Visualization and Mathematics

1995

Before going into the details of various image synthesis algorithms, it is worth considering their general aspects, and establishing a basis for their comparison in terms of eciency, ease of realization, image quality etc., because it is not possible to understand the specic steps, and evaluate the merits or drawbacks of dierent approaches without keeping in mind the general objectives. This chapter is devoted to the examination of algorithms in general, what has been called algorithmics after the excellent book of D.

Programming and Computer Software, 2017

A ray-tracing algorithm for interactive visualization of very large and structurally complicated scenes presented in the constructive solid geometry (CSG) form is suggested. The algorithm is capable of visualizing such scenes in real time by using a graphic processor. As primitives, classical shapes and objects represented in an analytical form (in particular, second-order surfaces and implicit functions) are used. Unlike other similar algorithms, our algorithm produces the final image in a single pass and has no constraints on the maximum number of primitives and on the CSG tree depth. The key feature of the algorithm is a method for optimizing CSG models, which converts the input tree to an equivalent spatially coherent and well-balanced form (a completely balanced equivalent tree may not exist). The performance of visualization after applying the optimization technique is shown to depend on only the computational resource of the GPU (in contrast to multi-pass algorithms whose performance is restricted by memory capacity). It has been shown experimentally that our algorithm is capable of rendering CSG models consisting of more than a million CSG primitives with the tree depth up to 24.

1981

1993

The parimod system is a Transputer based graphics system with an additional interactive solid modeling tool for fast rendering of arbitrary 3-dimensional scenes. It consists of an input tool, a calculation and an output unit which are independent of each other so that each of them is replaceable if changes in hard or software come through. The input unit is a X based solid modeling tool allowing the user to define scenes like an architect on his drawing board. With the massively parallel rendering tool, the user sees the defined scenes in various qualities on-line on the true color output device. The fast output is achieved by the implementation of different parallel strategies of well-known shading and rendering algorithms. The quick response time between changing and showing the different views of a scene makes parimod very popular in the application fields of architectural drawings or the visualization of molecules.

2008

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2013

This paper describes two procedures used to disseminate tangible cultural heritage through real-time 3D simulations providing accurate-scientific representations. The main idea is to create simple geometries (with low-poly count) and apply two different texture maps to them: a normal map and a displacement map. There are two ways to achieve models that fit with normal or displacement maps: with the former (normal maps), the number of polygons in the reality-based model may be dramatically reduced by decimation algorithms and then normals may be calculated by rendering them to texture solutions (baking). With the latter, a LOD model is needed; its topology has to be quad-dominant for it to be converted to a good quality subdivision surface (with consistent tangency and curvature all over). The subdivision surface is constructed using methodologies for the construction of assets borrowed from character animation: these techniques have been recently implemented in many entertainment applications known as "retopology". The normal map is used as usual, in order to shade the surface of the model in a realistic way. The displacement map is used to finish, in real-time, the flat faces of the object, by adding the geometric detail missing in the low-poly models. The accuracy of the resulting geometry is progressively refined based on the distance from the viewing point, so the result is like a continuous level of detail, the only difference being that there is no need to create different 3D models for one and the same object. All geometric detail is calculated in real-time according to the displacement map. This approach can be used in Unity, a real-time 3D engine originally designed for developing computer games. It provides a powerful rendering engine, fully integrated with a complete set of intuitive tools and rapid workflows that allow users to easily create interactive 3D contents. With the release of Unity 4.0, new rendering features have been added, including DirectX 11 support. Real-time tessellation is a technique that can be applied by using such technology. Since the displacement and the resulting geometry are calculated by the GPU, the time-based execution cost of this technique is very low.

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XL-5/W1, 181-188, doi:10.5194/isprsarchives-XL-5-W1-181-2013, 2013. , 2013

This paper describes two procedures used to disseminate tangible cultural heritage through real-time 3D simulations providing accurate-scientific representations. The main idea is to create simple geometries (with low-poly count) and apply two different texture maps to them: a normal map and a displacement map. There are two ways to achieve models that fit with normal or displacement maps: with the former (normal maps), the number of polygons in the reality-based model may be dramatically reduced by decimation algorithms and then normals may be calculated by rendering them to texture solutions (baking). With the latter, a LOD model is needed; its topology has to be quad-dominant for it to be converted to a good quality subdivision surface (with consistent tangency and curvature all over). The subdivision surface is constructed using methodologies for the construction of assets borrowed from character animation: these techniques have been recently implemented in many entertainment applications known as “retopology”. The normal map is used as usual, in order to shade the surface of the model in a realistic way. The displacement map is used to finish, in real-time, the flat faces of the object, by adding the geometric detail missing in the low-poly models. The accuracy of the resulting geometry is progressively refined based on the distance from the viewing point, so the result is like a continuous level of detail, the only difference being that there is no need to create different 3D models for one and the same object. All geometric detail is calculated in real-time according to the displacement map. This approach can be used in Unity, a real-time 3D engine originally designed for developing computer games. It provides a powerful rendering engine, fully integrated with a complete set of intuitive tools and rapid workflows that allow users to easily create interactive 3D contents. With the release of Unity 4.0, new rendering features have been added, including DirectX 11 support. Real-time tessellation is a technique that can be applied by using such technology. Since the displacement and the resulting geometry are calculated by the GPU, the time-based execution cost of this technique is very low.

