16. 3D Concepts
Dated: 13-05-2025
Coordinate Systems
These are measured frames of references in which geometry is
- Defined
- Manipulated
- Viewed
1D Coordinate System
Originas reference and has direction and magnitude along a single axis.- Locations are defined by a single coordinate.
- Can define
pointssegmentslinesrays
2D Coordinate System
Originas reference and has direction and magnitude along 2 axes.- Locations are defined by coordinate pair \((x, y)\).
- Can define
curvespolygons- 1D entities
3D Coordinate System
Originas reference and has direction and magnitude along 3 axes.- Locations are defined by coordinate triplet \((x, y, z)\).
- Can define
cubesconesspheres- Volumes in space
- 1D and 2D entities
Left-handed versus Right-handed
Left Hand
Right Hand
Mostly the right handed rule is used but cameras use left handed rule.
Professional Choices
Typically
Designers Choice
Animators Choice
Global Vs Local Coordinates
- Local coordinates are relative to the object
- Global coordinates are relative to the world
Multiple Frames of Reference within a 3D Scene
Defining Points in C
typedef struct {
float x;
float y;
float z;
} Point3D;
The Polar Coordinate System
These are generally not used in 3D graphics because the math is often harder and these are hard to manipulate comparatively.
Defining Geometry in 3D
Modeling
It is the process of describing an object or scene so that we can construct an image of it.
Primitives
These are fundamental geometric entities within a given data structure.
PointsVectors1PolygonsPolygon stripsMeshes
Meshes provide continuity across surfaces which is important for shading calculations.
A mesh of a dolphin
A quad strip
A triangle strip
Rendering
It is the process of constructing an image, using a combination of
- A 3D database
- Scene characteristics
- Viewing transformations
Different algorithms are employed for different rendering applications.
Tessellation
It is the process of dividing an entity or surface into multiple disjoint primitives.
Renderers typically decompose surfaces into triangles as part of the rendering process.
Sampling
The process of selecting a representative but finite number of values along a continuous function2 sufficient to render a reasonable approximation of the function for the task at hand.
Level of Detail (LOD)
Depending on the importance of a certain entity in the image, different versions (varying in details) of a model can be swapped out dynamically from the scene database.
Surface Models
These can be constructed from the mathematical descriptions.
Meta Balls (blobs)
Potential functions3 (usually radially symmetric Gaussian functions) are used to define surfaces surrounding points.