Motivation 2 groups of tools for free-from design Images credits go out to the FiberMesh SIGGRAPH presentation and other sources courtesy of Google

Motivation 2 groups of tools for free-from design Maya/3ds Max -user defines control points to add detail -difficult for inexperienced user

Research tools based on sketching -hide subtleties of surface description from user -difficult to refine the design or re-use existing designs Motivation 2 groups of tools for free-from design

Goal + =

Related Work 3D Paint 1990

Related Work SKETCH D Paint

Related Work Teddy 1999, 2003 SKETCH D Paint 1990

Related Work ShapeShop , 2003 SKETCH D Paint 1990 Teddy

Related Work SmoothSketch 2006 ShapeShop 1999, 2003 SKETCH D Paint 1990 Teddy 2005

Related Work SmoothSketch 2006 ShapeShop 2005 Teddy 1999, 2003 SKETCH D Paint 1990 Spore 2007

PriMo vs FiberMesh Excellent for simulation of physically plausible deformations Not suitable for use as a curve editing tool

Curve Deformation Algorithm Employ a detail-preserving deformation method -Represent the geometry in differential coordinates -Solve a sequence of least-squares problems to generate the final result

Conceptual Math Note: all 4 terms are weighted to yield pleasing results difference between resulting coordinates original coordinates positional constraints ensure smoothly varying rotations along the curve rotational constraints Minimize: +++

Conceptual Math difference between resulting coordinates original coordinates positional constraints ensure smoothly varying rotations along the curve rotational constraints Minimize: +++

Conceptual Math The rotations are currently: -Unconstrained and may cause shearing, stretching, and scaling (undesirable) -Not linear

Solution Use a linearized rotation matrix to represent small rotations

Solution difference between resulting coordinates original coordinates positional constraints ensure smoothly varying rotations along the curve rotational constraints Minimize: +++

Last Outstanding Problem Choosing differential coordinates: Two options -first order -second order

Second Order Second order is the popular choice for surface deformation, but is almost always degenerate in a smooth curve

First Order First order always has a certain length in an approximate sample curve Good reliable guide for estimating rotations Causes C1 discontinuities

Solution Use First order for iterative process Use Second order for computing the final vertex positions using estimated rotations