In CG, many methods have been developed over time. Basic and quite old methods of CG have been overviewed in Chapter 0. Newer methods relevant to 3D engines are reviewed in this section. In 3D engines it is important to visualize complex geometries with accurate shading at high frame-rates. Concerning shading in real-time, particularly shadows are challenging. Conventional ray tracing based methods have not been suitable in game engines for a long time, as they are too slow. Therefore, faster techniques such as shadow mapping [1] and shadow volumes [2] have been used. They can avoid ray tracing and suit well for triangle based visualizations. Another methods important for 3D engines include techniques that improve conventional bumpmapping in order to let flat surfaces appear bumpy. Here, parallax occlusion mapping [3], which was first published in 2004, is an evolution that creates much more realistic bumps than previous bump-mapping. Rather than just altering the normal vector, parallax occlusion mapping creates a parallax effect, which lets the bumps on a planar surface appear in 3D. Furthermore, it provides self-shadows and correct silhouettes in object borders on the screen. Recent methods related to animation evolve existing methods to realistic and physically correct skin deformations, proper cloth simulation [4], or hair animation and visualization. Another work in the area of animation focuses on creating realistic character locomotion animations procedurally. In the area of visualization, splat [5] and voxel-based [6] representations are researched as an alternative to visualizing geometries by triangles. For achieving faster visualizations, level of detail (LOD) was researched, where methods such as HLOD [7] and Far Voxels [8] were proposed to visualize large and complex scenes. To achieve proper lighting without using pre-computations, global illumination in real time was developed by Crassin et al [9]. The computation of global illumination is already complex, even for state of the art raytracing methods; therefore, achieving real-time performance is a challenge.

III Year B. Tech CSE-I Sem L T/P/D C 3-/-/-3 CORE ELECTIVE-I (R17A0517) Computer Graphics Objectives:  To make students understand about fundamentals of Graphics to enable them to design animated scenes for virtual object creations.  To make the student present the content graphically. UNIT-I: Introduction: Application areas of Computer Graphics, overview of graphics systems, videodisplay devices, raster-scan systems, random scan systems, graphics monitors and work stations and input devices Output primitives: Points and lines, line drawing algorithms, mid-point circle and ellipse algorithms.Filled area primitives: Scan line polygon fill algorithm, boundary-fill and flood-fill algorithms UNIT-II: 2-D geometrical transforms: Translation, scaling, rotation, reflection and shear transformations, matrix representations and homogeneous coordinates, composite transforms, transformations between coordinate systems 2-D viewing : The viewing pipeline, viewing coordinate reference frame, window to view-port coordinate transformation, viewing functions, Cohen-Sutherland and Cyrus-beck line clipping algorithms, Sutherland-Hodgeman polygon clipping algorithm

Proceedings of Seventh Annual IEEE Visualization '96, 1996

The Visualization Toolkit (vtk) is a freely available C++ class library for 3D graphics and visualization. In this paper we describe core characteristics of the toolkit. This includes a description of object-oriented models for graphics and visualization; methods for synchronizing system execution; a summary of data representation schemes; the role of C++; issues in portability across PC and Unix systems; and how we automatically wrap the C++ class library with interpreted languages such as Java and Tcl. We also demonstrate the capabilities of the system for scalar, vector, tensor, and other visualization techniques.

Computers & Graphics, 1978

In this paper we give an overview of the current research trends and explore the challenges in several subfields of the scientific discipline of computer graphics: interactive and photorealistic rendering, scientific and information visualization, and visual analytics. Five challenges are extracted that play a role in each of these areas: scalability, semantics, fusion, interaction, acquisition. Of course, not all of these issues are disjunct to each other, however the chosen structure allows for a easy to follow overview of the concrete future challenges.

Three-dimensional (3D) visualization is the process of creating the three-dimensional object using a special computer program. Today computer graphics technologies such as 3D visualization technology are becoming more and more in demand. The technology has earned popularity among designers because it allows creating three-dimensional objects of any shape. It is widely used throughout the world to create the interiors of houses, offices, hotels, etc. This paper provides a brief introduction to 3D visualization.

2001

Current computer graphics research tend to be more concerned with applications than image production techniques. Most of the latter research is concerned more with global illumination models than local illumination models. Does this mean that everything that could be said about fundamental algorithms have already been said? Examples of how reformulations of mathematical formulas have led to faster algorithms especially for shading will be given in this paper. A comparison of three different techniques for bivariate shading will exemplify that better formulations of old problems are still possible and necessary.

2008

Rea l-time visualization of 3D scenes is a very important feature of many computer graphics solutions. Current environments require complex scenes which contain an increasing number of objects composed of thousands or even millions of polygons. Nevertheless, this complexity poses a problem for achieving interactive rendering. Among the possible solutions, stripification, simplification and level of detail techniques are very common approaches to reduce the rendering cost. In this paper, we present set of techniques which have been developed for offering higher performance when rendering 3D models in real-time applications. Furthermore, we also present a standalone application useful to quickly simplify and generate multiresolution models for arbitrary geometry and for trees.