preprocessing DEM image Smoothing Techniques Texturing Amortized refinement Very efficient Higher Frame Rate (45FPS) Continuity: Geo-morph sequence Less variation in frame rate

Proposed Priority Function for Split Queue Determines Refinement Distribute LOD to preferred area Can be changed f=face, C=Camera U=Uniformity F=Frustum priority D=Curvature priority P=Distance priority DET=Curvature (preprocessed) Lev(f)=Subdivision level of face f

Speeding up the process Amortizing refinement Updating the Split queue over multiple frames Allow split queue (heap) to degenerate Refine integrity using error threshold test Re-generate queue after constant number of frames Dramatic gain in speed

Maintaining Degenerated S-Queue

Understanding Geo-Morph Smooth interpolation of vertex over subdivision Requires maintenance of one additional queue (G-queue)

Smoothing Compute face normal Compute vertex normal Local computation of normal during refinement (Geo-Morph) Apply vertex normal when rendering Advanced shading: Linear combination of face and vertex normal (Hybrid)

Result with Texturing

End of Lecture 05 Questions?