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Parametric polynomial curves are defined by polynomial functions of a parameter, such as time, steps, or angle. These curves are valued for their smoothness and ease of manipulation and control. Although these curves can be of any polynomial degree, parametric cubic curves are often preferred. Lower-degree curves offer too little flexibility in shaping the curve, while higher-degree curves can introduce unwanted wiggles, result in a loss of local control, and require more computation....

In the last two posts, we explored the connections between computer science, graphics and animation. We observed a parent-child relationship were computer science is the parent, computer graphics is the child and computer animation is the grandchild. Now, I would like to delve deeper into technical aspects of computer graphics, focusing on key concepts that are crucial for understand. Graphics system A graphics system is an integrated set of hardware and software components designed to create, manage, and display visual content on a computer screen....

The definitions of Computer Graphics CG and Computer Animation CA are often indistinguishable, as both can involve the use of typography or imagery. However, there is a subtle distinction between the two, and it lies in the concept of movement. Computer Graphics encompasses both static and dynamic graphics, while Computer Animation specifically focuses on dynamic graphics. Most of the information presented in this post was extracted from the books: Fundamentals of Computer Graphics - Fourth Edition, by Steve Marschner and Peter Shirley Computer Graphics: Principles and Practice - Third Edition, by John Hughes, Andries Van Dam, Morgan McGuire, David Skylar, James Foley, Steven Feiner and Kurt Akeley....

Building a puzzle without a clear picture of the final image is nearly impossible. While this seems obvious, in many situations, defining the desired outcome isn’t straightforward. Expertise and problem complexity can create doubt and uncertainty. When facing uncertainty, I find it helpful to explore a field broadly before diving into specifics. This general exploration includes understanding basic concepts, applications, and foundational knowledge—elements that might seem irrelevant but are crucial for forming a comprehensive mental picture....

The mesh of vertices, a cube is created by 8 vertices, 18 edges and 12 triangles. PLY File Is a computer file format know as the polygon file format of the standor triangle format. It was principally desgined to store three-dimensional data from 3D scanners. The data storage foramt supports a relatively simple description of a single object as a list of nominally plat polygons. OBJ file Wavefron OBJ file format is a format for defining the 3D geometry for the surface of one or more objects....

Polygonal representation Parametric representation Implcit surface representation Constructive solid geometry volumetric representatin

Im doing a MSc in computer animation and visual effects at BU Univeristy. I started a couple months ago and in middle of my math class I thought that to post and higlight the concepts that i feel relevant in the area would be more poroductive to me, because, the class feel quite bored and im not studying by myself indenpently!. Its better for me to go into somethinf if i want to post it in my blog, and how the graphics is a journal, would be match perfeclty to help me to dive into the math concepts....