Fundamentals of Graphics Using MATLAB

Ranjan Parekh

• Verlag: CRC Press
• Jahr: 2019
• ISBN:
  9780429589799
• Auflage: 1
• Thema: Informatica
• Thema: Grafica per computer

This book introduces fundamental concepts and principles of 2D and 3D graphics and is written for undergraduate and postgraduate students of computer science, graphics, multimedia, and data science. It demonstrates the use of MATLAB ® programming for solving problems related to graphics and discusses a variety of visualization tools to generate graphs and plots. The book covers important concepts like transformation, projection, surface generation, parametric representation, curve fitting, interpolation, vector representation, and texture mapping, all of which can be used in a wide variety of educational and research fields. Theoretical concepts are illustrated using a large number of practical examples and programming codes, which can be used to visualize and verify the results.

Key Features:

• Covers fundamental concepts and principles of 2D and 3D graphics
• Demonstrates the use of MATLAB ® programming for solving problems on graphics
• Provides MATLAB ® codes as answers to specific numerical problems
• Provides codes in a simple copy and execute format for the novice learner
• Focuses on learning through visual representation with extensive use of graphs and plots
• Helps the reader gain in-depth knowledge about the subject matter through practical examples
• Contains review questions and practice problems with answers for self-evaluation

CHAPTER 1

Interpolating Splines

1.1 Introduction

Splines are irregular curve segments with known mathematical properties. Splines are frequently encountered in vector graphics when graphic objects are required to have a defined shape in 2D planes (Figure 1.1a) or 3D space (Figure 1.1b) or moved along a specified path (Figure 1.1c). Based on the coordinates of some of the points on the curves, or slopes of lines along the curves, the graphics system needs to calculate a mathematical representation of the curve before storing them onto a disk. This representation usually takes the form of “vectors” or a series of values stored in matrices. The values are calculated using an orthogonal 2D coordinate system consisting of the origin, X-axis, and Y-axis. These coordinate axes are often called the primary or principal axes.

The term “spline” has been derived from the ship building industry where it is used to refer to wooden planks bent between wooden posts for building the curved hull of ships (O’Rourke, 2003). The location of the fixed posts controlled the shape of the plank. In graphics, we use specific points along the spline curve to control the shape of the spline and hence they are aptly referred to as “control points,” shortened as CPs. Depending on the relationship between the CPs and the actual curves, the splines can be...