Frisvad [2012b] describes a widely-used computational method for efficiently augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. However, the implementation has a precision problem: as the z component of the input vector approaches −1, floating point cancellation causes the frame ...

As our frame of reference, we begin with Cartesian coordinates in 3space R. Assume the frame is non-accelerating (inertial). Suppose there is a mass m at a fixed point in space r′ = (x′, y′, z′). This is a point source. It produces a gravity field around it, which can be sensed by a test mass at another point in space. How strong and in what direction is the tug of the field as it acts on the t...

Occlusion-compatible traversals and z-buffering are often regarded as the only choices for resolving visibility in the imageand point-based rendering community. These algorithms do either per-frame or per-pixel computations. This paper first discusses visibility orderings for point samples in general and then discusses orderings that are valid for multiple views. Then we present a novel, highly...

Measurements ~t 1.2, 1.~, and 2.2 μm have been combined with visual spectrophotometry o~ 21 quasai:s havmg. redshifts z ;:;: 2.66. T~e primary result of this study is that the rest frame vism~.l/ultravIC?let contmua of the high-redshift quasars are well described by a sum of a power-law contmuum with slope -.-0.~ ~nd a 3000 A bump. The rest frame visual/ultraviolet continua of these quasars are...

This paper studies the problem of sequence-to-sequence alignment, namely establishing correspondences in time and in space between two di erent video sequences of the same dynamic scene. The sequences are recorded by uncalibrated video cameras, which are either stationary or jointly moving, with xed (but unknown) internal parameters and relative inter-camera external parameters. Temporal variat...

motivating the perturbations of frames in hilbert and banach spaces, in this paper we introduce the invariance of fr'echet frames under perturbation. also we show that for any fr'echet spaces, there is a fr'echet frame and any element in these spaces  has a series expansion.

We investigate the mechanical structure of a spin-1 particle. Introducing three different frameworks, i.e., three-dimensional (3D) Breit frame, two-dimensional (2D) and 2D infinite momentum frame (equivalently Drell-Yan frame), we scrutinize 3D energy-momentum tensor (EMT) distributions in these frames. first derive EMT by performing Abel transformation. The mass distribution contains an additi...

We introduce a new empirical function for modeling the spectral energy distributions of galaxies. We apply it to a sample of 590 galaxies in the region of the HDF with z < 1.5 using multi-color photometry with wide wavelength coverage combined with spectroscopic redshifts from our 93% complete R-selected redshift survey there. We find the following: • As expected, galaxies with strong signs of ...

We present results from the first robust investigation of galaxy morphology as a function of environment at z > 1.5. Our study is motivated by the fact that star-forming galaxies contained within a protocluster at z = 2.3 in the HS1700+64 field are characterized by significantly older ages and larger stellar masses on average than those at similar redshifts but more typical environmental densit...