CG Foundation & Basics

Coordinates, Primitives & Geometry

In 3D graphics, objects are located in a three-dimensional Cartesian coordinate system. The coordinates (X, Y, Z) define the position of a point or vertex in 3D space. The origin (0, 0, 0) is typically the reference point.

Coordinate Systems

In 3D graphics, objects are located in a three-dimensional Cartesian coordinate system. The coordinates (X, Y, Z) define the position of a point or vertex in 3D space. The origin (0, 0, 0) is typically the reference point.

To locate a point in 3D space, you use coordinates. A coordinate is a set of three values (X, Y, Z) that specify a point's position relative to the origin. For example, (3, 2, 1) represents a point located 3 units to the right (X), 2 units upward (Y), and 1 unit forward (Z) from the origin.

Coordinate Transformations

Transformations like translation (shifting), rotation (changing orientation), and scaling (changing size) are fundamental operations in 3D space. They are used to manipulate objects and points.

  • Position
  • Scale
  • Rotation
Fig 1. 2D vs 3D


Matrix

XYZ → PSR → RGB

Vectors

Vectors in 3D space are quantities with both magnitude and direction. They are often used to represent displacement, velocity, force, and other physical quantities. Vectors have three components (X, Y, Z) and can be added, subtracted, and multiplied by scalars.

An understanding of vectors are the key to create and move things in visual scripting, programming shaders, rendering and software such as houdini

Cartesian, polar, and spherical coordinates



Also see:

Cross Product and Dot Product

Orthogonal Projection

Distance and Magnitude







Primitives

Solid Geometry — Primitives vs Geometry

Solid geometry deals with three-dimensional shapes (solids) such as cubes, spheres, cylinders, and pyramids. Understanding the properties and volumes of these shapes is fundamental in geometry and engineering.

Geometry

Vertices, Edges, and Faces

3D models are constructed from vertices (points in space), edges (lines connecting vertices), and faces (flat surfaces defined by three or more vertices). These elements come together to create complex 3D shapes.


  • Polygon
  • Edges
  • Point



Mesh

A mesh is a collection of vertices, edges, and faces that define the overall structure of a 3D model. Meshes can be composed of different types of polygons, but triangles and quads are common due to their simplicity.

  • mesh
  • submeshes


Normals

Planes: A plane in 3D space is a flat, two-dimensional surface that extends infinitely in all directions. It can be defined by a point on the plane and a normal vector (a vector perpendicular to the plane).


Tris, quads & NGons


Structures

While selecting an object you can access the structure manager by selecting windows → Structure manager

Closed & Open Geometry

End of lesson