Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision.

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Presentation transcript:

Manuel Mesters - Subdivision Surfaces computer graphics & visualization Seminar Computer Graphics Geometric representation and processing: Subdivision Surfaces

computer graphics & visualization Manuel Mesters - Subdivision Surfaces At a glance Refinement 1Refinement 2 Refinement ∞

computer graphics & visualization Manuel Mesters - Subdivision Surfaces At a glance

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Making of Geri‘s Game

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Geri’s Game - 1st animation using Subdivision Surfaces - Playground for new technologies - Best Animated Short (1997)

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Draft s of drawings

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Clay Models - Double Life Size Model: - Head - Hands

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Digitizing - Laserscanner -> Point Cloud

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Mesh - Point Cloud -> Mesh - Controls for facial movements (manual insertion)

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Animation Process - Using Pixar’s RenderMan: - Animate Mesh - Call Controls / Subdivide

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Cloth Dynamics - Dynamic flexible mesh - Energy functions - Many equations...

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Watch Geri’s Game

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision - Definition Subdivision defines a smooth curve or surface as the limit of a sequence of successive refinements

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision - Definition Subdivision defines a smooth curve or surface as the limit of a sequence of successive refinements - Start: Control Mesh - Process: Apply refinement rules (many times) - Result: Smooth curve/surface

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision Curve Start: Polygon Apply refinement rule Result: Smooth curve

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision Curve - Rules

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision Curve

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Different Algorithms - Different Results Loop Catmull-Clark Butterfly Doo-Sabin

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Different Algorithms - Different Results Loop Catmull-Clark Butterfly Doo-Sabin

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop Subdivision

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop Subdivision original vertex v3 v1v2 v4

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop Subdivision edge point (ep): constructed on each edge original vertex v3 v1v2 v4 ep

computer graphics & visualization Manuel Mesters - Subdivision Surfaces vertex point  constructed for each old (original) vertex Loop Subdivision edge point original vertex

computer graphics & visualization Manuel Mesters - Subdivision Surfaces vertex point: constructed for each old (original) vertex Loop Subdivision A given vertex has n neighbor vertices. The new vertex point: For n = 3 For n > 3 v v

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Loop - Local Subdivision - Exclude some edges from Subdivision - More details later...

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision FACE EDGE

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision FACE EDGE

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Catmull-Clark Subdivision FACE EDGE VERTEX

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Sharp creases - Subdivision produces smooth surfaces 1.Tag Edges as “sharp” or “not-sharp” During Subdivision, 2.if an edge is “sharp”, use sharp subdivision rules. 3.If an edge is “not-sharp”, use normal smooth subdivision rules.

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Infinitely Sharp Creases - Tag Control vertices and edges as sharp - Face points: same as smooth rule - Edge points: place at midpoint of edge - Vertex points - One sharp incident edge (dart): same as smooth rule - Two sharp edges (crease): (e 1 + 6v i + e 2 ) / 8 - Three or more sharp edges (corner): do not modify point

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Sharp rules FACE (unchanged) EDGE VERTEX crease dart corner >2 2 0,1 # adj. Sharp edges

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Semi-sharp creases 1.Tag Edges as “sharp” or “not-sharp” n = 0 : “not sharp” n > 0 : sharp During Subdivision, 2.if an edge is “sharp”, use sharp subdivision rules. Newly created edges, are assigned a sharpness of n-1. 3.If an edge is “not-sharp”, use normal smooth subdivision rules.

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Subdivision - Sharpness!

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Outline - Motivation: Geri’s Game - Introduction: Subdivision Basics - Loop Subdivision Surfaces - Catmull-Clark Subdivision Surfaces - Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary Take home message

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary Subdivision defines a smooth curve or surface as the limit of a sequence of successive refinements

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary - There are different Algorithms - Mesh Type - Rules

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary - Loop - Catmull-Clark

computer graphics & visualization Manuel Mesters - Subdivision Surfaces Summary - Subdivision - Standard rules -> smoothness - Additional rules -> sharpness - Sharpness parameter -> flexibility

computer graphics & visualization Manuel Mesters - Subdivision Surfaces The End Thank you for your attention