Computer Graphics and Geometric Modeling

Basic Geometric Modeling Tools (Basic Computer Graphics) Part 4

Circle Formulas Formula. Letbe noncollinear points inand The unique circle that contains the points pi has centerwhere and radius r, where (a) Region subtended by curve (b) Approximation to ith interval Figure 6.20. Circle through three points. In the special case whereare    points    in    the    plane,    these    formulas    can be simplified. LetThen Proof. We shall […]

Basic Geometric Modeling Tools (Basic Computer Graphics) Part 5

Parametric or Implicit: Which Is Better? Two of the most common ways to present a geometric object X is via a parameterization or implicitly as the zeros of an equation. It is natural to ask which is better. The advantages and disadvantages of these two representations are seen best in the context of the following […]

Visible Surface Algorithms (Basic Computer Graphics) Part 1

Introduction After modeling the geometry, the next basic step in a realistic rendering of a scene from a given viewpoint involves determining those surface patches that will be visible from this viewpoint. This is the visible surface determination problem. In the past this was called the hidden surface removal problem, but the terminology is beginning […]

Visible Surface Algorithms (Basic Computer Graphics) Part 2

Warnock and Weiler-Atherton Area Subdivision The Warnock visible surface determination algorithm [Warn69] is an image space algorithm that attempts to find rectangular regions (here called windows) of the same intensity on the screen (area coherence). Algorithm 7.6.1 is an outline of the algorithm. The polygons referred to in the algorithm are the projected polygons. See […]

Visible Surface Algorithms (Basic Computer Graphics) Part 3

Octree Algorithms Because of the regular geometric structure underlying octrees, it is fairly easy to devise list priority visible surface algorithms for objects represented in this way if one is using a parallel projection. One lists the voxels in a back-to-front order. For example, consider Figure 7.11 and assume that the camera is in the […]

Color (Basic Computer Graphics) Part 1

Introduction This topic covers some rudimentary facts about color and its role in computer graphics. Describing what one needs to know for a basic modeling system is not that hard. This is the main goal of this topic, but we shall also sketch a more complete view of what color is all about. The reader […]

Color (Basic Computer Graphics) Part 2

Color Models The range of colors produced by an RGB monitor is called its gamut. There are a number of models for the gamut of an RGB monitor. The Color Cube or RGB Model. This is the "natural" gamut model that represents the gamut as the unit cube [0,1] x [0,1] x [0,1]. See Figure […]

Illumination and Shading (Basic Computer Graphics) Part 1

Introduction Image synthesis has been defined as the creation of images using an illumination model for the propagation of light, with the goal being photorealism. Actually, photography operates under some constraints defined by the camera and film being used, so that a much more general goal would be to produce a visual experience that matches […]

Illumination and Shading (Basic Computer Graphics) Part 2

Simple Approaches to Shading The last section described some simple illumination models and how one can use them to compute the illumination at each point of an object. In this section we show how this information is used to implement shading in a modeling program. The details depend on (1)  the visible surface determination algorithm […]

Illumination and Shading (Basic Computer Graphics) Part 3

The Rendering Equation Looking back over what has been covered with regard to illumination in this topic, we see lots of different formulas and approaches. Kajiya ([Kaji86]) attempted to unify the general illumination problem by expressing it in terms of finding a solution to a single equation that he called the rendering equation: where p […]

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