We present a study on sketch as input for modeling systems (i.e. sketch-based mod- eling, 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 Ra- dial 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 de- velop 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 mod- eling application, which successfully models Variational HRBF Implicit surfaces by interpolating the sketched curves (thus preserving the intended shape to be mod- eled).
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 im- plementing a pipeline tailored to use the developed theoretical framework.