Abstract
This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves. Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above. Bezier curves find real life applications in diverse areas of Engineering and Computer Science, such as computer graphics, robotics, animations, virtual reality, among others. Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations, proof of related theorems, first and second order calculus related computations, among others. A Practical case is demonstrated using a graphical design, physical hand sketching, and programmatic implementation of two opposite-faced handless cups, all evolved using quadratic Bezier curves. The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript. This work will no doubt find relevance in computational researches in the areas of graphics, web programming, automated theorem proofs, robotic motions, among others.
Highlights
The importance of parametric curves in Computer Graphics [1], Computer Aided Design (CAD), Animation, Robotics and a number of other areas of computing cannot be overemphasized
This work will no doubt find relevance in computational researches in the areas of graphics, web programming, automated theorem proofs, robotic motions, among others
Some of the most common are in Computer Graphics, Animation [12], and Virtual reality [13]
Summary
The importance of parametric curves in Computer Graphics [1], Computer Aided Design (CAD), Animation, Robotics and a number of other areas of computing cannot be overemphasized. Some of the most common are in Computer Graphics, Animation [12], and Virtual reality [13] These and many other real-life applications of Bezier curves make adequate use of the foundational concepts. This work demystifies evolutionary concepts that touch on theorems, proofs, algorithms, and computations in parametric Bezier curves relevant to computer graphics. This is followed by studies on blending function derivations, Bezier matrix, Bezier curve sketching, curve join and foundational proofs of two important theorems. The concluding part of this work focused on derivatives, system implementations, and a conclusion
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