Transcript Introductory slides presented by Ming-Hay

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
Motivation
2 groups of tools for free-from design
Research tools based on sketching
-hide subtleties of surface description from user
-difficult to refine the design or re-use existing designs
Goal
+
=
Related Work
3D Paint
1990
Related Work
3D Paint
1990
SKETCH
1996
Related Work
3D Paint
1990
SKETCH
1996
Teddy
1999, 2003
Related Work
3D Paint
1990
SKETCH
1996
Teddy
1999, 2003
ShapeShop
2005
Related Work
3D Paint
1990
SKETCH
1996
Teddy
1999, 2003
ShapeShop
2005
SmoothSketch
2006
Related Work
3D Paint
1990
SKETCH
1996
Teddy
1999, 2003
ShapeShop
2005
SmoothSketch
2006
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
Minimize:
difference
between
resulting
coordinates
original
coordinates
+
positional
constraints
+
ensure
smoothly
varying
rotations
along the
curve
Note: all 4 terms are weighted to yield pleasing results
+
rotational
constraints
Conceptual Math
Minimize:
difference between
resulting coordinates
original coordinates
+
positional constraints
+
ensure smoothly varying
rotations along the curve
+
rotational constraints
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
Minimize:
difference between
resulting coordinates
original coordinates
+
positional constraints
+
ensure smoothly varying
rotations along the curve
+
rotational constraints
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