Interactive decal compositing with discrete exponential maps

Abstract

A method is described for texturing surfaces using decals, images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O(N log N ) discrete approximation to the exponential map which requires only a single additional step in Dijkstra's graph-distance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/feature-matching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.

Particle-based parallel fluid simulation in three-dimensional scene with implicit surfaces

“…One study concerning a benchmark for shape reconstruction provides a thorough review of implicit surface modeling techniques [13]. Implicit representation is also useful for interactive shape modeling with user manipulation [14,15]. The functions obtained using the abovementioned shape modeling techniques can be converted approximately to a set of piecewise polynomials for efficient visualization [16].…”

Direct blue noise resampling of meshes of arbitrary topology

“…As this tool is based on the exponential maps technique [29] to compute inter-sample distances, measurement bias may occur in bumpy or sharp areas like corners or feature lines. To overcome this problem, and to take advantage of our discrete setting, we introduced in this analysis tool the Dijkstra's algorithm to compute more accurately the power spectra, and thus to analyze more precisely the sampling patterns.…”

“…cosinus function) to assess various sampling patterns. This method uses a geodesic computation method based on decals [29], that locally computes a parameterization from each sample to its neighbor ones. This parameterization is used to compute the geodesic distances between samples afterwards.…”

“…During our experimentations, and after several tests and an in-depth study of this tool, we observed that the discrete exponential maps [29] used to compute the local parameterization around each sample and consequently the geodesic distances between samples may be not convenient for complex shapes, in particular with sharp features and/or of high genus.…”

Connecting geodesics on smooth surfaces

“…A classical example is provided by the Dijkstra algorithm that computes shortest paths in graphs which are one of the simplest discrete approximations of space. More elaborated constructions apply to compute shortest paths on simplicial complexes or other discrete representations [5,11,15,17] that are able to capture the concept of spatial extension in more than the single dimension represented by arcs connecting nodes. For example, triangle meshes are the most common surface representation used in computer graphics and computational geometry.…”