Advanced Methods in Computer Graphics: With examples in OpenGL
Format: PDF / Kindle (mobi) / ePub
This book brings together several advanced topics in computer graphics that are important in the areas of game development, three-dimensional animation and real-time rendering. The book is designed for final-year undergraduate or first-year graduate students, who are already familiar with the basic concepts in computer graphics and programming. It aims to provide a good foundation of advanced methods such as skeletal animation, quaternions, mesh processing and collision detection. These and other methods covered in the book are fundamental to the development of algorithms used in commercial applications as well as research.
denoted by B(s): B.s/ D T .s/ N .s/ D P 0 .s/ jP 0 .s/ P 0 .t/ P 00 .s/ D P 00 .s/j jP 0 .t/ P 00 .t/ P 00 .t/j (2.37) The three unit vectors T, N, B form an orthonormal basis as shown in Fig. 2.8. This local reference system is called the Frenet frame. The derivative of the binormal vector B0 (s) is perpendicular to both B(s) and T(s), and hence parallel to N(s): B 0 .s/ D d .B.s// D ds .s/N .s/ (2.38) The term (s) is called the torsion of the curve at s. Torsion is a measure of how
parts of the sphere can be viewed by rotating it using the arrow keys. The initial, final and the interpolated values are also displayed in text form. Pressing key 1 selects Euler interpolation, key 2 selects angle-axis interpolation, and key 3 selects quaternion interpolation. 5.12 Bibliographical Notes The algebra of quaternions was first discovered by the Irish mathematician Sir William Rowan Hamilton (1805–1865). Most of his work on the quaternion group were later published as a book
coordinates of P(t) are divided by its fourth component to get the Cartesian coordinates. The additional parameter h acts as a weight that can be adjusted to change the shape of the curve. An example showing the variation of a cubic curve’s shape for three equivalent representations of the control point P3 is given in Fig. 7.12a. In this 2-D example, the third component is the homogeneous coordinate h. The homogeneous coordinate system also allows the representation of points at infinity, by
and interdisciplinary areas is the result of many factors such as the ever increasing power and capability of the graphics hardware, decreasing hardware costs, availability of a wide range of software tools, research advancements in the field, and significant improvements in graphics application programming interface (API). Additionally, vast amounts of resources including images, 3D models, and libraries are now easily available to developers and researchers for their work. With the emergence of
each technique, and to implement their own creative ideas. They are just tools which developers and researchers could use to build larger frameworks or to try better solutions. A simple programming approach is used so that students with minimal knowledge of C/CCC language and OpenGL will be able to start using the code and work towards more complex or useful applications. None of the software is optimized in terms of algorithm performance or speed. Similarly, object oriented programming concepts