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Register a new userPerspective Drawing of Surfaces with Line Hidden Line Elimination, Dibujando Superficies En Perspectiva Con Eliminacion De Lineas Ocultas
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Added by
Ignacio Vega-Paez M en C
Publication date
2011
fields
Informatics Engineering
and research's language is
English
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An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm automatically computes and eliminates hidden lines. The number of computations in the algorithm grows linearly with the number of sample points on the surface to be drawn. An analysis of the algorithm is presented, and extensions lo certain multi-valued functions are indicated. The algorithm is implemented and tested on .Net 2.0 platform that left interactive use. Running times are found lo be exceedingly efficient for visualization, where interaction on-line and view-point control, enables effective and rapid examination of a surfaces from many perspectives.
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The spatial anti-aliasing technique for line joins (intersections of the road segments) on vector maps is exclusively crucial to visual experience and system performance. Due to limitations of OpenGL API, one common practice to achieve the anti-aliased effect is splicing multiple triangles at varying scale levels to approximate the fan-shaped line joins. However, this approximation inevitably produces some unreality, and the system rendering performance is not optimal. To circumvent these drawbacks, in this paper, we propose a simple but efficient algorithm which uses only two triangles to substitute the multiple triangles approximation and then renders a realistic fan-shaped curve with alpha operation based on geometrical relation computing. Our experiment shows it has advantages of a realistic anti-aliasing effect, less memory cost, higher frame rate, and drawing line joins without overlapping rendering. Our proposed spatial anti-aliasing technique has been widely used in Internet Maps such as Tencent Mobile Maps and Tencent Automotive Maps.
Complex 3D curves can be created by directly drawing mid-air in immersive environments (Augmented and Virtual Realities). Drawing mid-air strokes precisely on the surface of a 3D virtual object, however, is difficult; necessitating a projection of the mid-air stroke onto the user intended surface curve. We present the first detailed investigation of the fundamental problem of 3D stroke projection in VR. An assessment of the design requirements of real-time drawing of curves on 3D objects in VR is followed by the definition and classification of multiple techniques for 3D stroke projection. We analyze the advantages and shortcomings of these approaches both theoretically and via practical pilot testing. We then formally evaluate the two most promising techniques spraycan and mimicry with 20 users in VR. The study shows a strong qualitative and quantitative user preference for our novel stroke mimicry projection algorithm. We further illustrate the effectiveness and utility of stroke mimicry, to draw complex 3D curves on surfaces for various artistic and functional design applications.
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering. However, most of the existing conformal parameterization algorithms only focus on simply-connected surfaces and cannot be directly applied to surfaces with holes. In this work, we propose two novel algorithms for computing the conformal parameterization of multiply-connected surfaces. We first develop an efficient method for conformally parameterizing an open surface with one hole to an annulus on the plane. Based on this method, we then develop an efficient method for conformally parameterizing an open surface with $k$ holes onto a unit disk with $k$ circular holes. The conformality and bijectivity of the mappings are ensured by quasi-conformal theory. Numerical experiments and applications are presented to demonstrate the effectiveness of the proposed methods.
It has often been conjectured that the effectiveness of line drawings can be explained by the similarity of edge images to line drawings. This paper presents several problems with explaining line drawing perception in terms of edges, and how the recently-proposed Realism Hypothesis of Hertzmann (2020) resolves these problems. There is nonetheless existing evidence that edges are often the best features for predicting where people draw lines; this paper describes how the Realism Hypothesis can explain this evidence.
The hidden broad-line regions (BLRs) in Seyfert 2 galaxies, which display broad emission lines (BELs) in their polarized spectra, are a key piece of evidence in support of the unified model for active galactic nuclei (AGNs). However, the detailed kinematics and geometry of hidden BLRs are still not fully understood. The virial factor obtained from reverberation mapping of type 1 AGNs may be a useful diagnostic of the nature of hidden BLRs in type 2 objects. In order to understand the hidden BLRs, we compile six type 2 objects from the literature with polarized BELs and dynamical measurements of black hole masses. All of them contain pseudobulges. We estimate their virial factors, and find the average value is 0.60 and the standard deviation is 0.69, which agree well with the value of type 1 AGNs with pseudobulges. This study demonstrates that (1) the geometry and kinematics of BLR are similar in type 1 and type 2 AGNs of the same bulge type (pseudobulges), and (2) the small values of virial factors in Seyfert 2 galaxies suggest that, similar to type 1 AGNs, BLRs tend to be very thick disks in type 2 objects.
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