3D Graphics Modelling Basics

Study Notes

Modelling is the first step in the 3D graphics pipeline, which includes animation and rendering.
Vertices and lines are the backbone of creating 3D geometry in the modelling phase.
There are two ways to represent geometry: explicit and implicit.
Explicit representation involves defining vertices and lines, while implicit representation visualizes or models a geometry implicitly using algebraic surfaces.
Polylines are a type of representation used to create smooth curves. They are sequences of vertices connected by straight line segments and are useful for representing simple shapes.
Polylines lack the smoothness of curves, so 3D curve polyline was developed as an alternative.
Cubic Bézier curves are a type of implicit curve representation used in 3D modelling. They are defined by four control points, which interpolate the first two and approximate the last two. The curve lies within the box generated by the control points and is tangent at the two end points.
The curve is expressed as a weighted combination of Bernstein polynomials, and all weights add up to 1.
Modelling involves using the power of imagination to craft a 3D world using vertices, lines, and polylines.
Polylines are useful for representing simple shapes, but lack the smoothness of curves. Cubic Bézier curves are a more advanced representation that can create smooth curves while still being easy to edit and generate.
The modelling phase is important because it sets the foundation for the rest of the 3D graphics pipeline.
Vertices and lines are the basic building blocks for creating 3D geometry, and polylines and curves are more advanced representations used to create smooth shapes.
Cubic Bézier curves are a popular type of implicit representation used in 3D modelling because they can create smooth curves that are easy to edit.
The modelling phase involves using the power of imagination to create a 3D world using a variety of representation types, from simple polylines to complex algebraic surfaces.
The choice between explicit and implicit representation depends on the desired level of control and the complexity of the geometry being modelled.
Polylines are useful for representing simple shapes, but lack the smoothness of curves. Cubic Bézier curves are a more advanced representation that can create smooth curves while still being easy to edit and generate.
The properties of cubic Bézier curves, such as lying within the box generated by the control points and being tangent at the end points, make them a popular choice for 3D modelling applications.
The use of matrix vector notation and Bernstein polynomials in cubic Bézier curves allows for efficient and precise manipulation of the curves in the modelling process.

Description

Learn about the first step in the 3D graphics pipeline - modelling. This quiz covers the basics of computer graphics, the stages of the pipeline, the power of imagination in crafting a 3D world, and the different types for representing geometry.