Interactive isosurfaces with quadratic C 1 splines on truncated octahedral partitions

Abstract

The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C 1 splines on uniform tetrahedral partitions to achieve a globally smooth function. The spline is based on a truncated octahedral partition of the volumetric domain, where each truncated octahedron is further split into a fixed number of disjunct tetrahedra. The Bernstein-Bézier coefficients of the piecewise polynomials are directly determined by appropriate combinations of the data values in a local neighbourhood. As previously shown, the splines provide an approximation order two for smooth functions as well as their derivatives. We present the first visualizations using these splines and show that they are well suited for graphics processing unit (GPU)based, interactive, high-quality visualization of isosurfaces from discrete data.

Accurate Isosurface Interpolation with Hermite Data

“…Many extensions of Marching Cubes have been proposed [20], including the reconstruction of bicubic spline surfaces [7] or continuous quadratic implicit functions for visualization purposes [17]. In contrast, our method does not compute a higher-order surface representation.…”

A hybrid representation for modeling, interactive editing, and real-time visualization of terrains with volumetric features

“…Kloetzli et al (2008) describe a volume representation format, called Bézier Tetrahedra (BT), and describe a raytracing-based isosurface rendering technique utilizing GPU. Marinc et al (2011) use ray-casting on the GPU to render quadratic C 1 splines extracted from the volumetric data represented as uniform tetrahedral partitions. Steinberger and Grabner (2010) describe an interactive multiresolution rendering method for isosurfaces of a voxel grid based on spline wavelet hierarchy.…”

Marching Surfaces: Isosurface Approximation using G$^1$ Multi-Sided Surfaces

“…This technique falls into the class of quasi-interpolation methods for trivariate splines. Related methods are [KZ08], [KKG09], and [MKRG12]; they leverage the relatively low total degree of the splines to construct a hardware accelerated implementation for real time reconstruction of isosurfaces. Tri-linear interpolation is a common choice of high-order approximation methods; unfortunately, smoothness of adjacent splines is not a trivial task.…”