Preprint C131/2011
On Sketches for Modeling

Emilio Vital Brazil

**Keywords: **
sketch-based modeling; surfaces representation; warping field; image warping; implicit surface.

We present a study on sketch as input for modeling systems (i.e., sketch-based modeling, or SBM), focusing on mathematical representations for sketch-based modeling system.
The representation of the model plays a fundamental role in this problem, requiring the underlying representations to be specially tailored for use in SBM application.
We develop a sketch warping field which satisfies the hard constrains applied to RGBN images deformation.
This problem of ``how to deform an image using sketches'' is reformulated as ``how to model a warping field''.
Therefore we developed tools for sketch-based modeling to define warping fields using Hermite--Birkhoff Radial Basis Functions.
In addition to this, we also developed an application using these tools for warping RGBN images.
Prototype free-form SBM systems can also benefit from using implicit surfaces, which provide a compact, flexible, mathematically precise representation.
We develop a set of modeling operators suited to create Hermite samples (points and normals), which are interpolated by a Hermite Radial Basis Function, defining an implicit surface.
These operators are implemented in a sketch-based surface modeling application, which successfully models Variational HRBF Implicit surfaces by interpolating the sketched curves (thus preserving the intended shape to be modeled).
We introduce a novel mathematical representation for sketch-based modeling, abstracting main qualities desired for many SBM applications. We also developed a SBM system based on the proposed mathematical representation, effectively implementing a pipeline tailored to use the developed theoretical framework.