Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface. Our method is capable of extracting valley surface skeletons as connected minimum structures. As our algorithm is inherently mesh-free and curvature adaptive, it is suitable for surface construction in fields with an arbitrary neighborhood structure. As an application for insightful visualization with valley surfaces, we choose a low frequency acoustics simulation. We use our valley surface construction approach to visualize the resulting complex-valued scalar pressure field for arbitrary frequencies to identify regions of sound cancellation. This provides an expressive visualization of the topology of wave node and antinode structures in simulated acoustics.

S.679-682

Abstract We present an acoustic rendering approach visualizing the listener‐specific contribution of frequency‐dependent pressure fields on a scene geometry with acoustic reflection and scattering properties. Our method facilitates the evaluation of simulated acoustics showing the effect of simulation parameters like absorption and scattering. The image‐based spatial localization of acoustic properties is complementary to the auditive evaluation by means of auralization. Our core contribution is a pressure‐based acoustic rendering equation and a corresponding raytracing method applying techniques from photorealistic rendering to the field of simulated room acoustics. Applications are directed at the visualization of interference patterns and analyzing the impact of acoustic reflection parameters.

We present a comparative visualization of the acoustic simulation results obtained by two different approaches that were combined into a single simulation algorithm. The first method solves the wave equation on a volume grid based on finite elements. The second method, phonon tracing, is a geometric approach that we have previously developed for interactive simulation, visualization and modeling of room acoustics. Geometric approaches of this kind are more efficient than FEM in the high and medium frequency range. For low frequencies they fail to represent diffraction, which on the other hand can be simulated properly by means of FEM. When combining both methods we need to calibrate them properly and estimate in which frequency range they provide comparable results. For this purpose we use an acoustic metric called gain and display the resulting error. Furthermore we visualize interference patterns, since these depend not only on diffraction, but also exhibit phase-dependent amplification and neutralization effects.

We present a new particle tracing approach for the simulation of mid- and high-frequency sound. Inspired by the photorealism obtained by methods like photon mapping, we develop a similar method for the physical simulation of sound within rooms. For given source and listener positions, our method computes a finite-response filter accounting for the different reflections at various surfaces with frequency-dependent absorption coefficients. Convoluting this filter with an anechoic input signal reproduces a realistic aural impression of the simulated room. We do not consider diffraction effects due to low frequencies, since these can be better computed by finite elements. Our method allows the visualization of a wave front propagation using color-coded blobs traversing the paths of individual phonons.

This paper investigates a number of numerical schemes applicable to the solution of the Boltzmann transport equation by means of a spherical-harmonics expansion (SHE). A new scheme is proposed that improves the solution at low energies, keeping the desired accuracy in the calculation of the mean quantities while saving a significant amount of CPU time. This is important in view of the applications of the method since the typical number of nodes to be used in the combined space-energy domain is in the range of 10/sup 4/-10/sup 5/.